Chemistry Lab

Chemistry Lab is a team lab-and-question event in which two partners work through a series of tasks about two areas of chemistry for 2027: gases, meaning how gases behave and the laws that describe them (plus their role in climate and the ozone layer), and kinetics, the study of how fast reactions go and why. Some tasks are written questions about a table, graph or equation. Others ask you to work with equipment: you may collect data with computer-interfaced sensors (probeware) after a supervisor demonstrates the setup, interpret a data set someone else collected, or watch a running experiment and explain what you see. Points are split evenly between the two topics, so a team needs to be strong on both.

The most useful way to think about the event is as a sequence of short problems that each resolve into one of three skills. You must set up a relationship (which gas law applies, which rate law fits the data). You must count (moles, partial pressures, rate constants, half-lives) with correct units. And you must explain a result in terms of particles and energy: why a heated gas pushes harder on its container, why a powder reacts faster than a lump, why a catalyst speeds a reaction without being used up. Teams that score well are fast on the counting and careful with the explaining, and they never lose points to a temperature left in Celsius or a rate constant without units.

Event format

The equipment list matters more than it looks. The host does not supply those items, so a team that arrives without a thermometer, graduated cylinders or a stirring rod is at a real disadvantage in a hands-on task. The Division C list also includes items such as filter paper and a funnel, a multimeter, mechanical calipers and a 9 V battery. The equipment list itself warns that bringing prohibited equipment can cost up to 10% of the score, so pack only what the list allows.

Safety rules are enforced strictly. Removing goggles or other safety clothing, or handling materials unsafely, is penalized, and the penalty can go as far as disqualification.

How points are split and scored

• High score wins. Points are divided evenly between kinetics and gases. A strong kinetics score cannot make up for leaving the gas tasks blank, and vice versa. Plan your 50 minutes so both halves get attention.
• Time is not scored. A supervisor can cap the time at each task, but time is never used for scoring or to break ties. Unanswered tasks cost you points; a slow but correct answer costs nothing extra.
• Ties are broken by preselected questions. You cannot know which ones, so treat every question as potentially decisive.
• Cleanup counts. Up to 10% can be taken off if you do not clean your area as instructed. Leave five minutes at the end for it.

What the rules cover

The 2027 rules replace last season's chemical reactions/stoichiometry topic with gases, keep kinetics, add mechanism checks and activation energy at the upper levels, and expand the list of ions you must know at State and National. Nomenclature, formula writing and stoichiometry are still named as essential tools that may appear in any task.

Two things are worth noticing about the scope. First, the gas topic is broad: it runs from kinetic-molecular theory and the named laws through hands-on determinations to atmospheric chemistry. Second, the reaction-classification, product-prediction, net-ionic and redox-balancing items from last season are no longer listed. You still need balanced equations to do stoichiometry, but you should not spend study time on solubility rules or activity series for their own sake.

Ions, formulas and stoichiometry

Nomenclature and stoichiometry are the bookkeeping that every gas and kinetics task depends on. A question about the rate of a reaction between potassium permanganate and oxalic acid assumes you can write KMnO₄; a question about gas produced from a carbonate assumes you can count moles.

The Regional ion list

Main-group monatomic ions take their charge from their group: Group 1 forms +1 ions (Na⁺, K⁺), Group 2 forms +2 (Mg²⁺, Ca²⁺), aluminum forms Al³⁺, Group 15 nonmetals form −3 (N³⁻, P³⁻), Group 16 forms −2 (O²⁻, S²⁻) and the halogens form −1 (Cl⁻, Br⁻). Anions named from a single element end in -ide.

Cyanide is the newcomer compared with last season's list. Note that two of these ions end in -ide even though they are polyatomic (hydroxide and cyanide), which is a favorite trick question.

The State and National additions

At the upper levels the list grows in three directions. The first is a set of named ions that appear constantly in kinetics experiments, because they are colored or strongly oxidizing:

The second is the common transition-metal ions, whose charges must come from the name because many metals have more than one. The rules give Cu⁺/Cu²⁺, Fe²⁺/Fe³⁺, Ag⁺ and Zn²⁺ as examples and say "etc.", so also learn the usual extras: Ni²⁺, Co²⁺, Mn²⁺, Cr³⁺, Hg²⁺ and the mercury(I) dimer Hg₂²⁺. In the Stock system the Roman numeral is the charge, so iron(III) chloride is FeCl₃ and copper(I) oxide is Cu₂O. Silver and zinc have only one common charge, so their names carry no numeral. Older -ous/-ic names are still used on tests: the -ous ending is the lower charge and -ic the higher, often on the Latin root. Ferrous Fe²⁺ / ferric Fe³⁺, cuprous Cu⁺ / cupric Cu²⁺, stannous Sn²⁺ / stannic Sn⁴⁺, plumbous Pb²⁺ / plumbic Pb⁴⁺, mercurous Hg₂²⁺ / mercuric Hg²⁺, cobaltous Co²⁺ / cobaltic Co³⁺, chromous Cr²⁺ / chromic Cr³⁺, vanadous V²⁺ / vanadic V³⁺. So ferric chloride is FeCl₃ and stannous fluoride is SnF₂. A name with no numeral for a metal that has several charges ("tin hydroxide") is ambiguous: it could be Sn(OH)₂ or Sn(OH)₄, so write the formula you chose with its numeral (tin(IV) hydroxide, Sn(OH)₄) to show your assumption.

The third is the oxyanion naming system. For a family of oxygen-containing anions of the same element and charge, the name tells you the oxygen count relative to the "-ate" ion:

The charge stays the same across the family. Learn the "-ate" ion for each element and generate the rest. Bromine and iodine follow chlorine's pattern exactly, so bromate is BrO₃⁻ and iodite is IO₂⁻.

Writing formulas and names

A neutral ionic formula balances total positive charge against total negative charge with the smallest whole-number ratio. Calcium nitrate is Ca(NO₃)₂, aluminum sulfate is Al₂(SO₄)₃, ammonium dichromate is (NH₄)₂Cr₂O₇ and iron(III) thiocyanate is Fe(SCN)₃. Use parentheses whenever a polyatomic ion appears more than once. Going the other way, find the anion's charge first, then work out the metal's charge: in Mn(NO₃)₂ the two nitrates give −2, so manganese is +2 and the name is manganese(II) nitrate.

Molecular gases use Greek prefixes instead of charges: CO is carbon monoxide, N₂O is dinitrogen monoxide (nitrous oxide), N₂O₅ is dinitrogen pentoxide and SF₆ is sulfur hexafluoride. These names come up constantly in greenhouse-gas and kinetics questions. The prefixes are mono- 1, di- 2, tri- 3, tetra- 4, penta- 5, hexa- 6, hepta- 7, octa- 8, nona- 9, deca- 10; "mono" is dropped on the first element (CO₂ is carbon dioxide, not monocarbon dioxide).

Further naming patterns that appear on tests:

• "Bi-" and "hydrogen". Adding H⁺ to a −2 anion gives a −1 ion named with "hydrogen" or the older prefix "bi-": HCO₃⁻ bicarbonate (hydrogen carbonate), HSO₄⁻ bisulfate, HSO₃⁻ bisulfite (so sodium bisulfite is NaHSO₃), HPO₄²⁻ hydrogen phosphate, H₂PO₄⁻ dihydrogen phosphate.
• "Peroxo-" and "thio-". "Peroxo" adds one more O as a peroxide link: peroxonitrate is NO₄⁻ (so sodium peroxonitrate is NaNO₄). "Thio" replaces an O with S: thiosulfate S₂O₃²⁻, thiocyanate SCN⁻.
• Acids from anions. -ate anion → -ic acid; -ite anion → -ous acid; -ide anion → hydro-…-ic acid. So HClO₄ is perchloric acid, HClO₃ chloric, HClO₂ chlorous, HClO (also written HOCl) hypochlorous, HCl(aq) hydrochloric, H₂SO₄ sulfuric, H₂SO₃ sulfurous, HNO₃ nitric, HNO₂ nitrous, H₃PO₄ phosphoric (3 H⁺ + PO₄³⁻), HC₂H₃O₂ acetic. The same pattern names unusual ones: hypofluorous acid is HOF (HFO).
• Hydroxides and ammonium. Ammonium hydroxide is NH₄OH; magnesium hypochlorite is Mg(ClO)₂; aluminum carbonate is Al₂(CO₃)₃ (2 × +3 balances 3 × −2).
• Other elements in the same group follow the pattern. Selenium and tellurium copy sulfur: selenate SeO₄²⁻, selenite SeO₃²⁻, tellurate TeO₄²⁻, tellurite TeO₃²⁻; bromine and iodine copy chlorine. A salt with two cations lists both, cations first, and balances the total charge: potassium sodium tartrate KNaC₄H₄O₆, ammonium iron(II) sulfate (NH₄)₂Fe(SO₄)₂.
• Oxy-cations. A few metal-oxygen cations have their own names: uranyl UO₂²⁺ (uranyl nitrate is UO₂(NO₃)₂), vanadyl VO²⁺, and the "oxy-" prefix in salts such as bismuth oxychloride BiOCl. Sulfur oxyanions rarely follow the full chlorine pattern; the photographer's "hypo" is sodium thiosulfate, Na₂S₂O₃, historically misnamed sodium hyposulfite.
• Complex ions. Ferrocyanide is [Fe(CN)₆]⁴⁻ (iron(II)), ferricyanide is [Fe(CN)₆]³⁻ (iron(III)); potassium ferrocyanide is K₄[Fe(CN)₆].

