High School Chemistry

Chemistry is the study of matter and the changes it goes through. Matter is anything that has mass and takes up space, from the air you breathe to the water you drink to this screen. Because there is so much variety in matter, chemists sort it into a few clear groups so it is easier to understand.

Pure substances and mixtures

A pure substance always has the same makeup. It comes in two kinds. An element cannot be broken into anything simpler by ordinary chemistry. There are about 118 elements, and each has its own one or two letter symbol, such as oxygen (O), gold (Au), or iron (Fe). A compound is two or more elements chemically joined in a fixed ratio, such as water (H₂O) or table salt (NaCl). A compound behaves nothing like the elements inside it: sodium is a soft metal that reacts violently with water, and chlorine is a poisonous green gas, yet together they make ordinary, edible salt.

A mixture is a physical blend of two or more substances that keep their own identities and can be mixed in any amounts. A homogeneous mixture (also called a solution) looks the same throughout, like salt water or clean air. A heterogeneous mixture has parts you can point to, like a bowl of cereal in milk or sand stirred into water. Because the parts of a mixture are not chemically bonded, you can pull them apart by physical means such as filtering, evaporating, or using a magnet.

The states of matter

Matter usually shows up in one of three familiar states. A solid keeps a fixed shape and volume because its particles are packed tightly and locked in place. A liquid keeps a fixed volume but takes the shape of its container because its particles can slide past each other. A gas has neither a fixed shape nor a fixed volume; its particles spread out to fill whatever space they are given. Adding heat or taking it away drives changes between these states, such as ice melting or water boiling.

Properties and changes

A physical property can be observed without changing what the substance is, such as color, density, or melting point. A chemical property describes how a substance reacts to form something new, such as how easily it burns or rusts. The same split applies to changes. In a physical change, the substance is the same before and after: melting ice gives liquid water, still H₂O. In a chemical change, brand new substances form: burning wood makes ash and gases that you cannot easily turn back into wood. Good clues that a chemical change has happened are a color change, bubbles of a new gas, a solid appearing out of two liquids, or heat and light being given off.

Separating mixtures

Because a mixture is only a physical blend, you can undo it with physical tools that exploit a difference in properties. Filtration traps a solid on paper while a liquid passes through, which is how you would recover sand from sandy water. Evaporation boils off a liquid and leaves a dissolved solid behind, which is how salt is harvested from seawater. Distillation boils a liquid, then cools the vapor back to liquid in a fresh container, separating substances that boil at different temperatures, such as pure water from salt water. A magnet can pull iron filings out of a sand-and-iron mixture. Notice that none of these methods works on a compound: no amount of filtering or boiling turns water back into hydrogen and oxygen, because those are held by chemical bonds, not just mixed together.

Worked example: classify and separate

Suppose you are handed a cloudy glass of muddy salt water and asked to classify it and recover both the mud and the salt.

• Classify: The mud is visible and settles, so the sample is a heterogeneous mixture overall. The salt-and-water part, however, is a homogeneous mixture (a solution).
• Step 1, filter: Pour it through filter paper. The mud (an insoluble solid) stays on the paper; clear salt water passes through.
• Step 2, evaporate: Gently heat the clear salt water until the water leaves as vapor. Solid salt is left in the dish.

Two physical steps, chosen from two different property differences (particle size, then boiling point), fully separate the sample. Because every step was physical, the salt you recover is the same salt you started with.

Common misconceptions

• "Dissolving is a chemical change." Dissolving salt in water is physical: the salt is still salt, and evaporating the water brings it back unchanged.
• "If it looks uniform, it must be a pure substance." Air and salt water look uniform but are homogeneous mixtures, not pure substances. Uniform appearance means homogeneous, not pure.
• "A compound is just a really well-mixed mixture." A compound has a fixed ratio and new properties, and it can only be separated by chemistry. A mixture has variable amounts and keeps its parts' properties.
• "Bubbles always mean a chemical change." Boiling water bubbles, but that is a physical change (liquid to gas). Bubbles signal a chemical change only when a brand-new gas is being produced, as when vinegar meets baking soda.

Recap

Matter is anything with mass and volume. Pure substances (elements and compounds) have fixed makeup; mixtures (homogeneous or heterogeneous) are physical blends you can separate by physical means. Matter appears as solids, liquids, or gases. Physical properties and changes leave the substance's identity intact, while chemical properties and changes create new substances, often flagged by color change, gas, a new solid, or released heat and light.

Sources

1. OpenStax, Chemistry 2e, Chapter 1: Essential Ideas (Sections 1.2 Phases and Classification of Matter and 1.3 Physical and Chemical Properties). Rice University, 2019.
2. CK-12 Foundation, CK-12 Chemistry for High School, Chapter 1: Matter and Change (classification of matter; physical and chemical changes).
3. OpenStax, Chemistry: Atoms First 2e, Chapter 1: Essential Ideas. Rice University, 2019.

Science runs on careful measurement, and measurement needs agreed units. Chemists use the SI system, the modern metric system. A few base units cover most of what you will do: the meter (m) for length, the kilogram (kg) for mass, the second (s) for time, the kelvin (K) for temperature, and the mole (mol) for amount of substance. In everyday lab work you will also lean on the gram (g) and the liter (L).

Prefixes scale the unit

Metric prefixes multiply a base unit by a power of ten, which lets you handle very large and very small amounts without a page full of zeros.

Prefix	Symbol	Meaning
kilo	k	1000 (103)
centi	c	0.01 (10-2)
milli	m	0.001 (10-3)
micro	µ	0.000001 (10-6)

So 1 kg is 1000 g, 1 cm is 0.01 m, and 1 mL is 0.001 L. A handy fact to remember: 1 mL is exactly the same volume as 1 cubic centimeter (cm³).

Temperature scales

Chemists use both Celsius and Kelvin. To go from Celsius to Kelvin, add 273: K = °C + 273 (the precise value is 273.15). Water freezes at 0 °C (273 K) and boils at 100 °C (373 K) at ordinary pressure. Kelvin never goes negative because 0 K is absolute zero, the coldest anything can possibly be.

Density connects mass and volume

Density is how much mass is packed into a given volume. You find it by dividing mass by volume, usually in grams per milliliter (g/mL) for liquids or grams per cubic centimeter for solids:

density = mass ÷ volume

Worked example. A metal block has a mass of 54.0 g and a volume of 20.0 cm³. Its density is 54.0 g ÷ 20.0 cm³ = 2.70 g/cm³. That value matches aluminum, so the block is probably aluminum. You can also work backward: if a liquid has a density of 0.80 g/mL, then 50.0 mL of it has a mass of 50.0 mL × 0.80 g/mL = 40.0 g. Because density is a ratio, it stays the same no matter how big your sample is, which makes it a helpful fingerprint for identifying substances.

Rearranging the density equation

The single relationship density = mass ÷ volume answers three kinds of question, depending on which quantity is unknown. It helps to hold all three forms in mind:

• Unknown density: d = m ÷ V
• Unknown mass: m = d × V
• Unknown volume: V = m ÷ d

Worked example (find volume). Gold has a density of 19.3 g/cm³. What volume does a 96.5 g gold nugget occupy? Use V = m ÷ d = 96.5 g ÷ 19.3 g/cm³ = 5.00 cm³. Check by multiplying back: 5.00 cm³ × 19.3 g/cm³ = 96.5 g, which matches, so the answer is right.

Worked example (will it float?). An object floats if it is less dense than the liquid it sits in. A block of oak has a density of about 0.75 g/cm³, and water is 1.00 g/cm³. Since 0.75 is less than 1.00, oak floats. Ice (0.92 g/cm³) is also less dense than liquid water, which is why ice cubes float and icebergs poke above the sea.

Multi-step unit conversion with density

Worked example. A chemistry problem asks for the mass, in kilograms, of 2.5 L of ethanol, whose density is 0.789 g/mL. Work in careful steps and watch the units cancel:

2.5 L × (1000 mL ÷ 1 L) = 2500 mL

2500 mL × (0.789 g ÷ 1 mL) = 1972.5 g

1972.5 g × (1 kg ÷ 1000 g) = 1.97 kg

The liters became milliliters, density turned milliliters into grams, and the last factor turned grams into kilograms. Rounding to the two significant figures allowed by 2.5 L gives about 2.0 kg. Chaining conversion factors this way keeps large multi-unit problems from becoming guesswork.

Common misconceptions

• "Heavier objects are always denser." A large foam block can outweigh a small steel bolt yet still be far less dense. Density depends on mass and volume together, not mass alone.
• "Kelvin readings can be negative on a cold day." Kelvin starts at absolute zero and never goes negative. A cold night might be -10 °C, which is still 263 K.
• "A milliliter and a cubic centimeter are different sizes." They are exactly equal: 1 mL = 1 cm³. This lets you switch between liquid and solid volume units freely.
• "Density changes if you cut the sample in half." Halving a sample halves both its mass and its volume, so the ratio, and thus the density, is unchanged.

Recap

The SI system gives chemists shared units: meter, kilogram, second, kelvin, and mole, plus the everyday gram and liter. Metric prefixes scale a unit by powers of ten (kilo = 1000, centi = 0.01, milli = 0.001, micro = 0.000001). Convert Celsius to Kelvin with K = °C + 273. Density (mass ÷ volume) is an intensive property that identifies substances and predicts floating, and its three rearranged forms solve for mass, volume, or density as needed.

Sources

1. OpenStax, Chemistry 2e, Chapter 1: Essential Ideas (Sections 1.4 Measurements, 1.5 Measurement Uncertainty, Accuracy, and Precision, and 1.6 Mathematical Treatment of Measurement Results). Rice University, 2019.
2. National Institute of Standards and Technology (NIST), The International System of Units (SI), NIST Special Publication 330, base units and prefixes.
3. CK-12 Foundation, CK-12 Chemistry for High School, Chapter 3: Measurements (SI units, metric prefixes, density).

