1. Reaction Kinetics & Rate Laws
Kinetics asks how fast: the rate is the change in concentration per unit time, $$\text{rate} = -\frac{\Delta[\text{reactant}]}{\Delta t} = \frac{\Delta[\text{product}]}{\Delta t}$$ The rate law reveals the mechanism hiding underneath.
Rate Laws and Reaction Orders
$$\text{rate} = k[\text{A}]^m[\text{B}]^n$$ The exponents $m$ and $n$ come from experiment — never from the balanced equation — and $k$ is the rate constant.
Exp 1: [A] = 0.10, [B] = 0.10, rate = $2.0 \times 10^{-3}$
Exp 2: [A] = 0.20, [B] = 0.10, rate = $4.0 \times 10^{-3}$ — doubling [A] doubles the rate, so $m = 1$.
Exp 3: [A] = 0.10, [B] = 0.20, rate = $8.0 \times 10^{-3}$ — doubling [B] quadruples the rate, so $n = 2$.
Rate law: $\text{rate} = k[\text{A}][\text{B}]^2$ (third order overall).
Integrated Rate Laws and Half-Life
For a first-order reaction, the half-life is concentration-independent: $$t_{1/2} = \frac{\ln 2}{k} = \frac{0.693}{k}$$
Temperature Dependence — the Arrhenius Equation
$$k = Ae^{-E_a/RT}$$ The activation energy $E_a$ is the hill reactants must climb; a useful rule of thumb is that rate roughly doubles for every 10 °C rise.
Practice Problems
- For 2 NO + O2 → 2 NO2, doubling [NO] quadruples the rate and doubling [O2] doubles it. Write the rate law and overall order.
- A first-order reaction has k = 0.0231 min−1. Find its half-life.
- What fraction of reactant remains after 4 half-lives of a first-order reaction?
- Explain why raising the temperature speeds up a reaction, in terms of Ea.
Answers: 1. rate = k[NO]2[O2]; third order 2. 30.0 min 3. 1/16 4. More molecules have energy ≥ Ea, so a larger fraction of collisions are effective.