Mole conversions, limiting reagent and percent yield

Every stoichiometry calculation follows the same chain: amount you have → moles of that substance → moles of the substance you want (using the coefficient ratio from a balanced equation) → amount you want. For gases, the "amount" at either end can be a volume, converted through the ideal gas law.

The limiting reagent is the reactant that runs out first. Convert each reactant to moles and divide by its coefficient; the smallest quotient is limiting, and every product amount is calculated from it.

Percent yield is diagnostic. A low value usually means gas escaped before collection, the reaction did not finish, or product stuck to glassware. A value above 100% means something is wrong with the measurement, often water vapor counted as product gas (see Dalton's law below) or a wet solid.

Many reactions happen in solution, so keep molarity handy as well: M = mol of solute / L of solution. (Molarity is written M, as in 0.200 M; do not confuse it with molar mass, also written M, in g/mol.) A 25.0 mL sample of 0.200 M solution contains 0.200 × 0.0250 = 0.00500 mol of solute, and for a dilution the moles do not change, so $M_1V_1 = M_2V_2$. Kinetics tasks often ask for the concentration of each reactant after mixing, which is a dilution problem: 10.0 mL of 0.100 M KI mixed with 40.0 mL of other solutions gives 0.100 × 10.0 / 50.0 = 0.0200 M iodide in the reaction mixture.

Balancing equations

A balanced equation has the same number of atoms of each element, and the same total charge, on both sides. Change only the coefficients, never the subscripts (changing a subscript changes the substance). A reliable order of attack:

1. Write correct formulas for every reactant and product.
2. Balance the element that appears in the fewest formulas first, and leave free elements (O₂, H₂, Fe) and H and O for last.
3. Treat a polyatomic ion that survives unchanged (SO₄²⁻, NO₃⁻) as a single unit.
4. If you end with a half-integer, multiply everything by 2. Finish with the lowest whole-number set and check every element.

Redox equations in kinetics labs. Several classic rate experiments are oxidation-reduction reactions (permanganate with oxalic acid, iodide with peroxide, dichromate with iron(II)), so you may be asked to balance one. Use half-reactions in acid: (1) split into oxidation and reduction; (2) balance atoms other than O and H; (3) add H₂O to balance O; (4) add H⁺ to balance H; (5) add electrons to balance charge; (6) multiply so both halves transfer the same number of electrons, add, and cancel. For permanganate: MnO₄⁻ + 8 H⁺ + 5 e⁻ → Mn²⁺ + 4 H₂O. For oxalic acid: H₂C₂O₄ → 2 CO₂ + 2 H⁺ + 2 e⁻. Multiplying by 2 and 5 and adding gives 2 MnO₄⁻ + 5 H₂C₂O₄ + 6 H⁺ → 2 Mn²⁺ + 10 CO₂ + 8 H₂O: the purple color vanishes as MnO₄⁻ is used up, and the Mn²⁺ produced catalyzes the reaction (it is autocatalytic, so it starts slowly and then speeds up). Hydrogen peroxide can play either role: as an oxidizing agent it is reduced, H₂O₂ + 2 H⁺ + 2 e⁻ → 2 H₂O; as a reducing agent it is oxidized, H₂O₂ → O₂ + 2 H⁺ + 2 e⁻. With permanganate it is the reducing agent: 2 MnO₄⁻ + 5 H₂O₂ + 6 H⁺ → 2 Mn²⁺ + 5 O₂ + 8 H₂O. Write state symbols when asked: (s), (l), (g), (aq).

The basic reaction types are still useful vocabulary for recognizing what forms: synthesis (A + B → AB), decomposition (AB → A + B), single replacement (A + BC → AC + B), double replacement (AB + CD → AD + CB) and combustion (fuel + O₂ → oxides, CO₂ and H₂O for a hydrocarbon). Gas-forming versions of these are the ones this event uses most, because the gas can be collected and measured.

Percent composition and empirical formulas

Percent composition by mass is (mass of the element in one formula unit / molar mass) × 100. For example, CO₂ is 12.01/44.01 = 27.3% carbon and 72.7% oxygen, and 16 g of oxygen is contained in 0.50 mol CO₂ (each mole of CO₂ carries 32.00 g O). The same idea gives the mass percent of a solution: mass of solute / mass of solution × 100, so 3.00% H₂O₂ means 3.00 g H₂O₂ in every 100 g of solution, and a sample containing 12.15 g H₂O₂ weighs 12.15 / 0.0300 = 405 g. An empirical formula is the simplest whole-number ratio of atoms; the molecular formula is a whole-number multiple of it, found by comparing the molar mass (often measured with the gas laws) with the empirical-formula mass.

Combustion analysis works the same way: all the carbon in a sample ends up as CO₂ (12.01/44.01 of its mass is C) and all the hydrogen as H₂O (2.016/18.02 of its mass is H); any mass not accounted for by C and H is oxygen.

Gases: properties and kinetic-molecular theory

Gases are the one state of matter whose behavior can be predicted almost entirely from a simple particle model. The kinetic-molecular theory (KMT) makes five assumptions about an ideal gas:

1. A gas is made of a very large number of tiny particles in constant, random, straight-line motion.
2. The particles themselves take up a negligible fraction of the container's volume.
3. The particles exert no attractive or repulsive forces on each other between collisions.
4. Collisions with each other and with the walls are elastic: kinetic energy is conserved.
5. The average kinetic energy of the particles is proportional to the absolute (kelvin) temperature.

Every physical property of a gas follows from these. Gases are compressible because most of their volume is empty space. They expand to fill any container because nothing holds the particles together. They have low densities, roughly a thousandth of the liquid's. They mix completely and spontaneously because the particles move freely. And they exert pressure because particles hit the walls: pressure is the force of those collisions per unit area.

The fifth assumption is the key to most explanations. At the same temperature, all gases have the same average kinetic energy (each molecule's kinetic energy is ½mv², with m its mass and v its speed). A lighter molecule must therefore move faster on average, which is the basis of Graham's law. Raising the temperature raises the average speed, which means more frequent and harder wall collisions, which means higher pressure if the volume is fixed.

Gases compared with liquids and solids

Textbooks list the KMT postulates as four or five statements, depending on whether "particles are tiny compared with the distances between them" and "particles move constantly and randomly" are merged. Whatever the count, a full answer names: negligible particle volume, constant random straight-line motion, no attractive or repulsive forces, elastic collisions, and average kinetic energy proportional to kelvin temperature. Two consequences are tested directly. Temperature is a measure of the average kinetic energy of the particles, so two different gases at the same temperature have the same average kinetic energy even though their speeds differ. And absolute zero (0 K = −273.15 °C) is the temperature at which, in the ideal-gas picture, the particles would have no kinetic energy; real gases condense to liquids and solids long before reaching it.

The pressure of a gas comes from collisions with the walls, not from collisions between particles. It therefore depends on how many particles there are and how fast they move (the amount and the temperature), not on the identity of the gas: 1 mol of H₂ and 1 mol of CO₂ in identical containers at the same temperature exert the same pressure. Ways to raise the pressure of a gas: add more gas, heat it, or reduce its volume.