Every measurement has some uncertainty, and significant figures (sig figs) are how we honestly show how precise a value really is. The significant figures are all the digits you know for sure plus one final estimated digit. Writing more digits than your ruler or balance can justify is a false claim of precision, so learning these rules keeps you honest.

Counting significant figures

• Every nonzero digit counts. 24.7 has three.
• Zeros between nonzero digits count. 1005 has four.
• Leading zeros never count; they only place the decimal. 0.0034 has two.
• Trailing zeros count only if a decimal point is written. 2.50 has three, but 250 is ambiguous (treat it as two unless it is written 250. or 2.50 x 10²).
• Exact counted numbers (like 12 eggs) and defined conversions (100 cm per 1 m) have unlimited sig figs and never limit an answer.

Sig figs in calculations

Multiplication and division: the answer keeps as many sig figs as the measurement with the fewest. Example: 4.56 × 1.4 = 6.384 on the calculator, but 1.4 has only two sig figs, so the answer is 6.4.

Addition and subtraction: the answer keeps as many decimal places as the value with the fewest decimal places. Example: 12.11 + 0.3 = 12.41 on the calculator, but 0.3 has only one decimal place, so the answer is 12.4.

Round only at the very end of a multi-step problem so small rounding errors do not pile up.

Dimensional analysis

Dimensional analysis (the factor-label method) converts units by multiplying by fractions equal to one, called conversion factors, set up so the unwanted units cancel. To convert 3.50 kg to grams:

3.50 kg × (1000 g ÷ 1 kg) = 3500 g

The kilograms cancel, leaving grams. You can chain several factors in one line. To convert 90.0 km/h to meters per second:

90.0 km/h × (1000 m ÷ 1 km) × (1 h ÷ 3600 s) = 25.0 m/s

Always write the units, cancel them like you cancel in fractions, and check that what is left is exactly the unit the question asked for. If the units come out right, the arithmetic almost always follows.

Accuracy versus precision

These two words are not the same. Accuracy is how close a measurement is to the true value. Precision is how close repeated measurements are to each other. A dartboard makes the difference clear: darts clustered in the bullseye are accurate and precise; darts clustered tightly in one corner are precise but not accurate; darts scattered all over are neither. Significant figures communicate precision, while accuracy depends on a correctly calibrated instrument.

A fully worked significant-figure problem

Worked example. A student measures a rectangular metal sheet as 12.4 cm by 3.2 cm and a mass of 21.06 g, then reports the density per square centimeter of area. Track the sig figs at every stage.

• Area: 12.4 cm × 3.2 cm = 39.68 cm² on the calculator. The value 3.2 has only two sig figs, so area = 40. cm² (two sig figs).
• Mass per area: 21.06 g ÷ 39.68 cm² = 0.5307 g/cm² using the unrounded area. Limited by the two sig figs of 3.2, the answer is 0.53 g/cm².

Notice the key habit: carry extra digits through the middle of the calculation (use 39.68, not 40) and round only the final answer. Rounding too early would have shifted the last digit.

A worked rounding walk-through

Round 0.024856 to three significant figures. The three significant digits are 2, 4, and 8. The next digit is 5 (followed by more), so round the 8 up to 9, giving 0.0249. In scientific notation that is 2.49 × 10^-2, which makes the three sig figs unmistakable and removes any ambiguity about the leading zeros.

Common misconceptions

• "More decimal places always means a better answer." Writing 6.384 when your data supports only two sig figs overstates precision. Report 6.4 instead.
• "Leading zeros are significant." In 0.0034 the zeros only locate the decimal point; only the 3 and 4 count, so it has two sig figs.
• "Round after every step." Rounding mid-calculation lets errors accumulate. Keep guard digits and round once, at the end.
• "Accurate and precise mean the same thing." A scale that always reads 2 grams heavy is precise (repeatable) but not accurate (wrong value).

Recap

Significant figures report the honest precision of a measurement. Count them with the zero rules, and remember exact numbers never limit an answer. In multiplication and division, keep the fewest sig figs; in addition and subtraction, keep the fewest decimal places, rounding only at the end. Accuracy (closeness to truth) differs from precision (repeatability). Dimensional analysis converts units by multiplying by conversion factors so unwanted units cancel, and correct units are a strong check that the math is right.

Sources

1. OpenStax, Chemistry 2e, Chapter 1: Essential Ideas (Section 1.5 Measurement Uncertainty, Accuracy, and Precision and Section 1.6 Mathematical Treatment of Measurement Results). Rice University, 2019.
2. CK-12 Foundation, CK-12 Chemistry for High School, Chapter 3: Measurements (significant figures, accuracy and precision, dimensional analysis).
3. National Institute of Standards and Technology (NIST), Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, NIST Technical Note 1297.

All matter is built from atoms, and every atom shares the same basic parts. At the center is a tiny, dense nucleus that holds positively charged protons and neutral neutrons. Around the nucleus, in a cloud, move negatively charged electrons, which have almost no mass. The atom is mostly empty space: if the nucleus were the size of a marble, the electron cloud would stretch across a whole stadium.

Particle	Charge	Relative mass	Location
Proton	+1	1	Nucleus
Neutron	0	1	Nucleus
Electron	-1	about 1/1836	Electron cloud

Atomic number and mass number

The atomic number (Z) is the number of protons, and it defines the element. Every carbon atom has 6 protons; change that number and you have a different element. In a neutral atom, the number of electrons equals the number of protons. The mass number (A) is the total count of protons plus neutrons. So the number of neutrons is just A minus Z.

Isotopes

Isotopes are atoms of the same element (same number of protons) that have different numbers of neutrons, and therefore different masses. Carbon has three natural isotopes: carbon-12 (6 protons, 6 neutrons), carbon-13 (6 protons, 7 neutrons), and carbon-14 (6 protons, 8 neutrons). They act the same in chemical reactions because chemistry depends on electrons, not neutrons.

Atomic mass is a weighted average

The atomic mass printed on the periodic table is the average mass of an element's atoms, weighted by how common each isotope is. Chlorine is about 75% chlorine-35 and 25% chlorine-37. Its atomic mass is therefore close to:

(0.75 × 35) + (0.25 × 37) = 26.25 + 9.25 = 35.5 amu

That is why the table lists chlorine as about 35.5 amu even though no single chlorine atom has that exact mass. Mass here is measured in atomic mass units (amu), defined so that one carbon-12 atom weighs exactly 12 amu.

Reading an isotope symbol

Isotopes are often written with the mass number on top and the atomic number on the bottom, or simply as name-mass, such as oxygen-18. To decode any isotope you only need two counts. For oxygen-18: oxygen's atomic number is 8, so there are 8 protons; a neutral atom then has 8 electrons; and neutrons = mass number minus atomic number = 18 - 8 = 10 neutrons. For potassium-40 (Z = 19): 19 protons, 19 electrons, and 40 - 19 = 21 neutrons. The element name and the atomic number always agree, so if a problem gives you the name, you already know the proton count.

Worked example: weighted average atomic mass

Copper occurs as two isotopes: copper-63 with a mass of 62.93 amu at 69.17% abundance, and copper-65 with a mass of 64.93 amu at 30.83% abundance. A weighted average multiplies each isotope's mass by its fractional abundance, then adds:

(0.6917 × 62.93) + (0.3083 × 64.93)

= 43.53 + 20.02 = 63.55 amu

The periodic table lists copper as 63.55 amu, which matches. Note that the average sits closer to 63 than to 65 because copper-63 is the more abundant isotope. A weighted average always leans toward the most common isotope, which is a good sanity check on your arithmetic.

Worked example: build an atom from its counts

An atom has 17 protons, 18 neutrons, and 17 electrons. Identify it. The atomic number equals the proton count, 17, which is chlorine. The mass number is 17 + 18 = 35, so this is chlorine-35. Because protons and electrons are equal, the atom is neutral (no overall charge).

Common misconceptions

• "Isotopes are different elements." Isotopes of one element have the same number of protons, so they are the same element; only the neutron count (and mass) differs.
• "Atomic mass equals the number of protons." The atomic number is the proton count. Atomic mass is the weighted-average mass of the isotopes and is usually not a whole number.
• "The mass number is on the periodic table." The table shows the average atomic mass, not the whole-number mass number of any one isotope.
• "Electrons add noticeably to an atom's mass." An electron is only about 1/1836 the mass of a proton, so essentially all of an atom's mass is in its nucleus.

Recap

Atoms contain protons (+1) and neutrons (0) in a dense nucleus, with electrons (-1, nearly massless) in the surrounding cloud. The atomic number Z is the proton count and defines the element; the mass number A is protons plus neutrons, so neutrons = A - Z. Isotopes share Z but differ in neutrons and mass. The atomic mass on the periodic table is a weighted average of the isotope masses by abundance, measured in amu relative to carbon-12 = 12 amu exactly.

Sources

1. OpenStax, Chemistry 2e, Chapter 2: Atoms, Molecules, and Ions (Sections 2.2 Evolution of Atomic Theory and 2.3 Atomic Structure and Symbolism). Rice University, 2019.
2. CK-12 Foundation, CK-12 Chemistry for High School, Chapter 4: Atomic Structure (subatomic particles, isotopes, atomic mass).
3. National Institute of Standards and Technology (NIST), Atomic Weights and Isotopic Compositions, NIST Physical Measurement Laboratory database.

An atom's chemistry is decided almost entirely by its electrons, and electrons are not scattered at random. They occupy energy levels, often called shells, numbered 1, 2, 3, and so on outward from the nucleus. Lower-numbered shells sit closer to the nucleus, are lower in energy, and fill first. Each shell holds only so many electrons: the first holds up to 2, the second up to 8, and the third up to 8 for the main-group elements you will focus on here.

