General Chemistry — Chemical Kinetics and Rate Laws

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Theory — Chemical Kinetics and Rate Laws

The rate of a reaction is how quickly a reactant is consumed or a product forms. It usually depends on concentration through a rate law.

1. Rate laws and reaction order

For a reactant A, the rate law is rate = k[A]ⁿ, where k is the rate constant and n is the order. The order is found from experiment, not from the balanced equation.

2. Integrated rate laws

Integrating the rate law gives concentration as a function of time, and each order has its own straight-line form:

Integrated rate laws Zero order: [A] = [A]₀ − k t (plot [A] vs t)
First order: ln[A] = ln[A]₀ − k t (plot ln[A] vs t)
Second order: 1/[A] = 1/[A]₀ + k t (plot 1/[A] vs t)
Whichever plot is a straight line reveals the order; its slope gives k.

3. Half-life

The half-life is the time for the concentration to fall by half. For a first-order reaction it does not depend on concentration:

First-order half-life t_1/2 = 0.693 / k
Zero order: t_1/2 = [A]₀ / 2k · Second order: t_1/2 = 1 / (k[A]₀)

4. Temperature and activation energy

Reactions speed up when heated because more collisions have enough energy to react. The rate constant follows the Arrhenius equation, and comparing k at two temperatures gives the activation energy:

Arrhenius (two-temperature form) ln(k₂ / k₁) = −(E_a / R)(1/T₂ − 1/T₁)
R = 8.314 J/(mol K), T in kelvin
A catalyst speeds a reaction by lowering E_a, opening a new pathway.

A reaction usually proceeds through several elementary steps called the mechanism; the slowest step, the rate-determining step, controls the overall rate.

Apparatus

Kinetics measurements use tools to follow concentration over time and to control temperature. In the simulation these are modelled, but the readings match what each instrument would give.

Stopwatch

Times the reaction so concentration can be recorded at known intervals.

Spectrophotometer

Follows a coloured reactant or product by how much light it absorbs, giving concentration.

Thermostatic bath

Holds the reaction at a set temperature so rate can be studied against temperature.

Reaction flask

The vessel where reactants are mixed and the reaction is followed.

Rate plot

A graph of concentration against time whose linear form reveals the reaction order.

Catalyst

A substance that speeds the reaction by lowering the activation energy without being consumed.

Instructions

Work through both tabs. Calculate first by hand, then press the button to compare.

Part A — Order, rate constant, and half-life

Choose a reaction and read the concentration-versus-time data.
For a first-order reaction, compute k = ln([A]₀/[A]) / t from two points, then the half-life t_1/2 = 0.693 / k.
Enter your rate constant and press Check; it compares within 4 percent.

Part B — Activation energy

Read the rate constant at two temperatures.
Compute E_a from ln(k₂/k₁) = −(E_a/R)(1/T₂ − 1/T₁).
Enter your activation energy in kJ/mol and press Check.

Simulation

First-order reaction

[A]₀ (M)

Time t (s)

Your k (1/s)

T1 (K)

k1 (1/s)

T2 (K)

k2 (1/s)

Your Ea (kJ/mol)

Team Questions

1. For a first-order reaction, the half-life:

Doubles as concentration doubles Is constant, equal to 0.693/k Depends on the initial concentration Is always 1 second

2. The reaction order is determined from:

The balanced equation coefficients The molar mass Experiment (which plot is linear) The temperature only

3. A catalyst increases the rate by:

Lowering the activation energy Raising the activation energy Being consumed in the reaction Changing the products

Example Report

Worked example: a first-order rate constant and half-life

A first-order reaction starts at [A]₀ = 1.00 M; after t = 30 s, [A] = 0.55 M.

k = ln([A]₀/[A]) / t = ln(1.00/0.55) / 30 = 0.598 / 30 ≈ 0.0199 s^-1.

Half-life: t_1/2 = 0.693 / k = 0.693 / 0.0199 ≈ 34.8 s. Determining the order, extracting k from the data, and finding the half-life is the calculate-then-compare core of the lab.

Chemical Kinetics and Rate Laws