The Maxwell-Boltzmann distribution and three kinds of speed

The molecules in a gas do not all move at the same speed. The Maxwell-Boltzmann distribution (figure in the Arrhenius section) is a lopsided hump: few slow molecules, a peak at the most probable speed, and a long tail of fast molecules. Because of that tail, the average (mean) speed sits slightly to the right of the peak, and the root-mean-square speed slightly further right still. The same is true of the energy distribution: the average kinetic energy lies to the right of the peak (at 3 times the most probable energy).

Raising the temperature moves the peak to higher speed and flattens and widens the curve (the area under it, the total number of molecules, stays the same). A heavier gas at the same temperature has a narrower curve peaked at lower speed. The fast tail explains everyday observations: water in an open cup evaporates completely at room temperature, far below its boiling point, because at any moment some molecules at the surface have enough energy to escape, and the remaining molecules keep redistributing energy into the tail. The fraction of molecules with energy above a threshold $E_a$ is roughly $e^{-E_a/RT}$, the same factor that appears in the Arrhenius equation.

A gas that expands rapidly as it escapes from a pressurized container, such as a CO₂ cartridge or an aerosol can, cools down: the molecules do work pushing back the surroundings and, in a real gas, pulling apart against their mutual attractions, both of which use up kinetic energy. (Cooling of a real gas forced through a valve or nozzle, driven by those attractions, is the Joule-Thomson effect, which is used to liquefy gases.)

Pressure units and standard conditions

Pressure is force per unit area, $P = F/A$. Its SI unit, the pascal (Pa), is one newton per square meter (1 Pa = 1 N/m²), which is tiny, so gas work uses kPa, atm, mmHg or torr. Because pressure is force spread over area, the same force on a larger area gives a smaller pressure: snowshoes spread a person's weight so they do not sink, and a 1500 Pa pressure acting on 15 m² pushes with F = PA = 22 500 N. Pressure is measured with a barometer (atmospheric pressure) or a manometer or electronic sensor (a gas sample). Know the conversions cold, because supervisors mix units on purpose:

STP (standard temperature and pressure) in most high-school texts means 0 °C (273.15 K) and 1 atm (101.325 kPa), where one mole of ideal gas occupies 22.4 L. IUPAC now defines STP at 1 bar (100 kPa), where the molar volume is 22.7 L. If a test says STP without defining it, use 22.4 L and 1 atm, and state your assumption. Other bodies use other reference states (NIST's "normal temperature and pressure", NTP, is 20 °C and 1 atm; the natural-gas industry often uses 15 °C and 101.325 kPa), so always read the conditions a question gives. Do not confuse STP with SATP (standard ambient temperature and pressure: 25 °C and 1 bar, 24.8 L/mol) or "room conditions" (25 °C and 1 atm, 24.5 L/mol). Gauge pressure (as read from a tire gauge) is the pressure above atmospheric, so absolute pressure = gauge pressure + atmospheric pressure. A tire reading 34 psi at sea level is really 34 + 14.7 = 48.7 psi absolute (3.31 atm), and only the absolute value goes into a gas law.

Barometers, manometers and liquid columns

A mercury barometer is a glass tube filled with mercury and inverted in a dish of mercury. The mercury falls until the weight of the column is balanced by the atmosphere pushing on the dish; the space above the column is a near-vacuum. At sea level the column stands about 760 mm tall, which is where the mmHg unit comes from. A column 735 mm tall means P = 735/760 = 0.967 atm. Mercury is used because it is very dense (13.6 g/cm³); a water barometer would need a column 13.6 times taller, about 10.3 m, to balance 1 atm. In general the column height is inversely proportional to the liquid's density: $h_1 \rho_1 = h_2 \rho_2$.

An open-ended manometer is a U-tube of liquid with one arm connected to the gas and the other open to the air. If the liquid is pushed down on the gas side, the gas is above atmospheric pressure: $P_\text{gas} = P_\text{atm} + h$. If the liquid is higher on the gas side, $P_\text{gas} = P_\text{atm} - h$ (with h in mmHg for a mercury manometer). A closed-ended manometer has a vacuum above one arm, so the height difference is the gas pressure directly.

Atmospheric pressure is simply the weight of the air above you per unit area, which is why the pressure (and the air's density) falls with altitude: roughly halving for every 5.5 km of height, so at 6 km it is close to 50 kPa and at the summit of Everest (8.8 km) it is about a third of sea-level pressure. That weight is enormous: multiply 1.01 × 10⁵ Pa by Earth's surface area (4πr², with r = 6.4 × 10⁶ m) and the whole atmosphere weighs about 5.2 × 10¹⁹ N. It is also why the two evacuated Magdeburg hemispheres could not be pulled apart by teams of horses: with a vacuum inside, nothing pushed back against the atmosphere pressing on the outside. Pressure differences drive flow, always from high pressure to low: an aerosol can sprays because the propellant inside is above atmospheric pressure, and you drink through a straw because lowering the pressure in your mouth lets the atmosphere push the liquid up.

Real gases

Real gases behave ideally when the particles are far apart and moving fast: low pressure and high temperature. At high pressure the particles' own volume is no longer negligible, so the real volume is larger than ideal. At low temperature, attractions pull particles together, reducing wall collisions, so the real pressure is lower than ideal. Small, nonpolar gases such as He and H₂ are the most ideal; polar or large gases such as NH₃, H₂O and SO₂ deviate most. For this event, name the condition and the KMT assumption that fails.

In one phrase: real gases deviate at high density (high pressure, small volume) and near condensation (low temperature). A gas just above its boiling point, such as oxygen near −183 °C, is a real gas in every practical sense, and the ideal gas law is never valid "under all conditions". An ideal gas is a model that obeys PV = nRT exactly; no real gas does.

The two corrections pull in opposite directions. Attractions tug each molecule back toward its neighbors just as it is about to hit a wall, so the measured pressure is lower than ideal, and the term $an^2/V^2$ is added to the measured P to recover the ideal value. The molecules' own volume leaves less free space to move in, so the "empty" volume is $V - nb$, and the gas takes up more room than an ideal gas would.

The compressibility factor $Z = PV/(nRT)$ measures the deviation directly: Z = 1 for an ideal gas. Z < 1 means attractions dominate (moderate pressure, low temperature), so the real PV is smaller than ideal; Z > 1 means the particles' volume dominates (very high pressure), so the real PV is larger than ideal. Ranking questions ("which gas behaves most ideally?") reward the smallest, least polar, lowest-boiling gas: helium is the usual answer, then the other small nonpolar gases (H₂, Ne, N₂), while large or polar gases (CO₂, NH₃, SO₂, H₂O vapor, CCl₃F) deviate most.

The gas laws

Each named law holds two of the four variables (P, V, T, n) constant and relates the other two. All of them are special cases of the ideal gas law, and the figure below shows how they connect.

A Cartesian diver (a small inverted vial with an air bubble, floating in a sealed bottle of water) shows Boyle's law and buoyancy together: squeezing the bottle raises the pressure, which is transmitted through the water and compresses the trapped air, so water enters the vial, its average density rises above the water's, and it sinks; release the bottle and it rises again. Everyday examples: a basketball or car tire goes soft on a cold morning (Charles or Gay-Lussac: less volume or pressure at lower T), a bubble rising from the bottom of a lake grows as the pressure on it falls (Boyle), a sealed bag of chips puffs up at altitude (Boyle), and an aerosol can must never be heated (Gay-Lussac).

When more than one variable changes, use the combined gas law, $P_1V_1/(n_1T_1) = P_2V_2/(n_2T_2)$, and cross out whatever is constant. This one equation covers every named law, so it is a good line for the note sheet. Strictly, many textbooks define the "combined gas law" for a fixed amount of gas, $P_1V_1/T_1 = P_2V_2/T_2$; the version with n is just the ideal gas law written as a ratio, since $PV/(nT) = R$ for every state. A statement such as "V is proportional to nT/P" is therefore the ideal gas law.

Proportional reasoning: what happens when one variable changes

Many questions give no numbers. Decide which variables are fixed, then use direct (∝) or inverse (∝ 1/x) proportion.

