Chapter 7 — Chemical Kinetics Exercise Solutions
Chemical Kinetics is numerical-friendly. Always identify the order of reaction before selecting the formula.
Key Concepts Quick Recap
| Term | Definition |
|---|---|
| Rate of reaction | Change in concentration per unit time; r = −(1/a)(d[A]/dt) |
| Rate law | Experimentally determined: rate = k[A]^m[B]^n |
| Order of reaction | Sum of powers m + n in the rate law; experimentally found |
| Molecularity | Number of molecules colliding in a single elementary step; theoretical |
| Rate constant (k) | Proportionality constant; depends on temperature, not concentration |
| Half-life (t½) | Time for [A] to fall to half its initial value |
| Arrhenius equation | k = Ae^(−Ea/RT); relates k to temperature |
| Activation energy (Ea) | Minimum energy needed for a reaction to occur |
| Frequency factor (A) | Rate of collisions; pre-exponential factor in Arrhenius equation |
| Pseudo-first order | Higher order reaction behaves as first order when one reactant is in large excess |
Formula Recap
| Concept | Formula |
|---|---|
| Zero order: k | k = ([A₀] − [A]) / t |
| First order: k | k = (2.303/t) log([A₀]/[A]) |
| First order: t½ | t½ = 0.693 / k |
| Second order: k | k = (1/t)(1/[A] − 1/[A₀]) |
| Arrhenius | k = Ae^(−Ea/RT) or log(k₂/k₁) = (Ea/2.303R)(1/T₁ − 1/T₂) |
| Units of k | Zero order: mol L⁻¹ s⁻¹; First order: s⁻¹; Second order: L mol⁻¹ s⁻¹ |
I. Choose the Best Answer (MCQs)
1. The rate of a first order reaction does NOT depend on: (a) Temperature (b) Initial concentration (c) Nature of reactant (d) Catalyst
2. The unit of rate constant for a second order reaction is: (a) s⁻¹ (b) mol L⁻¹ s⁻¹ (c) L mol⁻¹ s⁻¹ (d) mol² L⁻² s⁻¹
3. For a first order reaction, a plot of log[A] vs time gives: (a) A curve (b) A straight line with positive slope (c) A straight line with negative slope (d) A parabola
4. The Arrhenius equation k = Ae^(−Ea/RT) shows that k increases when: (a) Ea increases (b) T increases (c) A decreases (d) R increases
5. Which of the following reactions is pseudo-first order? (a) H₂ + I₂ → 2HI (b) CH₃COOC₂H₅ + H₂O (excess) → acid hydrolysis (c) 2NO → N₂ + O₂ (d) 2H₂ + O₂ → 2H₂O
6. Doubling the concentration of reactant A doubles the rate. Tripling [A] triples the rate. The order with respect to A is: (a) 0 (b) 1 (c) 2 (d) 3
7. A catalyst increases the rate of a reaction by: (a) Increasing the activation energy (b) Decreasing the activation energy (c) Increasing the temperature (d) Changing the equilibrium constant
II. Short Answer Questions
Worked Examples
Example 1 — Finding k for a first order reaction
A first-order reaction decreases [A] from 0.8 M to 0.2 M in 20 min. Find k.
Example 2 — Half-life of a first order reaction
A first-order reaction has k = 0.0231 min⁻¹. Find its half-life.
Example 3 — Activation energy using Arrhenius equation
A reaction has k₁ = 0.1 s⁻¹ at 300 K and k₂ = 0.4 s⁻¹ at 320 K. Find Ea.
Example 4 — Units of rate constant
Example 5 — Integrated rate law: zero order
A zero-order reaction has k = 0.05 mol L⁻¹ min⁻¹. If [A₀] = 1 M, when does [A] = 0.5 M?
Numerical Pattern
1. Identify reaction order from given data or question. 2. Write the correct integrated rate equation. 3. Substitute known values (concentrations, time). 4. Keep log base correct (2.303 × log₁₀ = ln). 5. Write unit of rate constant based on order. 6. Check that the answer is dimensionally correct.
Common Mistakes
- Confusing order and molecularity (order is experimental; molecularity is for elementary steps).
- Missing the unit of k — always write it.
- Using ln formula when question expects log₁₀ (2.303 factor must be included).
- Not converting time units (hours → minutes → seconds) consistently.
- Saying catalyst changes equilibrium constant — it does not; Keq is unchanged.
Exam Checklist
- Order of reaction is clearly identified.
- Correct formula (zero/first/second order) is used.
- Unit of k is stated.
- Activation energy units are J/mol or kJ/mol.
- Final numerical answer has proper significant figures.