Chemical Kinetics- Practice with Solutions

What Is Chemical Kinetics?

Chemical kinetics is the study of reaction rates—how fast chemical reactions happen and what affects that speed. That's it. Nothing fancy. You measure rates, you find patterns, you predict behavior.

Most students struggle because they try to memorize everything instead of understanding the relationships. Don't do that. Focus on rate laws, order of reaction, and the Arrhenius equation. Master those three and you've got 80% of the exam covered.

Core Concepts You Need to Know

Rate of Reaction

The rate is the change in concentration over time. For a reaction A → Products:

Rate = −(1/a)(Δ[A]/Δt) = (1/b)(Δ[B]/Δt)

The negative sign appears because concentration of reactants decreases. Don't forget it when writing rate expressions.

Rate Law and Reaction Order

The rate law tells you how rate depends on concentration:

Rate = k[A]^m[B]ⁿ

Where:

• k = rate constant
• m = order with respect to A
• n = order with respect to B
• m + n = overall reaction order

Critical point: You cannot determine reaction order from the balanced equation. You get it from experimental data only. Every student forgets this. Don't be that person.

Zero, First, and Second Order Reactions

Each order has distinct characteristics:

• Zero order: Rate is constant, independent of concentration. Half-life depends on initial concentration.
• First order: Rate depends linearly on concentration. Half-life is constant and independent of initial concentration.
• Second order: Rate depends on concentration squared. Half-life increases as concentration decreases.

Key Formulas Reference

The Arrhenius Equation

This equation connects temperature and reaction rate:

k = Ae^−Ea/RT

Or in logarithmic form:

ln(k₂/k₁) = (−Ea/R)(1/T₂ − 1/T₁)

Where:

• A = frequency factor
• Ea = activation energy
• R = 8.314 J/mol·K
• T = temperature in Kelvin

Higher temperature or lower activation energy means faster reaction. Simple.

Practice Problems with Solutions

Problem 1: Determining Rate Law from Data

Given: For the reaction 2NO + Cl₂ → 2NOCl, the following experimental data was collected:

Find: The rate law expression

Solution:

Compare experiments 1 and 2 (Cl₂ constant, [NO] doubles):

Rate ratio = 0.072/0.018 = 4

Concentration ratio = 0.20/0.10 = 2

4 = 2^m → m = 2 (order with respect to NO is 2)

Compare experiments 1 and 3 ([NO] constant, [Cl₂] doubles):

Rate ratio = 0.036/0.018 = 2

Concentration ratio = 0.20/0.10 = 2

2 = 2ⁿ → n = 1 (order with respect to Cl₂ is 1)

Answer: Rate = k[NO]²[Cl₂] — overall order is 3

Problem 2: First Order Kinetics Calculation

Given: The decomposition of N₂O₅ is first order with k = 4.8 × 10⁻⁴ s⁻¹. Initial concentration is 0.80 M.

Find: (a) Half-life, (b) Concentration after 30 minutes

Solution:

(a) Half-life:

t_1/2 = 0.693/k = 0.693/(4.8 × 10⁻⁴) = 1444 s = 24.1 min

(b) Concentration after 30 min (1800 s):

For first order: ln([A]_t/[A]₀) = −kt

ln([A]_t/0.80) = −(4.8 × 10⁻⁴)(1800)

ln([A]_t/0.80) = −0.864

[A]_t/0.80 = e^−0.864 = 0.421

[A]_t = 0.80 × 0.421 = 0.337 M

Problem 3: Arrhenius Equation Application

Given: A reaction has Ea = 85 kJ/mol. The rate constant at 300 K is 2.5 × 10⁻³ s⁻¹.

Find: Rate constant at 350 K

Solution:

ln(k₂/k₁) = (−Ea/R)(1/T₂ − 1/T₁)

ln(k₂/2.5 × 10⁻³) = (−85000/8.314)(1/350 − 1/300)

ln(k₂/2.5 × 10⁻³) = (−10222)(−0.000476)

ln(k₂/2.5 × 10⁻³) = 4.87

k₂/2.5 × 10⁻³ = e^4.87 = 130.6

k₂ = 130.6 × 2.5 × 10⁻³ = 0.327 s⁻¹

Problem 4: Determining Order and Half-Life

Given: For a reaction A → products, the following data was collected:

Find: (a) Is the reaction zero, first, or second order? (b) Calculate the rate constant

Solution:

Test each order by checking for linearity:

Zero order test: [A] vs time should be linear

Δ[A]/Δt = (0.35 − 0.50)/10 = −0.015 M/min (not constant)

First order test: ln[A] vs time should be linear

ln(0.35) = −1.05, ln(0.25) = −1.39, ln(0.18) = −1.71

Plot looks linear → First order

Rate constant:

Using two points: ln([A]_t/[A]₀) = −kt

ln(0.35/0.50) = −k(10)

−0.357 = −10k

k = 0.0357 min⁻¹

Half-life = 0.693/0.0357 = 19.4 minutes

Common Mistakes Students Make

• Solving rate from stoichiometry: Wrong. Rate comes from experiment, not from the balanced equation.
• Forgetting units: k units change with reaction order. Always check your units match expected values.
• Confusing half-life formulas: First order half-life is constant. Zero and second order half-lives depend on initial concentration.
• Temperature in Celsius: Must convert to Kelvin for Arrhenius calculations.
• Not checking linearity: Always verify the order by testing which graph gives a straight line.

Quick Study Guide

If you're cramming before an exam, memorize this checklist:

• Rate law format: Rate = k[A]^m[B]ⁿ
• Reaction order comes from experiment only
• First order half-life: t_1/2 = 0.693/k (constant!)
• For first order graphs: plot ln[A] vs time → straight line
• For second order graphs: plot 1/[A] vs time → straight line
• Arrhenius: higher T or lower Ea = faster reaction
• Units of k: M^1−orders⁻¹

That's chemical kinetics. No fluff, just the math and the logic. Work through the practice problems until you can solve them without looking at the solutions.