Avogadro's law has a famous corollary: equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. It also means that for gases measured at the same T and P, volume ratios equal mole ratios, which is Gay-Lussac's law of combining volumes. In N₂ + 3 H₂ → 2 NH₃, 1 L of N₂ reacts with 3 L of H₂ to give 2 L of NH₃; you never need the molar volume for a volume-to-volume question.

The ideal gas law, density and molar mass

The density form comes from substituting n = m/M into PV = nRT. It shows that gas density is proportional to molar mass and pressure and inversely proportional to temperature. That is why CO₂ collects in low places and a helium balloon floats.

Note that $8.314$ J·mol⁻¹·K⁻¹ is the same number as $8.314$ L·kPa·mol⁻¹·K⁻¹, because 1 J = 1 kPa·L. So R has a value for every unit pair: 0.08206 L·atm, 8.314 L·kPa (or J), 62.36 L·mmHg (or L·torr), and 0.08314 L·bar, all per mol per K. The units of R are energy per mole per kelvin; R is also Boltzmann's constant times Avogadro's number.

Gas density in the real world

The density of air depends on three things: temperature, pressure (and so altitude) and humidity. Dry air behaves like a gas of average molar mass 28.97 g/mol (about 78% N₂, 21% O₂, 1% Ar). At the same temperature and pressure, any gas with M > 29 g/mol is denser than air and sinks (CO₂, propane, chlorine, SF₆), and any gas with M < 29 rises (H₂, He, CH₄, NH₃). Three results follow from $d = PM/RT$:

• Hot air rises. At constant pressure, density is inversely proportional to kelvin temperature, so heating air from 280 K to 310 K lowers its density by a factor 280/310: 1.24 kg/m³ becomes 1.12 kg/m³. A hot-air balloon floats because its hot air is less dense than the cooler air it displaces, and an attic is hotter than the floors below it.
• Moist air is less dense than dry air at the same T and P. Water vapor (18.02 g/mol) replaces some N₂ and O₂ molecules (same number of molecules per liter, by Avogadro), so the average molar mass drops.
• Air thins with altitude: the pressure is lower, so at the same temperature the density is lower too.

Gas stoichiometry

A gas stoichiometry problem is an ordinary mole-ratio problem in which one end is a gas volume. Convert the gas volume to moles with PV = nRT (or with 22.4 L/mol at STP only), use the coefficients, and convert back.

When a reaction changes the number of moles of gas, the pressure in a rigid container changes in proportion. In 2 NH₃ → N₂ + 3 H₂, two moles of gas become four, so complete decomposition at constant T and V doubles the pressure. This is the basis of following a gas-phase reaction with a pressure sensor.

Dispensing gas from a tank. A rigid cylinder can only deliver gas until its pressure falls to the outside pressure; the gas still inside at 1 atm stays behind. A 20.0 L tank at 150. atm holds gas that would occupy 20.0 × 150./1.00 = 3000 L at 1.00 atm (same temperature), but only 3000 − 20.0 = 2980 L can come out. If each party balloon holds 5.00 L, that fills 596 balloons. Correct for temperature with the combined gas law if the tank and balloons are at different temperatures.

How far apart are gas molecules? The volume available to each molecule is V/N. At STP that is 22.4 L / 6.022 × 10²³ = 3.72 × 10⁻²³ L = 3.72 × 10⁻²⁶ m³, and its cube root, about 3.3 nm, is the average spacing: roughly ten times the diameter of a small molecule. That is why a gas is mostly empty space and why the particle-volume assumption works at ordinary pressures.

Dalton's law of partial pressures

In a mixture of gases that do not react, each gas behaves as if it were alone in the container. Its partial pressure is the pressure it would exert by itself, and the total pressure is the sum of the partial pressures. Because pressure is proportional to moles at fixed T and V, each partial pressure equals the gas's mole fraction times the total pressure.

The most common lab application is collecting a gas over water. The gas in the collection tube is saturated with water vapor, so the measured pressure (equal to atmospheric pressure once the water levels inside and outside the tube match) includes the vapor pressure of water. Subtract it, using the table the supervisor provides; water's vapor pressure is about 17.5 mmHg at 20 °C, 19.8 mmHg at 22 °C and 23.8 mmHg at 25 °C.

Other molar-mass labs follow the same logic. In the Dumas method, a volatile liquid is vaporized in a flask of known volume in a boiling-water bath, the excess escapes, and the flask is cooled and weighed: the mass of the condensed vapor, plus the flask's volume, the bath temperature and the barometric pressure, gives M = mRT/PV. Any procedure that gives you m, P, V and T for a gas sample is a molar-mass determination.

Vapor pressure and dissolved gases

A volatile liquid in a closed container evaporates until its vapor reaches the liquid's vapor pressure, a property that depends only on the substance and the temperature (not on the volume or on how much liquid is present). If there is not enough liquid to reach that pressure, it all evaporates and the gas law gives a lower pressure. To decide, calculate the pressure the whole sample would exert as vapor: 10.0 g of CH₂Cl₂ (0.118 mol) in 5.0 L at 20 °C would give P = nRT/V = 0.567 atm = 431 mmHg as vapor, which is more than its vapor pressure of 350 mmHg. So the pressure stops at 350 mmHg and some liquid remains. Vapor pressure rises steeply with temperature; a liquid boils when its vapor pressure equals the surrounding pressure, which is why water boils below 100 °C at altitude. Water's vapor pressure is the term you subtract when collecting a gas over water.

The amount of a gas that dissolves in a liquid follows Henry's law: solubility is proportional to the partial pressure of that gas above the liquid.

Two levers raise a gas's solubility: increase its partial pressure (a soda is bottled under CO₂ pressure and fizzes when opened because the pressure drops) and lower the temperature (gas solubility falls as temperature rises, the opposite of most solids). Warm water holds less dissolved O₂, which is why fish struggle in warm, still water, and warming oceans take up less CO₂. Divers who surface too fast suffer "the bends" because nitrogen dissolved in the blood at high pressure comes out of solution as bubbles.

Graham's law: effusion and diffusion

Effusion is gas escaping through a tiny hole into a vacuum; diffusion is one gas spreading through another. Because all gases at the same temperature have the same average kinetic energy, lighter particles move faster, and the rate of effusion is inversely proportional to the square root of molar mass. Diffusion follows the same trend approximately, although collisions with the other gas slow it down.

Ranking diffusion or effusion speed is just ranking molar mass in reverse: H₂ (2) > He (4) > CH₄ (16) > NH₃ (17) > H₂O (18) > N₂ (28) > O₂ (32) > HCl (36.5) > CO₂ (44) > SO₂ (64) > Cl₂ (71). Temperature affects all gases the same way (faster when hotter), so the ratio is independent of temperature as long as both gases are at the same one.

The classic diffusion demonstration puts cotton soaked in concentrated ammonia at one end of a glass tube and cotton soaked in hydrochloric acid at the other. A white ring of NH₄Cl forms where the gases meet, closer to the HCl end, because NH₃ (17.03 g/mol) moves faster than HCl (36.46 g/mol). Graham's law predicts the ratio of distances to be √(36.46 / 17.03) = 1.46, so in a 1.00 m tube the ring should form 1.46/2.46 = 0.59 m from the ammonia end (0.41 m from the HCl end); real results are usually a little different because the gases are diffusing through air, not effusing into a vacuum. A supervisor may give you the tube length and the ring position and ask for the ratio, or ask why the experiment does not match theory exactly.

Gas-law labs with probeware

The rules list three relationships to examine experimentally, and each has a standard sensor setup:

The extrapolation is a favorite question. If your P–T data in Celsius fall on the line P = 0.00366 T + 1.000 (atm, °C), the line reaches P = 0 at T = −1.000 / 0.00366 = −273 °C, an experimental value of absolute zero. Common error sources are a slow leak at the tubing connection (pressure drifts down), not waiting for the gas to reach the bath temperature, and the small volume of gas in the tubing that is not at bath temperature. Always record the conditions of each run and the units the sensor reports.

Lab equipment, safety and data handling

Every task is a lab, so supervisors routinely add a few points on equipment, safety and measurement. These are the easiest points on the test if you have seen the vocabulary.

