The Rate Equation
\( \text{Rate} = k[A]^m[B]^n \)
k = rate constant, m and n = orders (found experimentally, not from stoichiometry)
Order of Reaction
| Order | Effect on Rate | [A] vs Time Graph | Rate vs [A] Graph |
|---|---|---|---|
| 0 | No effect | Straight line (linear decrease) | Horizontal line |
| 1 | Rate ∝ [A] | Exponential decay (constant half-life) | Straight line through origin |
| 2 | Rate ∝ [A]² | Curve (steeper initial decrease) | Parabola through origin |
Finding Orders Experimentally
Use the initial rates method: compare experiments where only one concentration changes.
- If doubling [A] has no effect on rate → order 0
- If doubling [A] doubles rate → order 1
- If doubling [A] quadruples rate → order 2
The Arrhenius Equation
\( k = Ae^{-E_a/RT} \)
A = frequency factor, Ea = activation energy, R = 8.314 J K⁻¹ mol⁻¹
The linear form (for graphing):
\( \ln k = \ln A - \frac{E_a}{R} \cdot \frac{1}{T} \)
Plot ln k vs 1/T → straight line with gradient = −Ea/R
Think About It
The rate equation for: 2NO + O₂ → 2NO₂ is found to be Rate = k[NO]²[O₂]. What is the overall order?
Overall order = 2 + 1 = 3. Note that the orders match the stoichiometric coefficients here, but this is coincidental — orders must always be determined experimentally.