Subshells and orbitals

Inside a shell, electrons live in subshells labeled s, p, d, and f. An orbital is a region where an electron is likely to be found, and each orbital holds at most 2 electrons. The s subshell has one orbital (2 electrons), and the p subshell has three orbitals (6 electrons). Electrons fill the lowest-energy subshells first, a rule called the Aufbau principle.

Writing electron configurations

An electron configuration lists which subshells are filled and how many electrons are in each. For example:

• Hydrogen (1 electron): 1s¹
• Carbon (6 electrons): 1s² 2s² 2p²
• Sodium (11 electrons): 1s² 2s² 2p⁶ 3s¹

The superscripts always add up to the total number of electrons in the atom.

Valence electrons drive bonding

The electrons in the outermost shell are the valence electrons, and they are the ones that take part in bonding. For the main-group elements, the number of valence electrons matches the group number on the periodic table: Group 1 has 1, Group 2 has 2, and Groups 13 through 18 have 3 through 8. Atoms are especially stable when their outer shell is full, which for most elements means 8 valence electrons. This is the octet rule, and it explains why the noble gases in Group 18, which already have full outer shells, barely react at all. The drive to reach a full octet is the single most useful idea for predicting how atoms bond.

The filling order

Subshells do not always fill in a simple outward march, because their energies overlap. The order that works for the elements in this course is: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p. Notice that 4s fills before 3d. A memory aid is the diagonal rule, where you list the subshells in rows and read along diagonals. For the first 20 elements you rarely go past 4s, so the pattern stays manageable.

Worked example: configuration of phosphorus

Phosphorus has 15 electrons. Fill the subshells in order, giving each its capacity until the electrons run out:

• 1s holds 2 (13 left), 2s holds 2 (11 left), 2p holds 6 (5 left), 3s holds 2 (3 left), 3p takes the last 3.

So phosphorus is 1s² 2s² 2p⁶ 3s² 3p³. Check the total: 2 + 2 + 6 + 2 + 3 = 15, correct. The outermost shell is the third, holding 3s² 3p³ = 5 valence electrons, which matches phosphorus's position in Group 15.

Worked example: counting valence electrons

Take calcium, element 20. Its configuration is 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² (total 20). The highest shell number present is 4, and it contains 4s², so calcium has 2 valence electrons, exactly what Group 2 predicts. To reach an octet, calcium finds it far easier to lose those 2 outer electrons than to gain 6, which is why calcium forms a 2+ ion.

Common misconceptions

• "Shells fill strictly 1, 2, 3, 4 with no overlap." Energies overlap, so 4s fills before 3d. Follow the filling order, not just the shell number.
• "Valence electrons are all the electrons in the atom." Valence electrons are only those in the outermost (highest-numbered) shell, and they are the ones involved in bonding.
• "Every atom wants exactly 8 valence electrons." The octet rule is a strong guide, but hydrogen and helium are full with just 2 because the first shell holds only 2.
• "An orbital and a shell are the same thing." A shell contains subshells, which contain orbitals; each orbital holds at most 2 electrons.

Recap

Electrons occupy shells (energy levels) that fill from the inside out, subject to the overlapping filling order 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p. Each orbital holds 2 electrons; s subshells have 1 orbital and p subshells have 3. An electron configuration's superscripts sum to the total electron count. Valence electrons (the outermost shell) equal the group number for main-group elements and drive bonding as atoms seek a full octet.

Sources

1. OpenStax, Chemistry 2e, Chapter 6: Electronic Structure and Periodic Properties of Elements (Sections 6.3 Development of Quantum Theory and 6.4 Electronic Structure of Atoms). Rice University, 2019.
2. OpenStax, Chemistry: Atoms First 2e, Chapter 3: Electronic Structure and Periodic Properties. Rice University, 2019.
3. CK-12 Foundation, CK-12 Chemistry for High School, Chapter 5: Electrons in Atoms (electron configurations, Aufbau principle, valence electrons).

The periodic table lists the elements in order of increasing atomic number, laid out in a grid that reveals repeating patterns. A vertical column is a group (or family); elements in a group have the same number of valence electrons and behave in similar ways. A horizontal row is a period; going across a period, a shell is being filled. Because properties repeat at regular intervals, the arrangement is called periodic.

Regions of the table

Metals take up the left and center: they are shiny, conduct heat and electricity, and tend to lose electrons. Nonmetals sit in the upper right and tend to gain or share electrons. A staircase of metalloids (such as silicon) divides the two and have properties in between. A few named families are worth knowing: Group 1 alkali metals are soft and very reactive, Group 2 alkaline earth metals are reactive but a bit less so, Group 17 halogens are reactive nonmetals, and Group 18 noble gases are nearly unreactive.

Three key trends

Atomic radius is the size of an atom. Going down a group, atoms get larger because each period adds a new shell. Going across a period from left to right, atoms get smaller because the growing positive charge in the nucleus pulls the same shell in tighter.

Reactivity follows a pattern too. Metals get more reactive going down a group because their outer electrons are farther from the nucleus and easier to lose. Nonmetals get more reactive going up and to the right because they pull in electrons more strongly. Fluorine is the most reactive nonmetal for this reason.

Electronegativity measures how strongly an atom pulls on shared bonding electrons. It increases across a period and decreases down a group. Fluorine, in the upper right (setting aside the noble gases), is the most electronegative element. These trends move together in a sensible way, and remembering the top-right corner of the table as small and highly electronegative will carry you a long way.

Why the trends happen

Two competing effects explain almost every trend. The first is nuclear charge: more protons pull electrons in more strongly. The second is shielding: inner-shell electrons partly block the outer electrons from feeling the full nuclear pull, and each new shell adds distance. Across a period, protons increase while the shell stays the same, so the pull wins and atoms shrink. Down a group, each step adds a full new shell, so distance and shielding win and atoms grow. Every trend below is just these two ideas applied.

Worked example: rank atoms by size

Put lithium (Li), fluorine (F), and cesium (Cs) in order of increasing atomic radius. Li and F are both in period 2, and since size shrinks left to right, F is smaller than Li. Cs sits far down Group 1, so it has many more shells and is by far the largest. Increasing order: F < Li < Cs. The reasoning combines the across-period trend (F smaller than Li) with the down-group trend (Cs much larger).

Worked example: compare electronegativity

Which is more electronegative, oxygen (O) or sulfur (S)? Both are in Group 16, but oxygen sits above sulfur. Electronegativity decreases down a group because the bonding electrons are farther from the nucleus and more shielded, so oxygen is more electronegative. This is why oxygen pulls electrons so strongly in bonds and forms compounds with almost every other element.

A fourth trend: ionization energy

Ionization energy is the energy needed to pull one electron off an atom. It follows the same logic as electronegativity: it increases across a period (electrons are held tighter) and decreases down a group (outer electrons are farther out and easier to remove). This is exactly why metals, on the left, give up electrons easily (low ionization energy) while nonmetals, on the right, hold theirs tightly.

Common misconceptions

• "Atoms get bigger across a period because you are adding particles." You add protons and electrons to the same shell, so the stronger nuclear pull actually makes atoms smaller across a period.
• "The period number is the same as the group number." Periods are rows (they give the number of occupied shells); groups are columns (they give the valence-electron count for main-group elements).
• "Noble gases are the most electronegative because they are in the top right." Noble gases already have full shells and generally do not attract more electrons, so fluorine, not neon, is the most electronegative element.
• "Metalloids are a type of metal." Metalloids lie along the staircase and have properties between metals and nonmetals; they are their own category.

Recap

The periodic table orders elements by atomic number into groups (columns, shared valence electrons) and periods (rows, filling a shell). Metals sit left and center, nonmetals upper right, metalloids along the staircase. Balancing nuclear charge against shielding gives the trends: atomic radius grows down and to the left, while electronegativity and ionization energy grow up and to the right, peaking near fluorine. Reactivity rises down a group for metals and up-and-right for nonmetals.

Sources

1. OpenStax, Chemistry 2e, Chapter 6: Electronic Structure and Periodic Properties of Elements (Section 6.5 Periodic Variations in Element Properties). Rice University, 2019.
2. CK-12 Foundation, CK-12 Chemistry for High School, Chapter 6: The Periodic Table (groups and periods, periodic trends).
3. OpenStax, Chemistry: Atoms First 2e, Chapter 3: Electronic Structure and Periodic Properties (periodic trends). Rice University, 2019.

Atoms are most stable when their outer shell is full, and one way to get there is to gain or lose electrons. When an atom does this, it becomes an ion, a particle with an electric charge because its protons and electrons no longer balance.

Cations and anions

A cation is a positive ion, formed when an atom loses one or more electrons. Metals do this readily because they have only a few valence electrons and low pull on them. Sodium loses one electron to become Na⁺. An anion is a negative ion, formed when an atom gains electrons. Nonmetals do this because they are only a few electrons short of a full shell. Chlorine gains one electron to become Cl^-. An easy memory aid: a cation is "paw-sitive," and gaining electrons (which are negative) makes an anion negative.

Predicting ion charges from the group

For the main-group elements, the periodic table tells you the likely charge.

Group	Typical ion charge	Example
1	+1	Na+
2	+2	Mg2+
13	+3	Al3+
15	-3	N3-
16	-2	O2-
17	-1	Cl-

The ionic bond

When a metal meets a nonmetal, the metal hands over electrons and the nonmetal takes them. Now you have a positive cation and a negative anion, and opposite charges attract. That electrostatic attraction is the ionic bond. Sodium gives an electron to chlorine, and Na⁺ and Cl^- lock together as NaCl. Ionic compounds form rigid crystal patterns called lattices, have high melting points, and conduct electricity when melted or dissolved in water because their ions are then free to move.