Safety basics. Wear splash goggles at all times when chemicals or glassware are out, not only when the chemicals are "dangerous". Closed-toe shoes, long pants and a lab coat or apron; natural fibers such as cotton are preferred to synthetics, which can melt onto skin. Tie back long hair. Never use chipped or cracked glassware, and never pick up broken glass with bare hands: sweep it up with a brush and dustpan and put it in the labeled broken-glass container, not the trash. Point a heated test tube away from people, and never heat a sealed container (by Gay-Lussac's law its pressure rises until it bursts). Add acid to water, not water to acid. Acids and bases cause chemical burns by damaging proteins in tissue; flush any splash with running water for 15 minutes and tell the supervisor. Smell a gas only by wafting it toward you. Know the NFPA 704 diamond on reagent bottles: blue = health hazard, red = flammability, yellow = instability/reactivity, white = special hazards (such as W with a bar for "reacts with water" or OX for oxidizer), each rated 0 (minimal) to 4 (severe). Safety data sheets (SDS) give the full hazards of each chemical.

Heating safely. Light a Bunsen burner with the gas barely on and the match or striker held to the side of the barrel top; open the air collar until the flame is blue with an inner cone (a yellow, sooty flame means too little air, and the hottest part is just above the tip of the inner blue cone). Keep paper, hair and sleeves clear, use tongs or a test-tube holder for hot objects (hot glass looks exactly like cold glass), never leave a flame unattended, and turn the gas off at the valve when done. For flame tests, hold the wire loop or wooden splint with tongs and dip it in clean acid between samples.

Measurement and error. Accuracy is closeness to the true value; precision is closeness of repeated measurements to each other. Percent error = |experimental − accepted| / accepted × 100%: a voltage read as 1.54 V against a true 1.10 V is a 40.0% error. Record every measurement to one estimated digit past the smallest scale marking. In calculations, multiplication and division keep the fewest significant figures of any input, and addition and subtraction keep the fewest decimal places. Useful equivalences: 1 mL = 1 cm³, 1 L = 1000 mL = 1 dm³, 1 m³ = 1000 L, 1 kg = 1000 g.

Gases and the atmosphere

The rules include the effect of greenhouse gases and ozone depletion on the climate, so expect conceptual questions on the chemistry behind both. Keep the two problems separate: they involve different gases, different layers of the atmosphere and different kinds of radiation.

Greenhouse gases

Sunlight reaches Earth mostly as visible and near-infrared radiation, which passes through the atmosphere and warms the surface. The warm surface radiates energy back as infrared (IR) radiation. A greenhouse gas absorbs some of that IR and re-emits it in all directions, including back toward the surface, so the lower atmosphere stays warmer than it would otherwise be.

Whether a gas absorbs IR depends on its molecular vibrations. A molecule absorbs IR only if a vibration changes its dipole moment. N₂ and O₂, which make up about 99% of dry air, are symmetric diatomic molecules whose only vibration (stretching) does not create a dipole, so they are transparent to IR. CO₂ is linear and nonpolar overall, but its bending and asymmetric-stretching vibrations do change its dipole, so it absorbs strongly. Water vapor, methane and nitrous oxide absorb for the same reason.

Global warming potential (GWP) compares the warming caused by a kilogram of a gas over a time horizon (usually 100 years) with a kilogram of CO₂; the values above are from the IPCC's Sixth Assessment Report. A question that asks which gas is "most important" needs care: CO₂ has the largest total human-caused effect because there is so much of it, while methane and the fluorinated gases have the largest effect per molecule.

Water vapor is both the most abundant greenhouse gas and the one with the largest total contribution to the natural greenhouse effect, but humans do not control it directly: its concentration is set by temperature, so it amplifies warming caused by other gases (a positive feedback). Molecules with three or more atoms, or two different atoms, can absorb IR: H₂O, CO₂, CH₄, N₂O, O₃ and the halocarbons are the main greenhouse gases, and NO₂ and SO₂ also absorb IR, although they are short-lived pollutants (SO₂ forms sulfate aerosols that reflect sunlight and on balance cool). N₂, O₂ and Ar do not absorb IR. Other gas-related climate vocabulary: the Keeling curve is the record of CO₂ at Mauna Loa since 1958, rising each year with a seasonal zigzag as Northern Hemisphere plants take up CO₂ in summer; carbon capture removes CO₂ from exhaust by absorbing it in amine solutions (such as monoethanolamine), adsorbing it on solids (zeolites, activated carbon), or reacting it with metal oxides to form stable carbonates (CaO + CO₂ → CaCO₃), followed by underground storage.

Gas laws connect here too. Warmer oceans dissolve less CO₂ (gas solubility falls with temperature), and greenhouse-gas concentrations in parts per million are mole fractions, so a 420 ppm CO₂ concentration at 1.00 atm is a partial pressure of 420 × 10⁻⁶ atm, or 4.2 × 10⁻⁴ atm.

Ozone and its depletion

About 90% of Earth's ozone (O₃) sits in the stratosphere, roughly 15–35 km up, where it absorbs ultraviolet radiation (UV-B and UV-C) that would otherwise damage DNA and living tissue. Stratospheric ozone is constantly made and destroyed by sunlight in the Chapman cycle:

1. O₂ + UV → 2 O (high-energy UV splits oxygen molecules)
2. O + O₂ + M → O₃ + M (M is any third molecule that carries away excess energy)
3. O₃ + UV → O₂ + O (ozone absorbs UV and splits; this is the shielding step)
4. O + O₃ → 2 O₂ (slow removal step)

Chlorofluorocarbons (CFCs) such as CFCl₃ are unreactive in the lower atmosphere, so they survive long enough to drift into the stratosphere. There, UV breaks a C–Cl bond and releases a chlorine atom, which destroys ozone in a catalytic cycle:

• Cl + O₃ → ClO + O₂
• ClO + O → Cl + O₂
• Net: O₃ + O → 2 O₂

The chlorine atom comes out unchanged, so it is a catalyst, and a single atom can destroy many thousands of ozone molecules before it is locked up in a stable compound. This is a favorite crossover question because it ties the gas topic to kinetics: the catalyst provides a lower-activation-energy path for the same net reaction as Chapman step 4. Bromine (from halons and methyl bromide) does the same thing even more efficiently per atom.

Nitrogen oxides run the same kind of cycle. Nitric oxide from N₂O breakdown (or, historically worried about, supersonic aircraft exhaust) destroys ozone catalytically: NO + O₃ → NO₂ + O₂, then NO₂ + O → NO + O₂, net O₃ + O → 2 O₂. Counting the photolysis step that supplies the O atom (O₃ + UV → O₂ + O), the overall change is 2 O₃ → 3 O₂. In every one of these cycles, NO or Cl is the catalyst (consumed, then regenerated) and NO₂ or ClO is the intermediate. Reading such a mechanism is a classic mixed gases-kinetics question: in the Chapman cycle, the step written O₃ + UV → O₂ + O is photolysis (a bond broken by light), and the step needing a third body M is termolecular.

The Antarctic ozone hole forms each southern spring because polar stratospheric clouds, which form only in the extreme cold of the polar winter, provide surfaces where stable chlorine compounds are converted into forms that sunlight then splits into reactive chlorine. The Montreal Protocol (1987) phased out CFCs, and the ozone layer is slowly recovering.

Kinetics: rates and what changes them

Kinetics asks how fast a reaction proceeds and why. Two different questions hide inside that sentence. The first is quantitative: how much does a concentration change per second, and how does that rate depend on concentrations and temperature? The second is mechanistic: why does heat or a catalyst make a difference? At Regional the event is mostly the second question plus rate measurement; at State and National it is both.

Why reactions speed up: collisions and energy

Collision theory says a reaction occurs when particles collide with enough energy and with the right orientation. Two numbers control the rate. The collision frequency rises with concentration (more particles per liter), with pressure for gases (more particles per volume), and with temperature (faster particles collide more often). The fraction of collisions with enough energy depends on the activation energy, Eₐ, the minimum energy the reactants need to reach the transition state (activated complex). That fraction rises very steeply with temperature.

A catalyst does not change the energy of the reactants or products. It provides a different pathway with a lower activation energy, so more collisions carry enough energy to react, and it is regenerated at the end. Because it lowers the barrier for both directions, it speeds up the forward and reverse reactions equally and does not change ΔH. Enzymes are biological catalysts; the chlorine atom in ozone depletion is an atmospheric one.

