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The rate of reaction is the change in concentration of a reactant or product per unit time. For a general reaction:
aA + bB -> products
we can define:
rate = -(1/a) d[A]/dt = -(1/b) d[B]/dt = (1/c) d[C]/dt
The negative signs on the reactants ensure that the rate is always a positive quantity, because reactant concentrations decrease with time.
Units of rate: mol dm^-3 s^-1 (moles per cubic decimetre per second). This is the standard OCR convention — you may also see mol dm^-3 min^-1 or mol dm^-3 h^-1 for slow reactions, but always convert to seconds in calculations.
Collision theory tells us that particles must collide with sufficient energy and correct orientation for a reaction to occur. Increasing the concentration of a reactant increases the frequency of collisions per unit volume, which generally increases the rate. The relationship between concentration and rate is not always linear, however — it depends on the mechanism of the reaction.
For a reaction A + B -> products, the rate equation (or rate law) has the form:
rate = k[A]^m[B]^n
where:
The orders m and n must be determined experimentally. They are not taken from the stoichiometric coefficients in the balanced equation.
For example, the reaction:
2NO(g) + O2(g) -> 2NO2(g)
has been found experimentally to follow rate = k[NO]^2[O2]. The order with respect to NO happens to match the stoichiometry here, but this is coincidence. Consider instead the reaction:
H2(g) + I2(g) -> 2HI(g)
You might guess rate = k[H2][I2] from the stoichiometry. Experimentally this is true at moderate temperatures, but at high temperatures the mechanism changes and the rate equation becomes different. Only experiment reveals the real rate law.
The order of reaction with respect to a reactant is the power to which the concentration of that reactant is raised in the experimentally determined rate equation.
The overall order is the sum of the powers. Typical orders encountered at A-Level are 0, 1, 2 (and occasionally fractional orders for radical mechanisms, though OCR focuses on integer orders).
| Order w.r.t. A | Effect on rate when [A] doubles |
|---|---|
| 0 | No change (rate independent of [A]) |
| 1 | Rate doubles |
| 2 | Rate quadruples (x4) |
| 3 | Rate increases x8 |
For the reaction 2NO(g) + 2H2(g) -> N2(g) + 2H2O(g), the experimentally determined rate equation is:
rate = k[NO]^2[H2]
(a) What is the order with respect to NO, H2, and overall?
(b) If [NO] is doubled, what happens to the rate?
Rate increases by 2^2 = 4 times.
(c) If [NO] and [H2] are both doubled, what happens to the rate?
Rate increases by 2^2 x 2^1 = 8 times.
The rate equation for a reaction is rate = k[A][B]^2 with k = 2.5 x 10^-3 mol^-2 dm^6 s^-1. Calculate the rate when [A] = 0.20 mol dm^-3 and [B] = 0.10 mol dm^-3.
rate = k[A][B]^2
= (2.5 x 10^-3)(0.20)(0.10)^2
= (2.5 x 10^-3)(0.20)(0.010)
= 5.0 x 10^-6 mol dm^-3 s^-1
The rate constant k is a measure of how fast a reaction occurs at a given temperature. A large k means a fast reaction; a small k means a slow reaction.
Key features of k:
A catalyst also increases k by lowering the activation energy; this is covered later.
graph LR
A["High [A], [B]"] --> B[High collision frequency]
B --> C[Large rate]
D["Low [A], [B]"] --> E[Low collision frequency]
E --> F[Small rate]
G[High T] --> H[Higher fraction of molecules with E >= Ea]
H --> I[Larger k -> larger rate]
The rate of reaction is the change in concentration per unit time, expressed in mol dm^-3 s^-1. The rate equation takes the form rate = k[A]^m[B]^n where m and n are experimentally determined orders — not stoichiometric coefficients. The overall order is m + n. The rate constant k is a measure of how fast a reaction is at a given temperature and depends on T but not on concentration. In the next lesson we examine what each order (0, 1, 2) means physically, and how concentration-time and rate-concentration graphs reveal them.