Worked example: predict the formula of an ionic compound

Combine magnesium and chlorine. Magnesium is in Group 2, so it forms Mg²⁺. Chlorine is in Group 17, so it forms Cl^-. A compound must be electrically neutral overall, so the positive and negative charges have to cancel. One Mg²⁺ supplies +2, and each Cl^- supplies -1, so you need two chloride ions: (+2) + 2(-1) = 0. The formula is MgCl₂. A quick shortcut, the crossover method, is to take each ion's charge number and use it as the other ion's subscript: Mg gets subscript 1 (from Cl's charge of 1) and Cl gets subscript 2 (from Mg's charge of 2), giving MgCl₂. Always check that the charges truly cancel.

Worked example: aluminum oxide

Aluminum forms Al³⁺ (Group 13) and oxygen forms O^2- (Group 16). To balance +3 and -2, find the least common multiple of 3 and 2, which is 6. You need two Al³⁺ (total +6) and three O^2- (total -6), so the formula is Al₂O₃. Verify: 2(+3) + 3(-2) = +6 - 6 = 0. The crossover method gives the same result: aluminum takes subscript 2 and oxygen takes subscript 3.

Polyatomic ions

Some ions are groups of atoms carrying an overall charge, called polyatomic ions. Common ones include nitrate (NO₃^-), sulfate (SO₄^2-), hydroxide (OH^-), and ammonium (NH₄⁺), the one common positive polyatomic ion. They bond ionically just like single-atom ions. When you need more than one of a polyatomic ion, wrap it in parentheses: calcium nitrate is Ca(NO₃)₂, because one Ca²⁺ needs two NO₃^- to balance.

Common misconceptions

• "Cations are negative because they come from cats." A cation is positive; it forms when an atom loses electrons. Anions are negative from gaining electrons.
• "Ionic compounds are made of molecules." Ionic solids are giant lattices of ions, not discrete molecules. We use a formula unit (the smallest whole-number ratio) instead.
• "Solid salt conducts electricity." In the solid, ions are locked in place. Salt conducts only when melted or dissolved, when the ions are free to move.
• "You add subscripts and charges together." Subscripts count atoms; charges must cancel to zero. Keep the two ideas separate when writing formulas.

Recap

An ion is a charged atom or group: cations (positive) form by losing electrons, anions (negative) by gaining them. Main-group charges follow the group number (Group 1 is +1, Group 2 is +2, Group 13 is +3, Group 15 is -3, Group 16 is -2, Group 17 is -1). A metal transfers electrons to a nonmetal, and the resulting opposite charges attract in an ionic bond. Formulas are built so total charge is zero, using the crossover method and parentheses for polyatomic ions. Ionic solids form lattices, melt at high temperatures, and conduct when molten or dissolved.

Sources

1. OpenStax, Chemistry 2e, Chapter 2: Atoms, Molecules, and Ions (Sections 2.6 Molecular and Ionic Compounds and 2.7 Chemical Nomenclature). Rice University, 2019.
2. CK-12 Foundation, CK-12 Chemistry for High School, Chapter 8: Ionic and Metallic Bonding (ion formation, ionic bonds, formula units).
3. OpenStax, Chemistry: Atoms First 2e, Chapter 4: Chemical Bonding and Molecular Geometry. Rice University, 2019.

Ionic bonds work when a metal can hand electrons to a nonmetal. But when two nonmetals meet, neither one wants to give up electrons, so they solve the problem a different way: they share. A shared pair of electrons is a covalent bond, and the group of atoms held together this way is a molecule.

Sharing to reach an octet

Two hydrogen atoms each have one electron and each need two for a full first shell, so they share one pair and form H₂. Oxygen atoms need more, so two oxygen atoms share two pairs (a double bond) to make O₂. Nitrogen atoms share three pairs (a triple bond) in N₂. In each case, sharing lets both atoms count the shared electrons toward a full outer shell.

Polar and nonpolar bonds

Sharing is not always equal. If the two atoms have different electronegativities, the more electronegative atom pulls the shared electrons closer to itself. This creates a polar covalent bond, with a slightly negative end and a slightly positive end. If the two atoms are identical or very close in electronegativity, the sharing is even and the bond is nonpolar. The bond in H₂ is nonpolar because both atoms are the same; the bond in H-Cl is polar because chlorine pulls harder. Bonding is really a spectrum, from perfectly shared, to unevenly shared, to fully transferred (ionic).

Comparing the two kinds of compounds

Property	Ionic compounds	Covalent compounds
Made of	Metal + nonmetal	Nonmetal + nonmetal
Smallest unit	Formula unit in a lattice	Molecule
Melting point	High	Usually lower
Conducts when dissolved	Usually yes	Usually no

These differences all trace back to one idea: ionic compounds are held together by strong attractions between charged ions spread through a whole lattice, while covalent compounds are separate molecules with weaker attractions between them.

The seven diatomic elements

Seven elements never travel alone in nature; they always pair up as diatomic molecules: hydrogen (H₂), nitrogen (N₂), oxygen (O₂), fluorine (F₂), chlorine (Cl₂), bromine (Br₂), and iodine (I₂). A common memory trick is "Have No Fear Of Ice Cold Beer," where each first letter cues one element. This matters when you balance equations later: the reactant is O₂, not a lone O.

Worked example: counting shared pairs with the octet rule

Predict the bonding in a molecule of fluorine, F₂. Each fluorine atom has 7 valence electrons and needs just 1 more for an octet. Neither atom will give up electrons (both are highly electronegative nonmetals), so they share one pair. That single shared pair counts toward both atoms' octets: each fluorine now sees its own 6 unshared electrons plus the 2 shared, for a full 8. The result is a single covalent bond, F-F. The number of bonds an atom forms usually equals the number of electrons it needs to complete its octet: 1 for a halogen, 2 for oxygen, 3 for nitrogen, 4 for carbon.

Worked example: is the bond polar?

Compare the bonds in Cl₂ and HCl. In Cl₂, both atoms are chlorine with identical electronegativity, so the electrons are shared equally and the bond is nonpolar. In HCl, chlorine (electronegativity about 3.0) pulls harder than hydrogen (about 2.1). The difference of roughly 0.9 pulls the shared electrons toward chlorine, so chlorine carries a small negative charge and hydrogen a small positive charge, making it a polar covalent bond. As a rough guide, electronegativity differences below about 0.4 are nonpolar, from about 0.4 to 1.7 are polar covalent, and above about 1.7 tend toward ionic.

Common misconceptions

• "Covalent means the atoms give away electrons." Giving away electrons is ionic. Covalent bonding is sharing, so both atoms count the shared electrons.
• "Every covalent bond is polar." Bonds between identical atoms (H₂, O₂, Cl₂) are nonpolar because the sharing is perfectly even.
• "Oxygen exists as single O atoms in air." The oxygen you breathe is O₂, a diatomic molecule with a double bond, not lone oxygen atoms.
• "Molecular compounds conduct electricity like salt water." Most molecular compounds have no ions, so their solutions usually do not conduct.

Recap

When two nonmetals bond, they share electron pairs in covalent bonds, forming molecules. Sharing one, two, or three pairs makes single, double, or triple bonds, letting each atom reach an octet. Equal sharing between similar atoms is nonpolar; unequal sharing between atoms of different electronegativity is polar, giving partial charges. Seven elements occur as diatomic molecules. Compared with ionic compounds, covalent compounds are discrete molecules with lower melting points that usually do not conduct electricity.

Sources

1. OpenStax, Chemistry 2e, Chapter 7: Chemical Bonding and Molecular Geometry (Sections 7.2 Covalent Bonding and 7.3 Lewis Symbols and Structures). Rice University, 2019.
2. CK-12 Foundation, CK-12 Chemistry for High School, Chapter 9: Covalent Bonding (electron sharing, bond polarity, molecular compounds).
3. OpenStax, Chemistry: Atoms First 2e, Chapter 4: Chemical Bonding and Molecular Geometry (electronegativity and bond polarity). Rice University, 2019.

Nomenclature is the set of rules for naming compounds so that every chemist reads the same name the same way. The rules are different for ionic and molecular compounds, so first decide which type you have: a metal with a nonmetal is ionic, while two nonmetals are molecular.

Naming ionic compounds

Name the cation (metal) first, unchanged, then the anion (nonmetal) with its ending changed to -ide. So NaCl is sodium chloride and MgO is magnesium oxide. To write a formula from a name, balance the charges so the compound comes out neutral. Magnesium is Mg²⁺ and chloride is Cl^-, so it takes two chlorides per magnesium: MgCl₂.

Many transition metals can form more than one charge, so a Roman numeral in the name shows which one. Iron can be Fe²⁺ or Fe³⁺: FeCl₂ is iron(II) chloride and FeCl₃ is iron(III) chloride.

Polyatomic ions

A polyatomic ion is a charged group of atoms that stays together as a unit. A few common ones are worth memorizing.

Name	Formula
Nitrate	NO3-
Sulfate	SO42-
Carbonate	CO32-
Hydroxide	OH-
Ammonium	NH4+

When a formula needs more than one polyatomic ion, put it in parentheses: calcium nitrate is Ca(NO₃)₂, because Ca²⁺ needs two nitrate ions to balance.

Naming molecular compounds

For two nonmetals, use prefixes to show how many of each atom is present: mono (1), di (2), tri (3), tetra (4), penta (5). The first element keeps its name (dropping mono if it would start the name), and the second gets the -ide ending. So CO is carbon monoxide, CO₂ is carbon dioxide, and N₂O₄ is dinitrogen tetroxide. Notice that ionic names never use these prefixes; the charges already fix the ratio. Mixing up the two systems is the single most common naming mistake, so always check the type first.

Worked example: name an ionic compound with a variable metal

Name Fe₂O₃. Oxygen is reliably O^2-, and there are three of them, for a total negative charge of -6. That -6 must be balanced by two iron atoms, so together the irons carry +6, which means each iron is +3. Iron can be +2 or +3, so the name needs a Roman numeral: iron(III) oxide. The trick with variable metals is to work backward from the known anion charge to find the metal's charge.

