📚 Determine the Order of Reaction and Rate Equation | 确定反应级数与速率方程
In AQA A-Level Chemistry, one of the core mathematical and practical skills is to determine the order of a reaction with respect to each reactant, then use the results to construct the rate equation and calculate the rate constant. This article explains how to use initial rates data, continuous monitoring and graphical methods to determine reaction order, and how to interpret the rate equation in terms of reaction mechanism.
在 AQA A-Level 化学中，核心数学与实验技能之一就是确定反应对各反应物的级数，然后利用结果构建速率方程并计算速率常数。本文讲解如何使用初始速率法、连续监测法和图像法来确定反应级数，以及如何从反应机理的角度解释速率方程。
1. The Rate Equation and Order of Reaction | 速率方程与反应级数
For a general reaction A + B → products, the rate equation can be written as rate = k[A]m[B]n. Here k is the rate constant, m is the order with respect to A, and n is the order with respect to B. The overall order of the reaction is the sum m + n. At A-Level, the orders are usually 0, 1 or 2, and they must be determined experimentally. They cannot be deduced from the stoichiometric coefficients in the balanced equation.
对于一般反应 A + B → 产物，速率方程可写为 rate = k[A]m[B]n。其中 k 是速率常数，m 是对 A 的反应级数，n 是对 B 的反应级数。反应的总级数是 m + n 之和。在 A-Level 阶段，级数通常为 0、1 或 2，并且必须通过实验确定。它们不能从配平方程中的化学计量数直接推出。
rate = k[A]m[B]n
overall order = m + n
2. Why Orders Must Be Found Experimentally | 为什么级数必须通过实验确定
The stoichiometric equation shows the overall molar ratio of reactants to products, but it does not show the sequence of bond-breaking and bond-making steps. Many reactions occur through several elementary steps, and only the slowest step, called the rate-determining step, controls the overall rate. The orders that appear in the rate equation therefore give information about the species involved in the rate-determining step, not about the balanced equation.
化学计量方程只表示反应物与产物之间的总摩尔比，并不显示断键与成键步骤的顺序。许多反应通过多个基元步骤进行，只有最慢的步骤（即决速步骤）控制总反应速率。因此，速率方程中出现的级数提供的是参与决速步骤的物种信息，而不是配平方程的信息。
with respect to each ion, despite the coefficient of 2 in front of I⁻ in the balanced equation.
例如，过硫酸根离子与碘离子的反应，其化学计量方程为 S₂O₈²⁻ + 2I⁻ → 2SO₄²⁻ + I₂，但速率方程为 rate = k[S₂O₈²⁻][I⁻]。尽管配平方程中 I⁻ 前的系数为 2，但对两种离子的级数均为 1。
3. The Initial Rates Method | 初始速率法
The most common method for determining reaction orders is to measure the initial rate of reaction in several separate experiments. In each experiment, the initial concentration of only one reactant is changed while all other concentrations are kept constant. By comparing how the initial rate changes when the concentration of that reactant is doubled or tripled, the order with respect to that reactant can be deduced.
确定反应级数最常用的方法是测量若干次独立实验中的初始速率。在每次实验中，只改变一种反应物的初始浓度，而保持其他所有反应物浓度不变。通过比较该反应物浓度加倍或变为三倍时初始速率的变化，即可推断该反应物的级数。
- If doubling [A] has no effect on the rate, the order with respect to A is 0.
- 如果 [A] 加倍而速率不变，则对 A 的级数为 0。
- If doubling [A] doubles the rate, the order with respect to A is 1.
- 如果 [A] 加倍且速率也加倍，则对 A 的级数为 1。
- If doubling [A] quadruples the rate, the order with respect to A is 2.
- 如果 [A] 加倍且速率变为四倍，则对 A 的级数为 2。
Consider the following experimental data for a reaction involving A and B.
考虑以下涉及 A 和 B 的反应实验数据。
| Experiment | [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 | 4.0 × 10⁻³ |
| 3 | 0.10 | 0.30 | 1.8 × 10⁻² |
Comparing experiments 1 and 2 shows that doubling [A] doubles the rate, so the order with respect to A is 1. Comparing experiments 1 and 3 shows that tripling [B] increases the rate by a factor of 9, so the order with respect to B is 2.
比较实验 1 和 2 可知，[A] 加倍时速率加倍，因此对 A 的级数为 1。比较实验 1 和 3 可知，[B] 变为三倍时速率增大到 9 倍，因此对 B 的级数为 2。
4. Calculating the Rate Constant and Its Units | 计算速率常数及其单位
e reaction and can be worked out by rearranging the rate equation, because k = rate / ([A]m[B]n).
一旦确定了级数 m 和 n，就将一组完整的浓度和速率数据代入速率方程，即可计算速率常数 k。k 的单位取决于反应的总级数，并可通过重排速率方程推导，因为 k = 速率 / ([A]m[B]n)。
k = rate / ([A]m[B]n)
m experiment 1 above, the rate equation is rate = k[A][B]². Substituting the values gives:
使用上面实验 1 的数据，速率方程为 rate = k[A][B]²。代入数值可得：
k = (2.0 × 10⁻³) / (0.10 × (0.10)²) = 2.0 mol⁻² dm⁶ s⁻¹
The units of k for the most common overall orders are summarised below.
以下总结了最常见总级数下 k 的单位。
| Overall order | Units of k |
|---|---|
| 0 | mol dm⁻³ s⁻¹ |
| 1 | s⁻¹ |
| 2 | dm³ mol⁻¹ s⁻¹ |
| 3 | dm⁶ mol⁻² s⁻¹ |
5. Continuous Monitoring and Concentration-Time Graphs | 连续监测与浓度-时间图像
If the progress of a reaction can be followed by measuring the concentration of a reactant or product at regular time intervals, a concentration-time graph can be plotted. The shape of this graph depends on the order of reaction. For a zero-order reactant, the concentration decreases at a constant rate, producing a straight line with a negative gradient. For a first-order reactant, the half-life is constant. For a second-order reactant, the half-life increases as the concentration decreases.
如果可以通过定期测量反应物或产物的浓度来跟踪反应进程，就可以绘制浓度-时间图像。图像的形状取决于反应级数。对于零级反应物，浓度以恒定速率下降，产生一条负斜率的直线。对于一级反应物，半衰期恒定。对于二级反应物，半衰期随浓度降低而增大。
In many AQA practicals, the concentration of a coloured species such as iodine or bromine can be followed using colorimetry, or the volume of gas produced can be measured at intervals. The resulting data are then plotted and the order is confirmed from the shape of the graph or from half-life measurements.
在许多 AQA 实验中，可以使用比色法跟踪碘或溴等有色物质的浓度，或者每隔一段时间测量产生的气体体积。然后将所得数据绘图，并通过图像形状或半衰期测量来确认级
Published by TutorHao | A-Level Chemistry Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图