📚 Reaction Order and Rate Equations | 反应级数与速率方程
In chemical kinetics, a rate equation, also called a rate law, connects the reaction rate to the concentrations of the reactants. It is always determined experimentally and cannot be written reliably from the balanced chemical equation.
在化学动力学中，速率方程（rate equation）将反应速率与反应物浓度联系起来。它必须通过实验确定，不能仅凭配平后的化学方程式直接写出。
1. What Is a Rate Equation? | 什么是速率方程？
For a general reaction aA + bB → products, the rate is often written as:
对于一般反应 aA + bB → 产物，速率通常写成：
rate = k [A]ᵐ [B]ⁿ
Here, k is the rate constant, and m and n are the orders of reaction with respect to A and B. The values of m and n are not necessarily equal to the stoichiometric coefficients a and b.
其中，k 是速率常数，m 和 n 分别是相对于 A 和 B 的反应级数。m、n 不一定等于化学方程式中的计量系数 a、b。
2. Order of Reaction | 反应级数
The order with respect to a single reactant is the exponent to which its concentration is raised in the rate equation. The overall order of reaction is the sum of all the individual orders.
某一反应物的反应级数，是速率方程中该反应物浓度项的指数。反应的总级数等于各反应物级数之和。
Orders can be 0, 1, 2, or sometimes fractional or even negative values. A zero order means that changing that concentration has no effect on the rate.
反应级数可以是 0、1、2，有时也可以是分数甚至负值。级数为 0 表示改变该物质浓度对速率没有影响。
3. Zero-Order Reactions | 零级反应
For a zero-order reaction, the rate is independent of the reactant concentration. The rate equation is simply rate = k.
对于零级反应，速率与反应物浓度无关，速率方程简化为 rate = k。
rate = k
The concentration of A falls linearly with time, so the integrated equation is [A] = [A]₀ − kt. A graph of [A] against t is a straight line with a slope of −k.
A 的浓度随时间线性下降，因此积分式为 [A] = [A]₀ − kt。以 [A] 对 t 作图是一条直线，斜率为 −k。
The half-life of a zero-order reaction is t½ = [A]₀/(2k). This means the half-life becomes shorter as the initial concentration decreases.
零级反应的半衰期为 t½ = [A]₀/(2k)，也就是说初始浓度越小，半衰期越短。
4. First-Order Reactions | 一级反应
For a first-order reaction, the rate is directly proportional to one reactant concentration:
对于一级反应，速率与某一反应物的浓度成正比：
rate = k [A]
The integrated rate law is ln[A] = ln[A]₀ − kt. Therefore, plotting ln[A] against t gives a straight line with slope −k. A plot of [A] against t would be curved.
积分速率定律为 ln[A] = ln[A]₀ − kt。因此以 ln[A] 对 t 作图得到斜率为 −k 的直线；若以 [A] 对 t 作图则为曲线。
The half-life of a first-order reaction is t½ = 0.693/k. This value is constant and does not depend on the initial concentration of A.
一级反应的半衰期为 t½ = 0.693/k。该值恒定不变，与 A 的初始浓度无关。
5. Second-Order Reactions | 二级反应
A second-order reaction can have rate = k[A]² or rate = k[A][B], depending on the mechanism. For the simple case rate = k[A]², the integrated rate law is:
二级反应可以是 rate = k[A]²，也可以是 rate = k[A][B]，具体取决于反应机理。对于简单情形 rate = k[A]²，其积分速率定律为：
1/[A] = 1/[A]₀ + kt
This means that a plot of 1/[A] against t gives a straight line. The half-life is t½ = 1/(k[A]₀), so the half-life is inversely proportional to the initial concentration.
因此，以 1/[A] 对 t 作图得到一条直线。二级反应的半衰期为 t½ = 1/(k[A]₀)，即半衰期与初始浓度成反比。
6. Determining Orders by the Initial-Rate Method | 用初始速率法确定反应级数
The initial-rate method measures the rate at the very beginning of a reaction while changing one concentration at a time. Consider the reaction A + B → products with the data below.
初始速率法是在反应刚开始时测量速率，并每次只改变一种反应物的浓度。以反应 A + B → 产物为例，实验数据如下。
| Experiment 实验 | [A] / mol dm⁻³ | [B] / mol dm⁻³ | Initial rate / mol dm⁻³ s⁻¹ |
| 1 | 0.10 | 0.10 | 2.0 × 10⁻³ |
| 2 | 0.20 | 0.10 | 8.0 × 10⁻³ |
| 3 | 0.10 | 0.20 | 4.0 × 10⁻³ |
Comparing experiments 1 and 2, doubling [A] while keeping [B] constant quadruples the rate. Therefore, the order with respect to A is 2. Comparing experiments 1 and 3, doubling [B] while keeping [A] constant doubles the rate. Therefore, the order with respect to B is 1.
比较实验 1 和 2，保持 [B] 不变而将 [A] 加倍，速率变为原来的 4 倍，因此 A 的级数为 2。比较实验 1 和 3，保持 [A] 不变而将 [B] 加倍，速率变为原来的 2 倍，因此 B 的级数为 1。
rate = k [A]² [B]
The overall order for this reaction is 2 + 1 = 3.
该反应的总级数为 2 + 1 = 3。
7. Integrated Rate Laws and Half-Life | 积分速率定律与半衰期
Integrated rate laws are useful for determining order from concentration-time data. The table below summarises the common forms for zero-, first- and second-order reactions.
积分速率定律可用于根据浓度-时间数据判断反应级数。下表总结了零级、一级和二级反应的常见形式。
| Property 性质 | Zero-order 零级 | First-order 一级 | 更多咨询请联系16621398022（同微信）
CommentsMore posts |
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导