Reaction rates and collision reasoning

Chemical kinetics studies how fast reactions proceed, not just whether they are thermodynamically favourable.

Rate law

$$v = k\,[A]^{m}\,[B]^{n}$$

The exponents $m, n$ are the reaction orders (determined experimentally, not from the balanced equation).

Collision theory — For a reaction to occur, molecules must:

1. Collide with sufficient kinetic energy $\geq E_a$ (activation energy).
2. Have the correct orientation.

Arrhenius equation

k = A\,e^{-E_a / RT}

• $A$: pre-exponential (frequency) factor.
• $E_a$: activation energy.
• $R = 8.314\;\text{J mol}^{-1}\text{K}^{-1}$.

Temperature dependence — Taking the logarithm gives a linear form:

$$\ln k = \ln A - \frac{E_a}{R}\cdot\frac{1}{T}$$

A plot of $\ln k$ vs $1/T$ yields a straight line with slope $-E_a/R$.

Catalysts lower $E_a$ without being consumed, increasing the rate without shifting equilibrium.

Key insight: Doubling the temperature does not simply double the rate — the exponential Arrhenius dependence means the effect is much larger.

Common pitfall: A catalyst speeds the journey but never moves the destination: it lowers the activation barrier for forward and reverse reactions equally, changing the rate, not the equilibrium.