Worked example: write a formula from a name

Write the formula for ammonium sulfate. Ammonium is the polyatomic cation NH₄⁺ and sulfate is SO₄^2-. To balance +1 against -2, you need two ammonium ions per sulfate: 2(+1) + (-2) = 0. Because you need more than one polyatomic ion, wrap ammonium in parentheses: (NH₄)₂SO₄. Notice the sulfate needs no parentheses because only one is present.

Worked example: name a molecular compound

Name P₂O₅. Both are nonmetals, so use prefixes. There are two phosphorus atoms (di) and five oxygen atoms (penta), and the second element takes the -ide ending: diphosphorus pentoxide. The a in penta is dropped before oxide to keep the name easy to say. There is no Roman numeral here because molecular naming uses prefixes instead of charges.

Common misconceptions

• "Use prefixes like di and tri for ionic compounds." Prefixes are only for molecular (two-nonmetal) compounds. Ionic names never use them because the charges already fix the ratio.
• "The Roman numeral shows how many atoms there are." The Roman numeral shows the charge on the metal, not the number of atoms. Iron(III) means Fe³⁺, not three irons.
• "Every metal needs a Roman numeral." Only metals that can have more than one charge (many transition metals) need one. Group 1 and 2 metals have fixed charges.
• "Polyatomic ions break apart, so you never need parentheses." A polyatomic ion stays together as a unit, so when you need more than one you enclose it in parentheses, as in Ca(NO₃)₂.

Recap

Naming starts by deciding the type: metal plus nonmetal is ionic, two nonmetals is molecular. Ionic names give the metal, then the nonmetal with an -ide ending, adding a Roman numeral for metals with more than one possible charge, and never using prefixes. Molecular names use count prefixes (mono, di, tri, tetra, penta). Memorize common polyatomic ions such as nitrate, sulfate, carbonate, hydroxide, and ammonium, and use parentheses when a formula needs more than one of them.

Sources

1. OpenStax, Chemistry 2e, Chapter 2: Atoms, Molecules, and Ions (Section 2.7 Chemical Nomenclature). Rice University, 2019.
2. CK-12 Foundation, CK-12 Chemistry for High School, Chapter 7: Chemical Nomenclature (naming ionic and molecular compounds, polyatomic ions).
3. OpenStax, Chemistry: Atoms First 2e, Chapter 2: Atoms, Molecules, and Ions (chemical nomenclature). Rice University, 2019.

A chemical reaction rearranges atoms to make new substances. We describe it with a chemical equation: the reactants (starting materials) go on the left, an arrow shows the direction of change, and the products (new substances) go on the right. For example, hydrogen burning in oxygen is written H₂ + O₂ → H₂O.

Conservation of mass

The law of conservation of mass says that atoms are never created or destroyed in a reaction, only rearranged. That means the number of atoms of each element must be the same on both sides of the equation. The equation H₂ + O₂ → H₂O is not yet balanced: the left has 2 oxygen atoms but the right has only 1. A balanced equation is our way of respecting conservation of mass.

Balancing with coefficients

We balance by placing coefficients (big numbers in front of formulas) to change how many of each molecule we have. You may change coefficients, but you must never change the subscripts inside a formula, because that would turn the substance into something else.

1. Count the atoms of each element on both sides.
2. Add coefficients to make the counts match, one element at a time.
3. Save hydrogen and oxygen for last when possible, and recount at the end.

Worked example. Balance H₂ + O₂ → H₂O. Put a 2 in front of H₂O to get 2 oxygen atoms on the right, matching the O₂ on the left. That gives 2H₂O, which now has 4 hydrogen atoms, so put a 2 in front of H₂ on the left. The balanced equation is:

2 H₂ + O₂ → 2 H₂O

Check: left has 4 H and 2 O; right has 4 H and 2 O. It balances.

Second worked example. Methane burning: CH₄ + O₂ → CO₂ + H₂O. Carbon is fine (1 each). Hydrogen: the left has 4, so put a 2 in front of H₂O to get 4 on the right. Now count oxygen on the right: 2 (in CO₂) + 2 (in 2 H₂O) = 4, so put a 2 in front of O₂. The result is CH₄ + 2 O₂ → CO₂ + 2 H₂O.

Handling polyatomic ions and fractions

Two tricks make harder equations easier. First, if a polyatomic ion appears unchanged on both sides, balance it as a single unit instead of atom by atom. Second, if balancing forces a fraction, clear it by multiplying every coefficient through.

Worked example (fraction cleared). Balance C₂H₆ + O₂ → CO₂ + H₂O. Balance carbon first: 2 CO₂ on the right. Balance hydrogen: 6 H on the left means 3 H₂O on the right. Now count oxygen on the right: 2(2) + 3(1) = 7 atoms, so you need 7/2 O₂. To remove the fraction, multiply every coefficient by 2:

2 C₂H₆ + 7 O₂ → 4 CO₂ + 6 H₂O

Check: left 4 C, 12 H, 14 O; right 4 C, 12 H, (8 + 6) = 14 O. Balanced.

Types of reactions

Recognizing a reaction type helps you predict products. The main patterns are:

• Synthesis (combination): two or more reactants join into one product, A + B → AB, as in 2 H₂ + O₂ → 2 H₂O.
• Decomposition: one reactant splits into two or more products, AB → A + B, as in 2 H₂O₂ → 2 H₂O + O₂.
• Single replacement: one element takes another's place, A + BC → AC + B, as in Zn + 2 HCl → ZnCl₂ + H₂.
• Double replacement: two compounds swap partners, AB + CD → AD + CB, as in AgNO₃ + NaCl → AgCl + NaNO₃.
• Combustion: a fuel reacts with O₂ to give CO₂ and H₂O, as in the methane example above.

Common misconceptions

• "You can balance by changing subscripts." Changing H₂O to H₂O₂ makes a different substance. Only coefficients may be changed.
• "Balanced means equal numbers of molecules on each side." Balancing means equal numbers of each type of atom, not equal molecule counts.
• "A subscript of 1 or a coefficient of 1 must be written." A coefficient or subscript of 1 is understood and left off, as the single O in H₂O.
• "Fractions are always wrong in equations." A fraction is a valid intermediate step; you simply multiply through to clear it for the final whole-number answer.

Recap

A chemical equation shows reactants changing into products, and it must obey conservation of mass, so each element has equal atom counts on both sides. Balance by adjusting coefficients only, never subscripts: count atoms, match them one element at a time, save H and O for last, clear any fractions, and recount to check. Common reaction types (synthesis, decomposition, single and double replacement, combustion) make products easier to predict.

Sources

1. OpenStax, Chemistry 2e, Chapter 4: Stoichiometry of Chemical Reactions (Sections 4.1 Writing and Balancing Chemical Equations and 4.2 Classifying Chemical Reactions). Rice University, 2019.
2. CK-12 Foundation, CK-12 Chemistry for High School, Chapter 11: Chemical Reactions (balancing equations, reaction types).
3. OpenStax, Chemistry: Atoms First 2e, Chapter 7: Stoichiometry of Chemical Reactions. Rice University, 2019.

Atoms are far too small and too many to count one at a time, so chemists count them in giant bundles using the mole. A mole is just a fixed number of things, the way a dozen is 12. One mole is Avogadro's number of particles: about 6.022 × 10²³. That enormous number is chosen so that one mole of a substance has a mass in grams equal to its atomic or molecular mass in amu. This link between the atomic scale and the gram scale is the beating heart of quantitative chemistry.

Molar mass

The molar mass of a substance is the mass of one mole of it, in grams per mole (g/mol). For an element, it is just the atomic mass from the periodic table. For a compound, add up the molar masses of all the atoms in the formula.

Worked example. Find the molar mass of water, H₂O. Hydrogen is about 1.008 g/mol and oxygen is about 16.00 g/mol.

2 × 1.008 + 1 × 16.00 = 2.016 + 16.00 = 18.02 g/mol

So one mole of water weighs about 18.02 g. As a second example, the molar mass of carbon dioxide, CO₂, is 12.01 + 2(16.00) = 44.01 g/mol.

Converting grams, moles, and particles

Molar mass and Avogadro's number are the two conversion factors that link the three quantities. The core relationships are:

• moles = grams ÷ molar mass
• grams = moles × molar mass
• particles = moles × 6.022 × 10²³

Worked example. How many moles are in 36.0 g of water? Divide by the molar mass: 36.0 g ÷ 18.02 g/mol = 2.00 mol. And how many molecules is that? Multiply by Avogadro's number: 2.00 mol × 6.022 × 10²³ = 1.20 × 10²⁴ molecules. Set these up with dimensional analysis, watch the units cancel, and even long chains become routine.

Worked example: a full grams-to-particles chain

How many oxygen atoms are in 50.0 g of carbon dioxide, CO₂? This takes three linked steps. First convert grams to moles of CO₂ using the molar mass 44.01 g/mol:

50.0 g ÷ 44.01 g/mol = 1.136 mol CO₂

Next convert moles of CO₂ to molecules with Avogadro's number:

1.136 mol × 6.022 × 10²³ = 6.84 × 10²³ molecules CO₂

Finally, each CO₂ molecule contains 2 oxygen atoms, so multiply by 2:

6.84 × 10²³ × 2 = 1.37 × 10²⁴ oxygen atoms

The chain grams → moles → molecules → atoms used one conversion factor at each arrow, and every unit cancelled cleanly into the next.

Percent composition

Molar mass also tells you what fraction of a compound's mass comes from each element, called the percent composition. For each element: percent = (mass of that element in one mole ÷ molar mass of the compound) × 100. Worked example. In water (18.02 g/mol), the two hydrogens contribute 2.016 g, so hydrogen is (2.016 ÷ 18.02) × 100 = 11.2%, and oxygen is (16.00 ÷ 18.02) × 100 = 88.8%. The two percentages add to 100%, which is a quick check.