On an energy diagram, the activation energy for the forward reaction is the height from the reactants to the peak, and for the reverse reaction it is the height from the products to the peak. For an endothermic reaction the products sit above the reactants, so the forward activation energy is larger than ΔH; for an exothermic reaction the reverse barrier is the larger one.

An exothermic reaction releases energy (heat) to the surroundings, so the products are lower in energy and ΔH is negative; an endothermic reaction absorbs heat from the surroundings (a beaker gets cold), the products sit higher and ΔH is positive. The three quantities on the diagram are tied together:

Keep three terms apart. The transition state (activated complex) is the arrangement at the very top of an energy peak: bonds half-broken and half-formed, lasting about one molecular vibration, never isolable. An intermediate sits in a valley between two peaks: it is a real species with a finite lifetime, and some can be detected or even isolated. A reaction with several elementary steps has a diagram with several hills and valleys, one peak per step; the step whose transition state is the highest peak (measured up from the reactants) is usually the slow, rate-determining step. Kinetic isotope effect. Replacing an atom with a heavier isotope (H with deuterium D) leaves the chemistry the same but slows any step that breaks a bond to that atom: the heavier atom vibrates with lower zero-point energy, so its bond sits lower in the energy well and needs more energy to reach the transition state. A C–H bond broken in the rate-determining step typically reacts several times (often 2 to 7 times at room temperature) faster than the matching C–D bond, so a large isotope effect is evidence that the bond breaks in the slow step.

When one reactant can go to two different products, the one formed faster (lower Eₐ) is the kinetic product, and the more stable one (lower energy, releases more heat) is the thermodynamic product. At low temperature and short times the kinetic product dominates because few molecules can cross the higher barrier; at high temperature, with enough time for the reactions to reverse, the mixture drifts toward the thermodynamic product. Diamond turning into graphite is the extreme case of a favorable change with a barrier so high that it never happens at room temperature. A large Eₐ explains why a thermodynamically favorable reaction can be extremely slow: methane and oxygen, or N₂ and H₂ making ammonia, do not react at room temperature until a spark, heat or a catalyst gets them over the barrier.

Collision theory has two requirements, and you should be able to say which one a change affects. Energy: the collision must carry at least Eₐ. Orientation: the reacting atoms must meet the right way round (a steric requirement), which is why only a fraction of even energetic collisions react. Raising the temperature increases collision frequency and especially the energy of collisions, but it does not improve their orientation. Concentration and surface area increase how often collisions happen. A catalyst lowers the energy needed. Orientation matters least for a decomposition, where a single energized molecule falls apart without needing a partner.

The four factors

The rules name four factors: temperature, concentration, particle size and catalysts. Tests often add a fifth, the nature and physical state of the reactants, so it is the last row here.

Everyday versions of the same ideas: food keeps longer in a refrigerator and batteries self-discharge more slowly in the cold (lower temperature, slower reactions), while heat shortens a battery's life; a glow stick glows brighter in hot water; fine flour or coal dust can explode while a lump burns slowly; amylase in saliva starts digesting starch (catalyst). Industrial processes such as the Haber process run hot (about 450 °C) and with an iron catalyst chiefly to get a useful rate, even though the high temperature lowers the equilibrium yield of ammonia.

Pressure works through concentration. For a gas at constant temperature, concentration is n/V = P/(RT), so doubling the pressure by halving the volume doubles every concentration. Adding an inert gas at constant volume raises the total pressure but leaves each reactant's partial pressure, and so its concentration, unchanged, so the rate does not change. This is one of the most common distractor patterns in archived tests, and it is a direct application of Dalton's law.

Catalysts in depth

A catalyst speeds up a reaction by providing an alternative mechanism (pathway) with a lower activation energy: the two phrases describe one idea, the new pathway being the how and the lower Eₐ the why, so if a question offers "lowers the activation energy" and "provides an alternate pathway" as separate options and asks for the best single reason for the faster rate, the lower activation energy is the more direct answer. A catalyst is also regenerated, so its amount at the end equals its amount at the start. In a mechanism it is consumed in an early step and re-formed in a later one (an intermediate is the reverse: formed first, then consumed). It increases the rate constant k at a given temperature. It does not raise the temperature or the energy of the molecules, does not change the energies of reactants or products, ΔH or the spontaneity (ΔG) of a reaction, does not change the overall reaction, and does not change the equilibrium constant. Because it lowers the barrier by the same amount in both directions, a catalyst added to a reversible reaction speeds the forward and reverse rates equally: equilibrium is reached sooner, but the equilibrium amounts (yield) are the same.

A heterogeneous catalyst works in steps: reactant molecules adsorb onto the surface, bonds within them are weakened or broken at active sites, the new bonds form, and the products desorb, freeing the site. So a finely divided catalyst (powder, gauze, wool, a honeycomb coating) works better than a lump, because it has more surface. Because the surface has a fixed number of sites, a gas reacting on a fully covered catalyst surface often shows zero-order kinetics: the decomposition of N₂O or NH₃ on hot platinum or tungsten runs at a constant rate until the gas is nearly gone, because adding more gas cannot add more occupied sites. Transition metals make good catalysts because they have several accessible oxidation states (Cu⁰/Cu⁺/Cu²⁺, Fe²⁺/Fe³⁺) and can easily give or take electrons, and because their surfaces bind molecules moderately: strongly enough to weaken bonds, weakly enough to let products go. A catalyst poison binds the active sites permanently (lead and sulfur poison catalytic converters, which is why cars need unleaded fuel). An inhibitor is the opposite of a catalyst in effect: it slows a reaction, for example by tying up a catalyst or a reactive intermediate.

The classic lab demonstration is the decomposition of hydrogen peroxide, 2 H₂O₂ → 2 H₂O + O₂, which is slow on its own and fast with KI, MnO₂, yeast or potato (catalase). The oxygen produced is detected by a glowing splint that relights, and the rate is followed by gas volume or pressure. With iodide, the mechanism is H₂O₂ + I⁻ → H₂O + OI⁻ followed by H₂O₂ + OI⁻ → H₂O + O₂ + I⁻: the iodide is regenerated, OI⁻ is the intermediate, and the steps add to the overall equation.

Enzyme kinetics

Enzymes are protein catalysts. They lower Eₐ in several ways at once: binding holds the reacting molecules close together and in the right orientation (proximity and orientation effects), the active site binds and stabilizes the transition state more tightly than the substrate, and side chains in the active site can donate or accept protons or strain the substrate's bonds. The substrate binds at the active site, whose shape and chemistry fit it closely: the lock-and-key model pictures a rigid fit, while the more accurate induced-fit model has the active site reshape itself around the substrate as it binds. Enzymes typically lower Eₐ enough to speed reactions by factors of millions or more. They work best at an optimum temperature (around 37 °C for human enzymes) and an optimum pH: below the optimum temperature the rate rises as with any reaction, but above it the protein denatures (unfolds, losing the active-site shape) and the rate falls sharply. Strong acid or base denatures enzymes the same way.

The Michaelis-Menten model treats the enzyme (E) and substrate (S) as forming a complex that then makes product (P):

$$E + S \underset{k_{-1}}{\overset{k_1}{\rightleftharpoons}} ES \xrightarrow{k_2 \,(=k_\text{cat})} E + P$$

The model measures initial rates, when almost no product exists yet, so the reverse reaction E + P → ES can be ignored. Assuming also that the substrate is in large excess over the enzyme and that [ES] is constant (the steady-state approximation, using $[E] = [E]_\text{total} - [ES]$), the initial rate is:

The equation has two limits worth knowing. When $[S] \ll K_M$, $v \approx (V_\text{max}/K_M)[S]$: first order in substrate. When $[S] \gg K_M$, $v \approx V_\text{max}$: zero order in substrate, because every enzyme molecule is busy (saturated) and adding more substrate cannot speed things up. $V_\text{max}$ is proportional to the amount of enzyme, but $K_M$ is not: it is a property of the enzyme-substrate pair. Taking reciprocals gives the straight-line Lineweaver-Burk (double-reciprocal) plot:

$$\frac{1}{v} = \frac{K_M}{V_\text{max}}\cdot\frac{1}{[S]} + \frac{1}{V_\text{max}}$$

slope $K_M/V_\text{max}$, y-intercept $1/V_\text{max}$, x-intercept $-1/K_M$.

