AP Chemistry Unit 5 Kinetics: Building and Using Rate Laws

Reaction rate

A measure of how fast reactants are consumed or products are formed, typically tracked as a change in concentration over time.

Rate of disappearance

For a reactant A, the rate defined as −Δ[A]/Δt (or −d[A]/dt) so the reported rate is positive even though [A] decreases.

Rate of appearance

For a product P, the rate defined as Δ[P]/Δt (or d[P]/dt), which is positive as [P] increases.

Average rate

Rate calculated over a finite time interval using two data points, e.g., −([A]2−[A]1)/(t2−t1) for a reactant.

Instantaneous rate

The rate at a specific moment in time; mathematically the derivative (e.g., −d[A]/dt) and graphically the slope of the tangent line.

Initial rate

The instantaneous rate at the start of the reaction (near t = 0), often used because initial concentrations are known and reverse/side effects are minimal.

Rate units

Units of concentration per time, commonly M/s or M/min; time units must be kept consistent throughout a problem.

Stoichiometric rate relationship

For aA + bB → cC + dD, a single reaction rate can be written as −(1/a)d[A]/dt = −(1/b)d[B]/dt = (1/c)d[C]/dt = (1/d)d[D]/dt.

Rate law

An experimentally determined equation relating rate to reactant concentrations, e.g., rate = k[A]^m[B]^n.

Rate constant (k)

The proportionality constant in a rate law; depends on temperature and the specific reaction, and its units depend on overall reaction order.

Reaction order (with respect to a reactant)

The exponent on that reactant’s concentration in the rate law (e.g., m is the order in A).

Overall reaction order

The sum of all exponents in the rate law (m + n + …); used to predict how rate responds to concentration changes and to determine units of k.

Zero-order reaction

A reaction whose rate is independent of reactant concentration: rate = k.

Zero-order integrated rate law

Concentration changes linearly with time: [A]t = [A]0 − kt; a plot of [A] vs t is linear with slope −k.

First-order reaction

A reaction with rate proportional to concentration: rate = k[A]; concentration decreases exponentially with time.

First-order integrated rate law

ln[A]t = ln[A]0 − kt (equivalently ln([A]t/[A]0) = −kt); a plot of ln[A] vs t is linear with slope −k.

First-order half-life

For a first-order process, t1/2 = 0.693/k; the half-life is constant (independent of [A]0).

Second-order reaction (single reactant)

A reaction with rate = k[A]^2; doubling [A] increases rate by a factor of 4.

Second-order integrated rate law (single reactant)

1/[A]t = 1/[A]0 + kt; a plot of 1/[A] vs t is linear with slope +k.

Units of k (order-dependent)

Determined from k = rate/([A]^m[B]^n): zero order k in M/time; first order k in 1/time; second order k in 1/(M·time) (e.g., M⁻¹ s⁻¹).

Method of initial rates

Procedure to determine reaction orders by comparing initial rates from trials where only one reactant concentration changes and using rate ratios to solve exponents.

Linear plot test for reaction order

Order can be identified by which plot is linear: [A] vs t (zero), ln[A] vs t (first), or 1/[A] vs t (second).

Slope sign conventions in integrated plots

For [A] vs t and ln[A] vs t plots, slope = −k; for 1/[A] vs t, slope = +k.

Concentration–time curve

A graph of concentration vs time; often curved because rate changes as reactants are consumed (instantaneous rate comes from the tangent slope).

Indirect rate measurement

Experimental approach where a measurable signal correlated with concentration (e.g., gas pressure/volume, absorbance in spectrophotometry, mass loss, or pH) is tracked over time to infer concentration changes and rates.