Chemical Kinetics | CBSE - Wyatt's Notes

sources:

• text: Standard textbook reference

Chemical kinetics studies the rate of chemical reactions and the factors affecting them. It covers rate laws, reaction orders, Arrhenius equation, and reaction mechanisms.

• Reaction rate is the change in concentration per unit time
• Rate law: $\text{rate} = k[A]^m[B]^n$ where $m$ and $n$ are experimentally determined
• Order of reaction is the sum of exponents in the rate law
• Half-life $t_{1/2}$ depends on order: zero order $t_{1/2} = \frac{[A]_0}{2k}$, first order $t_{1/2} = \frac{0.693}{k}$
• Arrhenius equation: $k = Ae^{-E_a/RT}$ relates rate constant to temperature
• Activation energy $E_a$ is the minimum energy required for reaction

Problem: For the reaction $2\text{NO} + \text{O}_2 \rightarrow 2\text{NO}_2$, the following initial rates are observed:

Determine the rate law and rate constant.

Solution:

Comparing experiments 1 and 2 ([O$_2$] constant): $\frac{\text{Rate}_2}{\text{Rate}_1} = \frac{1.0 \times 10^{-4}}{2.5 \times 10^{-5}} = 4 = \left(\frac{0.020}{0.010}\right)^m = 2^m$

So $m = 2$ (second order in NO).

Comparing experiments 1 and 3 ([NO] constant): $\frac{\text{Rate}_3}{\text{Rate}_1} = \frac{5.0 \times 10^{-5}}{2.5 \times 10^{-5}} = 2 = \left(\frac{0.020}{0.010}\right)^n = 2^n$

So $n = 1$ (first order in O$_2$).

Rate law: $\text{rate} = k[\text{NO}]^2[\text{O}_2]$

Using experiment 1: $k = \frac{\text{rate}}{[\text{NO}]^2[\text{O}_2]} = \frac{2.5 \times 10^{-5}}{(0.010)^2(0.010)} = 2.5 \times 10^3 \text{ M}^{-2}\text{s}^{-1}$

Common mistake: Assuming the rate law from the stoichiometric coefficients. The exponents must be determined experimentally, not from the balanced equation.

Problem: A first-order reaction has a half-life of 20 minutes. What percentage of the reactant remains after 60 minutes?

Solution:

Number of half-lives in 60 minutes: $n = \frac{60}{20} = 3$

Fraction remaining after $n$ half-lives: $\frac{[A]}{[A]_0} = \left(\frac{1}{2}\right)^n = \left(\frac{1}{2}\right)^3 = \frac{1}{8} = 0.125$

Percentage remaining: $12.5\%$

Common mistake: Forgetting that first-order half-life is constant. Some students try to use integrated rate law unnecessarily when the half-life method is simpler.

Problem: The rate constant of a reaction doubles when the temperature increases from 300 K to 310 K. Calculate the activation energy.

Solution:

Using the Arrhenius equation in ratio form: $\ln\frac{k_2}{k_1} = \frac{E_a}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)$

Given $k_2/k_1 = 2$, $T_1 = 300$ K, $T_2 = 310$ K: $\ln 2 = \frac{E_a}{8.314}\left(\frac{1}{300} - \frac{1}{310}\right)$

$0.693 = \frac{E_a}{8.314} \times \frac{10}{300 \times 310}$

$0.693 = \frac{E_a}{8.314} \times 1.075 \times 10^{-4}$

$E_a = \frac{0.693 \times 8.314}{1.075 \times 10^{-4}} = 53.6 \text{ kJ/mol}$

Common mistake: Using $R = 8.314$ J/(mol·K) without converting $E_a$ to J/mol. The answer should be reported in kJ/mol by dividing by 1000.

1. For a reaction with rate law $\text{rate} = k[A][B]^2$, if [A] is doubled and [B] is tripled, by what factor does the rate increase?
2. A first-order reaction is 50% complete in 30 minutes. How long does it take to be 75% complete?
3. The rate constant at 25°C is $1.0 \times 10^{-3}$ s$^{-1}$ and at 35°C is $2.0 \times 10^{-3}$ s$^{-1}$. Calculate $E_a$.

• Always determine order experimentally from initial rate data
• For first-order reactions, remember $t_{1/2} = 0.693/k$ is independent of concentration
• In Arrhenius problems, watch units: $R = 8.314$ J/(mol·K) and $E_a$ is in most cases in kJ/mol
• Practice graphing: $\ln[A]$ vs $t$ is linear for first-order, $[A]$ vs $t$ is linear for zero-order

Chemical kinetics is about how fast reactions happen and why. Think of activation energy as a hill that molecules must climb before they can react — temperature gives them more speed to get over the hill, and catalysts lower the hill itself. The rate law tells you which ingredients matter most: doubling a first-order reactant doubles the speed, but doubling a zero-order reactant does nothing. The Arrhenius equation connects temperature to speed: a small temperature increase can dramatically speed up a reaction because more molecules suddenly have enough energy to overcome the activation barrier.

Deriving the rate law from stoichiometric coefficients. The rate law exponents (m and n) must be determined experimentally from initial rate data, not from the balanced equation. The reaction 2NO + O2 -> 2NO2 is second order in NO and first order in O2, not third order overall, even though the sum of coefficients is 4.

Confusing half-life formulas for different orders. The half-life formula t1/2 = 0.693/k applies only to first-order reactions. For zero-order reactions, t1/2 = [A]0/(2k), which depends on initial concentration. Using the wrong formula gives incorrect answers for non-first-order reactions.

Forgetting unit conversions in Arrhenius equation problems. The gas constant R = 8.314 J/(mol K) requires Ea in J/mol, but answers are in standard practice reported in kJ/mol. Always divide the final answer by 1000 when converting from J to kJ. Mixing units between R and Ea is the most common source of numerical errors.

• Electrochemistry — electron transfer rates
• Solutions — concentration and reaction rates
• CBSE Physics — kinetic theory and energy concepts