On a Lineweaver-Burk plot, competitive inhibition gives lines that cross on the y-axis, noncompetitive gives lines that cross on the x-axis, and uncompetitive gives parallel lines. Clavulanic acid, which blocks the bacterial enzyme β-lactamase (penicillinase), is a classic example of an inhibitor given with penicillin-type antibiotics. Allosteric enzymes with several cooperating binding sites do not follow Michaelis-Menten kinetics: their rate-versus-[S] curve is sigmoidal (S-shaped) instead of hyperbolic.

Measuring a reaction rate

You follow some property that changes with the amount of reactant or product, and convert it to concentration.

A gas-pressure run converts directly with the ideal gas law: at constant V and T, moles of gas produced = ΔP × V / (RT), so the slope of pressure vs time is proportional to the rate of gas formation.

A concentration-vs-time graph gives several kinds of rate. The average rate is the slope between two points. The instantaneous rate is the slope of the tangent at one time. The initial rate is the instantaneous rate at t = 0, which the initial-rates method uses because products have not yet built up. A curve that flattens with time means the rate falls as reactant is used. In a clock reaction the time is inversely proportional to the rate, so halving the time doubles the rate, and 1/t can be used as a relative rate.

Error analysis for rate labs. Work out the direction of each error from rate = Δamount / Δtime. Stopping the timer too early makes Δt too small, so the calculated rate is too high; starting it late does the same. Gas escaping before it is collected makes the measured amount too small, so the rate is too low. Solutions that are not at the bath temperature give rates for the wrong temperature (too low if the solution is cooler). Rinsing glassware with distilled water and not with the solution dilutes the reagent, lowering its concentration and so the rate. In a clock reaction, a reading taken by eye at the color change has a reaction-time error of a few tenths of a second, which matters most for the fastest runs, so design concentrations to give times of at least 20 to 30 seconds.

Rate and stoichiometry

For a balanced reaction, the rate depends on which species you measure, so divide by each coefficient to get one consistent rate.

For 2 H₂O₂ → 2 H₂O + O₂, H₂O₂ disappears twice as fast as O₂ appears. If a pressure sensor shows O₂ forming at 0.0040 M s⁻¹, H₂O₂ is being consumed at 0.0080 M s⁻¹, and the reaction rate is 0.0040 M s⁻¹.

Rates are usually expressed in M s⁻¹ (mol L⁻¹ s⁻¹), but a gas-phase rate can be reported in atm s⁻¹ or torr s⁻¹ and a mass-loss rate in g s⁻¹; convert with the gas law or molar mass when the question asks for molarity.

Kinetics: rate laws, mechanisms and activation energy

Everything in this section is guaranteed at State and National and is common at strong invitationals.

Differential rate laws and the method of initial rates

The differential rate law (usually just "rate law") gives the rate as a function of concentrations.

The method of initial rates finds the orders. Compare two runs in which only one concentration changes. If the concentration is multiplied by a factor x and the rate by a factor y, the order is log y / log x. Doubling with no effect means order 0, doubling the rate means order 1, quadrupling means order 2.

The units of k are a free check. If your orders add to 2 but your k comes out in s⁻¹, one of the orders is wrong.

Reading the table backwards answers a common question: a rate constant of 0.50 L mol⁻¹ s⁻¹ means a second-order reaction.

The rate constant depends only on the reaction and the temperature (and on whether a catalyst is present). It does not change with concentration or with time; the rate does. Two runs of the same reaction at the same temperature always have the same k even if their rates differ.

When a probe measures a property proportional to concentration, such as absorbance of a colored reactant (Beer's law: A = εbc), the integrated-rate-law plots (next section) work on that property directly. For crystal violet (purple) fading in excess NaOH, a straight line for ln(absorbance) against time means the reaction is first order in crystal violet; it says nothing about the order in OH⁻, which is in excess and essentially constant.

When one reactant is present in large excess, its concentration hardly changes during a run, so the reaction looks lower in order. This is a pseudo-order rate law: for crystal violet fading in a large excess of NaOH, rate = k[CV][OH⁻] behaves as rate = k′[CV] with k′ = k[OH⁻]. Running the experiment at two different OH⁻ concentrations and comparing the two k′ values gives the order in OH⁻.

Integrated rate laws and half-life

The integrated rate law gives concentration as a function of time. Each order has a straight-line form, which is how you determine the order from a single concentration-time data set: plot [A], ln[A] and 1/[A] against time and see which is linear.

The first-order half-life does not depend on concentration. The second-order half-life gets longer as the reaction proceeds (it depends on 1/[A]₀), and the zero-order half-life gets shorter.

First-order math is also the math of radioactive decay, so the same reasoning solves isotope half-life questions, which appear on kinetics tests as first-order practice. Because decay is first order, the half-life of a radioisotope does not depend on how much is present, and the activity (decays per second) is proportional to the number of nuclei: activity = kN. So a ratio of activities or counts can replace a ratio of amounts.

Parallel (competing) first-order reactions. If A can decay by two first-order routes at once, A → B (k₁) and A → C (k₂), A disappears with the sum of the rate constants, $k_\text{total} = k_1 + k_2$, so its half-life is 0.693/(k₁ + k₂), and the products form in the ratio [B]/[C] = k₁/k₂ throughout the reaction. With k₁ = 0.030 s⁻¹ and k₂ = 0.010 s⁻¹, t½ = 0.693/0.040 = 17.3 s and 75% of the product is B.

Mechanisms and the rate-determining step

Most reactions happen in several elementary steps. For an elementary step only, the rate law follows from the coefficients: a bimolecular step A + B → products has rate k[A][B]. An intermediate is made in one step and used up in a later one; a catalyst is used in one step and regenerated in a later one. The slowest step, the rate-determining step, controls the overall rate.

A proposed mechanism is acceptable only if (1) its steps add up to the overall equation and (2) the rate law it predicts matches the experimental one. Experiments can rule a mechanism out but can never prove it.

When the slow step involves an intermediate, rewrite it in terms of reactants. If a fast equilibrium comes first, use its equilibrium expression: for 2 NO ⇌ N₂O₂ (fast) followed by N₂O₂ + O₂ → 2 NO₂ (slow), [N₂O₂] = K[NO]², so rate = k₂K[NO]²[O₂], third order overall. If the intermediate forms and reacts at comparable rates, the steady-state approximation sets its rate of formation equal to its rate of consumption; one of the quiz questions below uses it.

Molecularity (how many particles collide in one elementary step) is a whole number of 1, 2 or 3 and applies only to elementary steps; order is experimental and applies to the overall rate law. If you are told a reaction is a single elementary step, its order and molecularity match, so a rate constant in s⁻¹ means a unimolecular step. Clues an experimental rate law gives about a mechanism: a reactant that does not appear in the rate law (zero order) reacts only after the slow step; a species with a negative order (such as [O₂] in the denominator) is usually a product of a fast pre-equilibrium that comes before the slow step.

To get the overall equation from a mechanism, add the steps and cancel anything that appears on both sides (intermediates, and catalysts that are used and regenerated). Adding 2 NO ⇌ N₂O₂, N₂O₂ + H₂ → N₂O + H₂O and N₂O + H₂ → N₂ + H₂O gives 2 NO + 2 H₂ → N₂ + 2 H₂O, with N₂O₂ and N₂O as intermediates. If the middle step is the slow one, the predicted rate law is k[NO]²[H₂]. Coefficients in front of a step multiply it before adding: if step 1 must happen twice for each time step 2 happens, double it.

Activation energy and the Arrhenius equation

Temperature changes the rate constant, not the form of the rate law. The Arrhenius equation gives the dependence, and determining Eₐ is now named explicitly in the State and National scope.

The middle form is a straight line: plot ln k against 1/T and the slope is −Eₐ/R. That is the standard way to get Eₐ from a lab, because it uses every temperature you measured rather than just two. In a hands-on task, you might time an iodine clock or a thiosulfate reaction at four or five water-bath temperatures; since the rate (and so k) is proportional to 1/time when the concentrations are the same, ln(1/t) vs 1/T gives the same slope as ln k vs 1/T.