Common misconceptions

• "A mole of any two substances weighs the same." A mole is a fixed count of particles, but the mass depends on the substance: a mole of water is 18.02 g while a mole of CO₂ is 44.01 g.
• "Molar mass and atomic mass are unrelated numbers." They are numerically equal: an element's atomic mass in amu equals its molar mass in g/mol.
• "To get particles you divide by Avogadro's number." Moles times Avogadro's number gives particles; you divide by it to go from particles back to moles.
• "You can convert grams straight to particles in one step." Grams connect to particles only through moles, so you must pass through moles using molar mass first.

Recap

The mole is a count of 6.022 × 10²³ particles (Avogadro's number) chosen so a substance's mass in grams matches its atomic or molecular mass in amu. Molar mass (g/mol) is the atomic mass for an element or the sum of atomic masses for a compound. Molar mass and Avogadro's number are the conversion factors linking grams, moles, and particles: moles = grams ÷ molar mass, and particles = moles × 6.022 × 10²³. Percent composition breaks a compound's mass down by element.

Sources

1. OpenStax, Chemistry 2e, Chapter 3: Composition of Substances and Solutions (Sections 3.1 Formula Mass and the Mole Concept and 3.2 Determining Empirical and Molecular Formulas). Rice University, 2019.
2. CK-12 Foundation, CK-12 Chemistry for High School, Chapter 10: The Mole (Avogadro's number, molar mass, mole conversions, percent composition).
3. National Institute of Standards and Technology (NIST), CODATA Value: Avogadro Constant, NIST Reference on Constants, Units, and Uncertainty.

Stoichiometry is the part of chemistry that uses a balanced equation to figure out how much of one substance reacts with or produces how much of another. It works because the coefficients in a balanced equation tell you the exact ratio of the particles involved.

The mole ratio

Consider the balanced equation for making ammonia:

N₂ + 3 H₂ → 2 NH₃

The coefficients say that 1 molecule of N₂ reacts with 3 molecules of H₂ to make 2 molecules of NH₃. Scale that up by Avogadro's number and the same ratio holds for moles: 1 mole of N₂ reacts with 3 moles of H₂ to make 2 moles of NH₃. Any two of these amounts form a mole ratio you can use as a conversion factor, such as (2 mol NH₃ ÷ 3 mol H₂).

Moles to moles

Worked example. How many moles of NH₃ form from 6.0 mol of H₂ (with plenty of N₂)? Multiply by the mole ratio that cancels H₂:

6.0 mol H₂ × (2 mol NH₃ ÷ 3 mol H₂) = 4.0 mol NH₃

Grams to grams

Real labs measure mass, not moles, so a full stoichiometry problem often has three steps: convert grams of the given substance to moles, use the mole ratio, then convert moles of the wanted substance back to grams.

Worked example. In the reaction 2 H₂ + O₂ → 2 H₂O, how many grams of water form from 8.0 g of H₂? (Molar masses: H₂ = 2.02 g/mol, H₂O = 18.02 g/mol.)

1. Grams of H₂ to moles: 8.0 g ÷ 2.02 g/mol = 3.96 mol H₂ (about 4.0 mol).
2. Mole ratio: 4.0 mol H₂ × (2 mol H₂O ÷ 2 mol H₂) = 4.0 mol H₂O.
3. Moles of H₂O to grams: 4.0 mol × 18.02 g/mol = 72 g H₂O.

So about 72 g of water forms. Notice how every step is a dimensional-analysis conversion: grams to moles, moles to moles, moles to grams. Master that three-step path and you can solve most basic stoichiometry problems.

The limiting reactant

Reactions rarely start with exactly the right ratio of ingredients. The limiting reactant is the one that runs out first; it caps how much product can form. The other reactant is left over in excess. A kitchen analogy: if a recipe needs 2 slices of bread and 1 slice of cheese per sandwich, and you have 10 bread and 3 cheese, the cheese limits you to 3 sandwiches, and 4 slices of bread are left over.

Worked example. For N₂ + 3 H₂ → 2 NH₃, suppose you have 2.0 mol N₂ and 3.0 mol H₂. Which limits the reaction? Compare what each could make. From N₂: 2.0 mol × (2 mol NH₃ ÷ 1 mol N₂) = 4.0 mol NH₃. From H₂: 3.0 mol × (2 mol NH₃ ÷ 3 mol H₂) = 2.0 mol NH₃. Hydrogen makes less, so H₂ is the limiting reactant and only 2.0 mol NH₃ can form. Nitrogen is in excess. The rule: whichever reactant yields the least product is the limiting one.

Percent yield

The amount of product predicted by stoichiometry is the theoretical yield. The amount you actually collect in the lab is the actual yield, and it is usually less because of spills, side reactions, or incomplete reactions. The percent yield compares them:

percent yield = (actual yield ÷ theoretical yield) × 100

Worked example. If a reaction should make 72 g of water (theoretical) but you recover 63 g (actual), the percent yield is (63 ÷ 72) × 100 = 87.5%. A percent yield can never sensibly exceed 100%; if it does, something (often leftover water or impurities in the product) has inflated the measured mass.

Common misconceptions

• "The limiting reactant is the one you have the least of." It is the one that makes the least product, which depends on the mole ratio, not just the raw amount. Always compare products, not starting amounts.
• "Mole ratios come from the subscripts." Mole ratios come from the coefficients of the balanced equation. Subscripts stay inside formulas and describe one molecule.
• "You can skip converting grams to moles." The mole ratio only works with moles, so you must convert masses to moles before applying it.
• "Percent yield above 100% just means a great reaction." Yields above 100% signal an error, usually an impure or still-wet product weighing more than the pure substance should.

Recap

Stoichiometry uses the coefficients of a balanced equation as mole ratios to relate amounts of substances. The core grams-to-grams path is: convert grams of the given substance to moles, apply the mole ratio, then convert moles of the wanted substance to grams. The limiting reactant is whichever produces the least product and caps the yield, leaving the other in excess. Percent yield = (actual ÷ theoretical) × 100 measures how much of the predicted product you actually obtained.

Sources

1. OpenStax, Chemistry 2e, Chapter 4: Stoichiometry of Chemical Reactions (Sections 4.3 Reaction Stoichiometry and 4.4 Reaction Yields). Rice University, 2019.
2. CK-12 Foundation, CK-12 Chemistry for High School, Chapter 12: Stoichiometry (mole ratios, limiting reactant, percent yield).
3. OpenStax, Chemistry: Atoms First 2e, Chapter 7: Stoichiometry of Chemical Reactions (reaction yields and limiting reactants). Rice University, 2019.

Why does a solid hold its shape while a gas fills a room? The answer is the kinetic molecular theory, which pictures matter as tiny particles in constant motion. Two ideas drive everything: particles are always moving, and temperature is a measure of their average speed. Heating adds energy and speeds particles up; cooling takes energy away and slows them down.

The states as particle motion

In a solid, particles are packed closely and only vibrate in place, held by strong attractions, so a solid keeps a fixed shape and volume. In a liquid, particles are still close but have enough energy to slide past one another, so a liquid keeps its volume but flows to fit its container. In a gas, particles have so much energy that they break free of one another and zoom around with lots of empty space between them, so a gas expands to fill any container and can be squeezed into a smaller one.

Changes of state

Adding or removing heat moves matter between states. Each change has a name:

Change	From	To	Energy
Melting	Solid	Liquid	Absorbed
Freezing	Liquid	Solid	Released
Vaporizing (boiling)	Liquid	Gas	Absorbed
Condensing	Gas	Liquid	Released

Notice a pattern: going toward a gas (melting, vaporizing) absorbs energy to loosen the particles, while going toward a solid (freezing, condensing) releases energy as the particles settle. During a change of state the temperature stays constant, because the added energy goes into breaking attractions rather than speeding particles up. This is why a pot of boiling water stays at 100 °C no matter how high you turn the burner.

Two changes skip the liquid state entirely. Sublimation goes straight from solid to gas, which is what dry ice (solid CO₂) does as it fogs. The reverse, gas straight to solid, is deposition, which is how frost forms on a cold window. Both follow the same energy rule: sublimation absorbs energy, deposition releases it.

Evaporation and cooling

A liquid does not have to boil to become a gas. At any temperature, some surface particles are moving fast enough to escape into the air, a process called evaporation. Because the fastest particles leave, the ones left behind have a lower average speed, so the remaining liquid cools. This is why sweat cools your skin: the fastest-moving water molecules evaporate and carry energy away, leaving you cooler. The same idea explains why a wet towel feels cold and why rubbing alcohol feels chilly on the skin, since it evaporates even faster than water.

Reading a heating curve

Imagine slowly heating a block of ice and graphing its temperature over time. The temperature rises while the ice warms, then flattens out at 0 °C during melting, rises again through the liquid range, flattens once more at 100 °C during boiling, and finally rises as steam. The two flat stretches are the changes of state, where energy breaks attractions instead of raising temperature. Worked reasoning. If ice starts at −10 °C and you heat it steadily, it first climbs to 0 °C, then pauses at 0 °C until every bit has melted, so a thermometer reading a steady 0 °C tells you the sample is still a mix of ice and water, not that heating has stopped.

Common misconceptions

• "Particles in a solid do not move at all." Solid particles still vibrate in place; they simply lack the energy to leave their fixed positions.
• "Temperature rises steadily while ice melts." During a change of state the temperature holds constant because the energy goes into breaking attractions, not into faster motion.
• "A liquid must reach its boiling point to become a gas." Evaporation happens at any temperature from the surface; boiling is just rapid vaporization throughout the liquid.
• "Heating always raises temperature." While a substance changes state, added heat converts to the energy of separating particles, so the temperature can stay flat even as you keep heating.

Recap

The kinetic molecular theory says matter is made of particles in constant motion, and temperature measures their average speed. Solids vibrate in fixed positions, liquids slide past one another, and gases move freely with lots of empty space. Adding heat drives changes toward the gas state (melting, vaporizing, sublimation) and absorbs energy; removing heat drives changes toward the solid state (freezing, condensing, deposition) and releases energy. During any change of state the temperature stays constant, and evaporation cools a liquid because its fastest particles escape.

