Reaction kinetics · ⁨حركية التفاعل⁩

A rate equation 速率方程 shows how the rate depends on the concentrations of the reactants:

• $m$ is the order of reaction 反应级数 with respect to A, and $n$ the order with respect to B. Each is $0$, $1$ or $2$.
• the overall order of reaction 总反应级数 is $m + n$.
• $k$ is the rate constant 速率常数. The rate equation can only be found by experiment, not from the balanced equation.

Finding the order

• initial rates method: change one concentration at a time and see how the starting rate changes. If doubling $[\text{A}]$ doubles the rate, the order in A is 1; if it quadruples the rate, the order is 2; if the rate is unchanged, the order is 0.

Worked example. In experiments on $\text{A} + \text{B} \rightarrow$ products, doubling $[\text{A}]$ (with $[\text{B}]$ fixed) doubles the rate, and doubling $[\text{B}]$ (with $[\text{A}]$ fixed) quadruples the rate. Write the rate equation and give the overall order.

Doubling $[\text{A}]$ doubles the rate, so first order in A. Doubling $[\text{B}]$ quadruples ($2^2$) the rate, so second order in B. Hence

• graphs: a concentration–time graph for a first-order reaction has a constant half-life 半衰期 (the time for the concentration to halve). A rate–concentration graph is a straight line through the origin for first order, and a curve for second order.

Half-life and the rate constant

For a first-order reaction the half-life is constant — it does not depend on the concentration. You can find the rate constant from it:

Worked example. A first-order reaction has a half-life of $120\ \text{s}$. Find its rate constant.

You can also find $k$ by putting initial-rate data into the rate equation.

Most reactions happen in several steps. The slowest step is the rate-determining step 决速步骤, and it controls the overall rate. Only the species involved up to and including this step appear in the rate equation.

• an intermediate 中间体 is a species made in one step and then used up in a later step. It is not in the overall equation.
• you can suggest a mechanism that fits both the rate equation and the overall equation, predict the order from a given mechanism, or pick out the rate-determining step.

If you compare the initial rate 初始速率 of different mixtures, you can deduce the rate equation, and from that work out the mechanism.

Effect of temperature

Raising the temperature increases the rate constant $k$ (more molecules pass the activation energy), so the rate goes up.

Catalysts 催化剂 can be homogeneous or heterogeneous.

Heterogeneous catalysts

A heterogeneous catalyst 多相催化剂 is in a different physical state from the reactants (usually a solid with gases). It works in three stages:

1. adsorption 吸附: reactant molecules stick to the catalyst surface.
2. the bonds in the reactants are weakened, so they react more easily.
3. desorption 脱附: the product molecules leave the surface.

Examples are iron in the Haber process, and platinum, palladium and rhodium in a catalytic converter.

Homogeneous catalysts

A homogeneous catalyst 均相催化剂 is in the same physical state as the reactants. It is used up in one step and then reformed in a later step, so it comes back unchanged. Examples are oxides of nitrogen helping to oxidise atmospheric sulfur dioxide, and $\text{Fe}^{2+}$ or $\text{Fe}^{3+}$ speeding up the reaction between $\text{I}^-$ and $\text{S}_2\text{O}_8^{2-}$.

• Find orders from initial-rate data: doubling a concentration that doubles the rate is first order, quadruples it is second order, no change is zero order.
• Write $\text{rate} = k[\text{A}]^m[\text{B}]^n$ and work out the units of $k$ from it.
• The rate-determining step contains the species (and orders) in the rate equation — use this to test a mechanism.
• A constant half-life means first order.