The figure below shows why the temperature effect is so large. Raising the temperature moves the distribution of molecular energies to the right, so the share of molecules above Eₐ grows much faster than the average energy does. A catalyst works the other way on the same graph: the curve stays put, but the Eₐ line moves left, so more of the existing molecules are above it.

A larger Eₐ means a steeper Arrhenius line and a reaction that is more sensitive to temperature. In a reversible reaction, both rate constants increase with temperature; the direction with the larger activation energy speeds up more.

Strategy

• Split by topic. Points are divided evenly between gases and kinetics, so give each partner primary responsibility for one, and have the other check the first one's units and arithmetic. In a hands-on task, one partner runs the procedure while the other records data and starts the calculations.
• Build two note sheets that complement each other. Each partner gets one sheet, so do not duplicate. A good split: one sheet for gases (R in three units, pressure conversions, the gas-law table, Dalton and water-vapor correction, Graham's law, u_rms, greenhouse-gas and ozone chemistry), the other for kinetics and tools (the ion tables including the oxyanion rule, the stoichiometric rate form, initial-rates method, integrated-rate-law table, mechanism rules, Arrhenius forms). Put one worked number next to each formula.
• Convert temperatures first. Write every temperature in kelvin before you touch a gas law or the Arrhenius equation.
• Show units on every number. Write M s⁻¹, M⁻¹ s⁻¹ or s⁻¹ next to every rate constant and check that k's units match the overall order.
• Explain in one or two sentences. A strong explanation names a particle-level cause and its effect: "At higher temperature the molecules move faster and hit the walls more often and harder, so the pressure rises at constant volume." That is worth more than a long paragraph.
• Treat the lab like a test of procedure. Read the instructions fully before starting, record raw data in a table with units, and note anything that could cause error (leaks, temperature not equilibrated, water vapor). Many points in hands-on tasks come from the error-analysis and "how would this change" questions.
• Budget time across both halves. Do one pass through every task, take the quick points first and come back to multi-step calculations. Save time for cleanup.

Common pitfalls

How tournaments test this

The Scio.ly archive holds 916 Chemistry Lab questions: 887 from the 2025-26 season and 29 from 2016-17. Because the 2025-26 event paired kinetics with chemical reactions and stoichiometry, the kinetics questions in the archive are directly useful for 2027, while the gas-law material is thinner than this season's tests will be. Of the archive questions, 429 (about 47%) have answers read from official keys and are trusted for quizzing.

What the full question bank says about 2027. The Scio.ly practice bank holds about 23,700 Chemistry Lab questions from many past rotations. Classifying them against the 2027 outline leaves roughly 3,400 that fit gases, kinetics and the tool skills. Within that set, the simple gas laws (Boyle, Charles, Gay-Lussac, Avogadro) are the single biggest block at about 15%, followed by the ideal gas law (8%), stoichiometry and balancing (8%), rate laws from initial rates (7%), integrated rate laws and half-life (6%), catalysts and enzymes (6%), the factors affecting rate (5%), gas stoichiometry (5%), mechanisms (5%), pressure and its units (5%), gas density and molar mass (5%), kinetic-molecular theory (4%), Dalton's law (4%), activation energy (3%) and real gases (3%). Greenhouse gases and ozone are almost absent from older tests because they are new to the outline, so expect this season's writers to add them; the section above covers what they are likely to ask.

Format. In the archive, 55% of questions are multiple choice (506) and 41% are free response (376); numeric, multi-select and true/false items make up the rest. The wider practice bank leans toward free response (about 59%). Expect to write a rate law, a derivation of k with units, or a short explanation even when much of the test is multiple choice.

Tasks. The most common archive task is to calculate something (16% of questions), followed by "which of the following" (9.9%), interpreting data from a graph, table or curve (7.9%), and explaining why (7.4%). Data interpretation is the heart of the hands-on stations: an initial-rates table, a pressure-vs-time trace, or a set of P–V readings to plot.

Topics. Many archive questions carry no subtopic tag (434 of 916). Among tagged questions, stoichiometry leads (177), then thermodynamics (126), equilibrium (89) and gas laws (55). Kinetics questions are often tagged under these other headings, so the counts understate kinetics. Equilibrium, thermodynamics and acid-base questions in the archive are outside the 2027 outline unless they are asked through a gas or rate lens.

Recurring language. Event-specific phrases include rate constant (363 questions across the archive and bank), rate law (321) and ideal gas law (82). When a prompt says "rate law" or "rate constant," expect an initial-rates table or a units check; when it names a gas and a temperature, convert to kelvin before anything else.

Most common correct answers. The most frequent keyed answers are directional: "decrease" (34 questions), "INCREASES" (33), "Decreases" (31) and "increase" (31), with "temperature" (27) close behind. The event loves asking what happens to a rate or a gas property when one variable changes.

Top tournaments. The tournaments with the most archive questions are the Captains Summer Exchange (92), Seven Lakes Invitational (64), University of Michigan Invitational (42), Princeton Invitational (37) and Columbia Invitational (32). Their kinetics sections are good models for 2027; for gases, supplement with the gas-law chapters in the references below.

There is no miss-rate data for this event yet, because the site has too few attempts to measure which questions students get wrong.

Test yourself

Real questions from public tournament tests in the Scio.ly archive. Click an answer to check it. Each question links to its full test. Work the problem yourself before reading the one-line explanation.

Test yourselfRate laws, integrated rate laws and half-life

0 / 0 correct

1. 1

   A reaction has a rate constant of k = 0.25 M⁻¹ s⁻¹. If the initial concentration of the reactant, A, is 2.0 M, what will be the concentration of A after 4 seconds?

   Question 1 options

   A1.0 MB0.67 MC0.33 MD0.25 M

   From: Seven Lakes Invitational, 2025-26, Division C

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Test yourselfRates, factors, catalysts and activation energy

0 / 0 correct

1. 1

   A change in concentration over time is the

   Question 1 options

   Areaction rateBtransition stateCactivated complexDintermediate product

   From: Crystal Lake Central Invitational - IL, 2025-26, Division C

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Test yourselfGases, gas-phase rates and mechanisms

0 / 0 correct

1. 1

   An equimolar mixture of C₂H₆ and C₅H₁₂ diffuses through a pinhole. What is ratio of C₂H₆/C₅H₁₂ that escapes?

   Question 1 options

   A0.645/1B1.290/1C1.55/1D2.4/1

   From: Cornell Invitational, 2016-17, Division C

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Test yourselfGas laws, pressure and the atmosphere

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1. 1

   0.100L of N2(g) takes 220s to completely diffuse through a pinhole. Under the same temperature and pressure, 0.100 L of an unknown gas takes 300s to completely diffuse through the same pinhole. What is the molar mass of the unknown gas?

   Question 1 options

   A0.733 g/molB1.36 g/molC26.0 g/molD52.1 g/mol

   From: Cornell Invitational 2017, Division C

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Notesheet

References and further reading

• Science Olympiad, Division C Chemistry Lab event page, the 2027 rules manual, the Chemistry Events Lab Equipment List and the General Rules: https://www.soinc.org
• OpenStax, Chemistry 2e, chapters on gases, kinetics and stoichiometry (free online textbook): https://openstax.org/details/books/chemistry-2e
• LibreTexts Chemistry, gas laws, integrated rate law and Arrhenius pages, for worked examples: https://chem.libretexts.org
• NOAA Global Monitoring Laboratory, trends in atmospheric carbon dioxide and other greenhouse gases: https://gml.noaa.gov/ccgg/trends/
• U.S. EPA, "Basic Ozone Layer Science" and "Overview of Greenhouse Gases": https://www.epa.gov/ozone-layer-protection and https://www.epa.gov/ghgemissions/overview-greenhouse-gases
• IPCC Sixth Assessment Report, Working Group I, for global warming potential values: https://www.ipcc.ch/report/ar6/wg1/
• NIST Chemistry WebBook, for molar masses and vapor-pressure data: https://webbook.nist.gov/chemistry/
• SciOly Wiki, Chemistry Lab (another summary of the event; read it for context, not as a source of rules): https://scioly.org/wiki/index.php/Chemistry_Lab
• Figure sources: Wikimedia Commons files cited in the figures above, each with its author and license.
• Practice more: the Scio.ly test archive has hundreds of public Chemistry Lab tests, including the 2025-26 Division C tests whose kinetics sections match the 2027 outline.