Sources

1. OpenStax, Chemistry 2e, Chapter 10: Liquids and Solids (Sections 10.1 Intermolecular Forces and 10.3 Phase Transitions). Rice University, 2019.
2. CK-12 Foundation, CK-12 Chemistry for High School, Chapter 13: States of Matter (kinetic molecular theory, changes of state, heating curves).
3. OpenStax, Chemistry: Atoms First 2e, Chapter 10: Liquids and Solids (phase transitions and the energy of changes of state). Rice University, 2019.

Gases respond in predictable ways when you change their pressure, volume, or temperature, and the gas laws capture those responses as simple relationships. Three quantities matter: pressure (P), the force the gas exerts on its container walls; volume (V), the space it fills; and temperature (T), which for gas laws must always be in kelvin.

Boyle's law: pressure and volume

Boyle's law says that at constant temperature, pressure and volume are inversely related: squeeze a gas into half the volume and its pressure doubles. In symbols, P₁V₁ = P₂V₂.

Worked example. A gas occupies 3.0 L at 2.0 atm. If it is allowed to expand to 6.0 L at the same temperature, what is the new pressure? Rearrange to P₂ = P₁V₁ ÷ V₂ = (2.0 atm × 3.0 L) ÷ 6.0 L = 1.0 atm. Doubling the volume halved the pressure, exactly as Boyle's law predicts.

Charles's law: volume and temperature

Charles's law says that at constant pressure, the volume of a gas is directly proportional to its temperature in kelvin: heat a gas and it expands. In symbols, V₁ ÷ T₁ = V₂ ÷ T₂.

Worked example. A gas fills 300 mL at 300 K. If it is heated to 400 K at constant pressure, what is the new volume? Rearrange to V₂ = V₁ × T₂ ÷ T₁ = 300 mL × 400 K ÷ 300 K = 400 mL. The gas expanded as it warmed.

Why kelvin is required

These temperature relationships only work on the Kelvin scale, because Kelvin starts at absolute zero, where particle motion is minimal. If you used Celsius, a value of 0 °C would wrongly suggest zero volume, and negative Celsius temperatures would give impossible negative volumes. Always convert to kelvin (K = °C + 273) before using a gas law. One more useful fact: at standard temperature and pressure (STP), meaning 0 °C and 1 atm, one mole of any gas takes up about 22.4 liters.

Gay-Lussac's law: pressure and temperature

Gay-Lussac's law covers the third pairing: at constant volume, the pressure of a gas is directly proportional to its kelvin temperature. Heat a sealed rigid container and the pressure climbs. In symbols, P₁ ÷ T₁ = P₂ ÷ T₂. This is why an aerosol can carries a warning never to heat it: rising temperature raises the pressure inside until the can can rupture.

Worked example. A sealed can holds gas at 3.0 atm and 300 K. If it is heated to 450 K at constant volume, what is the new pressure? Rearrange to P₂ = P₁ × T₂ ÷ T₁ = 3.0 atm × 450 K ÷ 300 K = 4.5 atm. The pressure rose by the same factor (1.5) as the temperature.

The combined gas law

When pressure, volume, and temperature all change at once, the three laws merge into the combined gas law:

(P₁V₁) ÷ T₁ = (P₂V₂) ÷ T₂

Worked example. A gas occupies 2.0 L at 1.0 atm and 300 K. What volume does it fill at 2.0 atm and 600 K? Solve for V₂:

V₂ = (P₁V₁T₂) ÷ (T₁P₂) = (1.0 atm × 2.0 L × 600 K) ÷ (300 K × 2.0 atm)

V₂ = 1200 ÷ 600 = 2.0 L

Doubling the pressure alone would have halved the volume to 1.0 L, but doubling the temperature at the same time expanded it back, so the two effects cancelled and the volume stayed at 2.0 L. Each of Boyle's, Charles's, and Gay-Lussac's laws is just the combined gas law with one quantity held constant.

Common misconceptions

• "You can plug Celsius into a gas law." Gas laws need absolute temperature, so always convert to kelvin (K = °C + 273) first; using Celsius gives wrong or even negative results.
• "Boyle's law means pressure and volume rise together." They are inversely related: as one goes up the other goes down, so their product stays constant.
• "Doubling the Celsius temperature doubles the volume." Only doubling the kelvin temperature doubles the volume; going from 20 °C to 40 °C is not a doubling in kelvin.
• "A rigid sealed container has constant pressure when heated." Its volume is fixed, so by Gay-Lussac's law the pressure rises as the temperature rises.

Recap

The gas laws relate a gas's pressure, volume, and kelvin temperature. Boyle's law (P₁V₁ = P₂V₂) links pressure and volume inversely at constant temperature. Charles's law (V₁/T₁ = V₂/T₂) links volume and temperature directly at constant pressure. Gay-Lussac's law (P₁/T₁ = P₂/T₂) links pressure and temperature directly at constant volume. The combined gas law, (P₁V₁)/T₁ = (P₂V₂)/T₂, handles changes in all three at once. Temperatures must always be in kelvin, and one mole of any gas fills about 22.4 L at STP.

Sources

1. OpenStax, Chemistry 2e, Chapter 9: Gases (Sections 9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law, covering Boyle's, Charles's, and Gay-Lussac's laws). Rice University, 2019.
2. CK-12 Foundation, CK-12 Chemistry for High School, Chapter 14: The Behavior of Gases (Boyle's law, Charles's law, Gay-Lussac's law, combined gas law, molar volume).
3. National Institute of Standards and Technology (NIST), Guide for the Use of the International System of Units (SI), thermodynamic temperature and the kelvin.

A solution is a homogeneous mixture, uniform all the way through. It has two parts: the solute is the substance being dissolved (present in the smaller amount), and the solvent is the substance doing the dissolving (present in the larger amount). In salt water, salt is the solute and water is the solvent. Water dissolves so many things that it is called the universal solvent, thanks to its polar molecules.

How dissolving works

When an ionic solid like salt meets water, the polar water molecules surround each ion and pull it away from the crystal, spreading the ions evenly through the liquid. A helpful rule of thumb is "like dissolves like": polar solvents such as water dissolve polar and ionic substances, while nonpolar solvents dissolve nonpolar substances such as oils. That is why oil and water do not mix.

Speeding up dissolving

Three things make a solid dissolve faster: stirring (which brings fresh solvent to the surface), heating (faster-moving particles collide with the solid more), and crushing the solid into smaller pieces (more surface area is exposed to the solvent). None of these change how much can dissolve, only how quickly.

Molarity measures concentration

Concentration describes how much solute is in a given amount of solution. The most common measure in chemistry is molarity (M), defined as moles of solute per liter of solution:

molarity = moles of solute ÷ liters of solution

Worked example. What is the molarity of a solution made by dissolving 0.50 mol of NaCl in enough water to make 2.0 L of solution? Molarity = 0.50 mol ÷ 2.0 L = 0.25 M. A solution labeled 0.25 M contains 0.25 mol of solute in every liter. You can rearrange the formula to find any missing piece: moles = molarity × liters, so 3.0 L of that 0.25 M solution would contain 0.25 M × 3.0 L = 0.75 mol of NaCl.

From grams to molarity

Often you know a mass, not moles, so you convert grams to moles with the molar mass first. Worked example. What is the molarity if you dissolve 58.5 g of NaCl (molar mass 58.5 g/mol) in enough water to make 0.500 L of solution? First find moles: 58.5 g ÷ 58.5 g/mol = 1.00 mol. Then divide by the volume: 1.00 mol ÷ 0.500 L = 2.00 M. Watch the volume unit: molarity uses liters, so a volume given in milliliters must be divided by 1000 first.

Saturation and solubility

There is a limit to how much solute a solvent can hold. A solution is unsaturated when more solute can still dissolve, saturated when it holds the maximum at that temperature, and any extra solute simply settles at the bottom. The maximum amount that dissolves is the solubility, and for most solids it rises with temperature, which is why hot water dissolves more sugar than cold. Gases behave in the opposite way, dissolving better in cold liquids, which is why a warm soda goes flat faster as its dissolved CO₂ escapes.

Diluting a solution

Adding solvent to a solution spreads the same amount of solute through more volume, lowering the concentration. Because the moles of solute do not change, dilutions follow M₁V₁ = M₂V₂. Worked example. How much water must you add to 100 mL of 6.0 M HCl to dilute it to 2.0 M? Solve for the final volume: V₂ = M₁V₁ ÷ M₂ = (6.0 M × 100 mL) ÷ 2.0 M = 300 mL. Since you start with 100 mL and need 300 mL total, you add 200 mL of water. (Safety note: always add acid to water, never water to acid, because the mixing releases heat.)

Common misconceptions

• "Molarity uses milliliters." Molarity is moles per liter, so any volume in milliliters must be converted to liters (divide by 1000) before dividing.
• "The solute is always solid and the solvent always liquid." Any state can play either role; in air, gaseous oxygen is a solute dissolved in gaseous nitrogen.
• "Stirring or heating lets you dissolve unlimited solute." Those only speed up dissolving; solubility sets the maximum, and past it extra solute just settles out.
• "Diluting a solution changes the number of moles of solute." Dilution adds only solvent, so the moles of solute stay the same while the concentration drops.

Recap

A solution is a homogeneous mixture of a solute (smaller amount) dissolved in a solvent (larger amount). Dissolving follows "like dissolves like," and stirring, heating, and crushing speed it up without changing how much can dissolve. Molarity, moles of solute per liter of solution, is the standard measure of concentration, and volumes must be in liters. Solubility is the maximum that dissolves at a given temperature, marking the line between unsaturated and saturated. Dilution follows M₁V₁ = M₂V₂, since adding solvent lowers concentration while the moles of solute stay fixed.

Sources

1. OpenStax, Chemistry 2e, Chapter 11: Solutions and Colloids (Sections 11.1 The Dissolution Process and 11.3 Molarity and Dilution). Rice University, 2019.
2. CK-12 Foundation, CK-12 Chemistry for High School, Chapter 16: Solutions (solute and solvent, factors affecting dissolving, solubility, molarity, dilution).
3. OpenStax, Chemistry: Atoms First 2e, Chapter 11: Solutions and Colloids (molarity and the dilution equation). Rice University, 2019.

Acids and bases are two families of compounds you meet every day, from the citric acid in lemons to the ammonia in cleaners. Chemists have a clear way to define them. An acid is a substance that produces hydrogen ions (H⁺) when dissolved in water, such as hydrochloric acid, HCl. A base produces hydroxide ions (OH^-) when dissolved in water, such as sodium hydroxide, NaOH.

Properties you can observe

Property	Acids	Bases
Taste	Sour (like lemons)	Bitter
Feel	-	Slippery
Litmus paper	Turns blue litmus red	Turns red litmus blue
Ion produced in water	H+	OH-

Never taste or touch laboratory chemicals to test them; these properties are described here only so you understand what the categories mean.

The pH scale

The pH scale measures how acidic or basic a solution is, running from 0 to 14. It is based on the concentration of hydrogen ions. A pH of 7 is neutral (pure water). A pH below 7 is acidic, and the lower it goes, the more acidic. A pH above 7 is basic, and the higher it goes, the more basic. Each step of 1 on the scale is a tenfold change in acidity, so a pH of 3 is ten times more acidic than a pH of 4.

When the hydrogen ion concentration is a simple power of ten, the pH is easy to find: pH is the negative of the exponent. If [H⁺] = 1 × 10^-3 mol/L, then the pH is 3, which is acidic. If [H⁺] = 1 × 10^-9 mol/L, the pH is 9, which is basic.

Neutralization

When an acid and a base are mixed, they cancel each other in a neutralization reaction, producing water and a salt. For example:

HCl + NaOH → NaCl + H₂O

The H⁺ from the acid joins the OH^- from the base to make water (H₂O), and the leftover ions (Na⁺ and Cl^-) form a salt. The result moves toward a neutral pH of 7, which is why antacids (bases) relieve an acidic stomach.

Worked example. Balance the neutralization of sulfuric acid with sodium hydroxide. Sulfuric acid, H₂SO₄, can supply two H⁺, so it needs two NaOH:

H₂SO₄ + 2 NaOH → Na₂SO₄ + 2 H₂O

Check the atoms: 4 H and 1 S and 6 O on each side (4 O in the sulfate plus 2 O in the two hydroxides), plus 2 Na on each side. The two H⁺ pair with the two OH^- to make two waters, and the salt formed is sodium sulfate.

Strong versus weak

Acids and bases differ in strength, which is how completely they break apart in water. A strong acid such as HCl ionizes almost completely, releasing nearly all its H⁺, so it gives a very low pH. A weak acid such as acetic acid (in vinegar) ionizes only slightly, so most molecules stay intact and the pH is much closer to 7 even at the same concentration. The same distinction applies to bases: NaOH is a strong base, while ammonia is a weak base. Strength (how completely it ionizes) is not the same as concentration (how much is dissolved); a dilute solution of a strong acid can be less acidic than a concentrated solution of a weak one.

Indicators

An indicator is a dye that changes color depending on pH, giving a quick read on acidity. Litmus is the classic example: red in acid, blue in base. Universal indicator goes further, shifting through a rainbow, from red in strong acid through green at neutral to purple in strong base, so its color maps to an approximate pH. In the lab, indicators reveal the exact moment an acid has been neutralized by a base.

Common misconceptions

• "A strong acid and a concentrated acid are the same thing." Strength is how completely an acid ionizes; concentration is how much is dissolved. They are independent.
• "A higher pH number means more acidic." It is the reverse: lower pH is more acidic, higher pH is more basic, and 7 is neutral.
• "Each pH step is a small change." Each unit is a tenfold change in acidity, so pH 2 is one hundred times more acidic than pH 4.
• "Neutralization always gives an exactly neutral solution." It moves toward neutral and makes water plus a salt, but the final pH depends on the particular acid and base and can land slightly off 7.

Recap

An acid produces H⁺ in water and a base produces OH^-. The pH scale from 0 to 14 measures acidity from the hydrogen ion concentration: below 7 is acidic, 7 is neutral, above 7 is basic, and each unit is a tenfold change. When [H⁺] is a simple power of ten, the pH is the positive value of that exponent. Strength (how completely something ionizes) differs from concentration (how much is dissolved). Neutralization mixes an acid and a base to make water and a salt, and indicators such as litmus signal pH by changing color.

Sources

1. OpenStax, Chemistry 2e, Chapter 14: Acid-Base Equilibria (Sections 14.1 Bronsted-Lowry Acids and Bases and 14.3 Relative Strengths of Acids and Bases). Rice University, 2019.
2. CK-12 Foundation, CK-12 Chemistry for High School, Chapter 21: Acids and Bases (properties, the pH scale, strong versus weak, neutralization, indicators).
3. National Institute of Standards and Technology (NIST), NIST Guidelines and Standard Reference Materials for pH Measurement, Standard Reference Database on pH.

Every chemical reaction involves energy, usually in the form of heat. Thermochemistry is the study of these energy changes. The key idea is that breaking bonds requires energy (you must pull atoms apart), while forming bonds releases energy (atoms settle into a more stable arrangement). Whether a reaction gives off or takes in heat overall depends on the balance between these two.

Exothermic and endothermic reactions

An exothermic reaction releases heat to its surroundings, making them warmer. Burning fuel and the reactions inside a hand warmer are exothermic. Because energy leaves the reacting chemicals, we say the enthalpy change (ΔH) is negative. An endothermic reaction absorbs heat from its surroundings, making them cooler. An instant cold pack works this way. Here energy enters the chemicals, so ΔH is positive. A simple memory aid: exo means exit (heat exits), and endo means into (heat goes in).

Why the sign works

If forming the product bonds releases more energy than breaking the reactant bonds required, there is energy left over to warm the surroundings, and the reaction is exothermic. If breaking the reactant bonds costs more than forming the product bonds gives back, the reaction must pull energy in from the surroundings, and it is endothermic.

Calculating heat with specific heat

How much a substance heats up for a given amount of energy depends on its specific heat (c), the energy needed to raise one gram by one degree Celsius. Water has an unusually high specific heat of 4.184 J/(g·°C), which is why it resists temperature change and is used as a coolant. The heat transferred is:

q = m × c × ΔT

where q is heat in joules, m is mass in grams, c is specific heat, and ΔT is the temperature change.

Worked example. How much heat is needed to warm 50.0 g of water from 20.0 °C to 50.0 °C? Here ΔT = 50.0 - 20.0 = 30.0 °C.

q = 50.0 g × 4.184 J/(g·°C) × 30.0 °C = 6276 J ≈ 6.28 kJ

A positive result means the water absorbed that much energy. If ΔT were negative (cooling), q would come out negative, meaning heat was released instead.

Worked example: solving for a missing piece. Suppose 209 J of heat raises the temperature of a water sample by 10.0 °C. What is the mass? Rearrange q = m × c × ΔT to solve for m: m = q ÷ (c × ΔT) = 209 J ÷ (4.184 J/(g·°C) × 10.0 °C) = 209 ÷ 41.84 = 5.00 g. Any one of the four quantities can be found when the other three are known.

Activation energy and energy diagrams

Even an exothermic reaction usually needs a push to get started. The activation energy is the minimum energy the reactants must gain, often as a small input of heat, to begin reacting; it is why a match must be struck before it burns. An energy diagram plots energy along the path of a reaction. The reactants start at one level, climb over an energy hill (whose height is the activation energy), and settle at the product level. If the products sit lower than the reactants, energy was released overall and the reaction is exothermic; if the products sit higher, energy was absorbed and the reaction is endothermic. The gap between the reactant and product levels is ΔH.

Conservation of energy

Energy is never created or destroyed, only transferred, so the heat lost by one thing is gained by another. When a hot metal is dropped into cool water, the heat released by the metal equals the heat absorbed by the water, and the two settle at one shared temperature. This bookkeeping, tracking where the joules go, is the heart of thermochemistry and the reason q for the surroundings is equal and opposite to q for the system.

Common misconceptions

• "Exothermic reactions do not need any energy to start." Most still require activation energy to begin; being exothermic only means they release more energy than they take in overall.
• "Breaking bonds releases energy." Breaking bonds always costs energy; it is forming bonds that releases it. The net ΔH compares the two.
• "A negative q or ΔH means the temperature is negative." The negative sign just means heat was released; the temperature can be perfectly ordinary.
• "A high specific heat means a substance heats up fast." The opposite is true: a high specific heat means it resists temperature change and heats up slowly, like water.

Recap

Thermochemistry studies the energy changes in reactions. Breaking bonds costs energy and forming bonds releases it, and the balance sets the sign of ΔH: exothermic reactions release heat (ΔH negative), while endothermic reactions absorb heat (ΔH positive). Heat transfer is q = m × c × ΔT, where a high specific heat means a substance resists temperature change. Activation energy is the push needed to start a reaction, energy diagrams show reactants climbing to products, and energy is conserved, so heat lost by one object is gained by another.

Sources

1. OpenStax, Chemistry 2e, Chapter 5: Thermochemistry (Sections 5.1 Energy Basics, 5.2 Calorimetry, and 5.3 Enthalpy). Rice University, 2019.
2. CK-12 Foundation, CK-12 Chemistry for High School, Chapter 17: Thermochemistry (exothermic and endothermic processes, specific heat, heat calculations, activation energy).
3. National Institute of Standards and Technology (NIST), NIST Chemistry WebBook, thermochemical data including specific heat capacity of water.