📚 Rate Equations and Order of Reaction | 速率方程与反应级数
Rate equations are central to AQA A-level Chemistry because they show the quantitative relationship between reactant concentrations and the initial rate of a chemical reaction. They must be determined experimentally, and they provide evidence for reaction mechanisms through the rate-determining step.
速率方程在 AQA A-level 化学中占有核心地位，它定量地表达了反应物浓度与化学反应的初始速率之间的关系。速率方程必须由实验测定，并且可以通过决速步为反应机理提供证据。
1. What is the Rate Equation? | 什么是速率方程？
For a general reaction A + B → products, the rate equation is 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 orders m and n are normally 0, 1 or 2 in A-level questions and must be found from experimental data.
对于一般反应 A + B → 产物，速率方程写作 rate = k[A]ᵐ[B]ⁿ。其中 k 为速率常数，m 为对 A 的反应级数，n 为对 B 的反应级数。在 A-level 题目中，m 和 n 通常为 0、1 或 2，必须通过实验数据确定。
er that the balanced stoichiometric equation does not tell you the orders; the rate equation is an empirical summary of how concentration affects rate.
反应的总级数是各反应物级数之和：总级数 = m + n。必须牢记，配平的化学计量方程式不能告诉你反应级数；速率方程是对浓度如何影响速率的经验总结。
2. Orders of Reaction | 反应级数
4. The order describes the power to which a concentration is raised in the rate equation.
对 A 为零级表示改变 [A] 不会影响反应速率；一级表示 [A] 加倍则速率加倍；二级表示 [A] 加倍则速率变为原来的 2² = 4 倍。反应级数描述的是速率方程中该浓度项被乘方的指数。
At A-level, orders are generally restricted to integers, but fractional orders exist in more advanced kinetics. In all cases, the order is determined experimentally, not from the coefficients of the overall equation unless the reaction is an elementary step.
在 A-level 阶段，反应级数通常限制为整数，但在更深入的动力学中也会出现分数级数。无论在何种情况下，级数都通过实验确定，不能由总反应方程式的系数直接得出，除非该反应是基元步骤。
3. The Rate Constant k | 速率常数 k
The rate constant k is the proportionality constant in the rate equation. At a fixed temperature, k has a fixed value for a given reaction, but k increases as temperature increases. This is because a higher temperature means more particles have energy greater than the activation energy.
速率常数 k 是速率方程中的比例常数。在一定温度下，对于给定反应 k 有确定数值，但 k 随温度升高而增大。这是因为温度越高，有更多粒子的能量大于活化能。
The units of k depend on the overall order of reaction because the rate itself is always expressed in mol dm⁻³ s⁻¹ and concentrations in mol dm⁻³. The table below summarises the common unit relationships.
k 的单位取决于反应的总级数，因为速率本身始终以 mol dm⁻³ s⁻¹ 表示，浓度以 mol dm⁻³ 表示。下表总结了常见的单位关系。
| Overall order | Units of k |
|---|---|
| 0 | mol dm⁻³ s⁻¹ |
| 1 | s⁻¹ |
| 2 | mol⁻¹ dm³ s⁻¹ |
| 3 | mol⁻² dm⁶ s⁻¹ |
ing the units for rate and concentration. Examiners often ask for the units of k after the overall order has been determined.
你可以通过重新整理 k = rate ÷ [A]ᵐ[B]ⁿ，并代入速率和浓度的单位来推导这些单位。考官经常在确定总级数后要求写出 k 的单位。
4. Determining Orders from Initial Rates | 通过初始速率法确定级数
The initial rates method involves measuring the initial rate of reaction at the very start, before concentrations have changed significantly. By changing one reactant concentration at a time while keeping the others constant, you can work out the order with respect to that reactant.
初始速率法是在反应刚开始、浓度尚未发生明显变化时测量反应初始速率。每次只改变一种反应物的浓度并保持其他浓度不变，就可以确定对该反应物的反应级数。
For example, if doubling [A] doubles the rate, the reaction is first order in A. Doubling [B] and observing no change in rate means zero order in B. Doubling [C] and finding the rate quadruples means second order in C.
例如，如果 [A] 加倍使速率加倍，则对 A 为一级；[B] 加倍而速率不变，则对 B 为零级；[C] 加倍而速率变为原来的四倍，则对 C 为二级。
Once the orders are known, the rate constant can be calculated by substituting any complete experiment into the rate equation. The value of k should be the same within experimental error for all runs at the same temperature.
一旦确定了各反应级数，就可以将任意一组完整实验数据代入速率方程计算速率常数。在相同温度下，不同实验得到的 k 值在实验误差范围内应相同。
5. Concentration-Time Graphs | 浓度-时间图
Concentration-time graphs show how the concentration of a reactant changes as time progresses. For a zero-order reaction, [A] decreases at a constant rate, producing a straight line with a negative gradient. The integrated form is [A] = [A]₀ − kt.
浓度-时间图显示反应物浓度随时间的变化。对于零级反应，[A] 以恒定速率减小，得到一条负斜率的直线。其积分形式为 [A] = [A]₀ − kt。
For a first-order reaction, the concentration-time graph is an exponential decay curve. The half-life is constant, and the integrated equation is [A] = [A]₀ e−kt. A second-order reaction gives a steeper curve, and a plot of 1/[A] against time is linear.
对于一级反应，浓度-时间图是一条指数衰减曲线。其半衰期恒定，积分方程为 [A] = [A]₀ e−kt。二级反应的曲线更陡，且以 1/[A] 对时间作图会得到直线。
You should be able to identify reaction order from the shape of a concentration-time graph and, for first order, use the constant half-life to find the rate constant k.
你应该能够根据浓度-时间图的形状判断反应级数，并对于一级反应利用恒定的半衰期求出速率常数 k。
6. Rate-Concentration Graphs | 速率-浓度图
A rate-concentration graph plots the initial rate against the concentration of a reactant while other concentrations are kept constant. For zero order, the graph is a horizontal line, showing that rate is independent of [A].
速率-浓度图是在其他浓度保持恒定时，以初始速率对某一反应物浓度作图。对于零级反应，图形是一条水平线，表明速率与 [A] 无关。
For first order, the rate-concentration graph is a straight line through the origin, and its gradient is equal to the rate constant k. For second order, the graph is an upward-curving parabola, showing that rate increases more rapidly than concentration.
对于一级反应，速率-浓度图是一条过原点的直线，其斜率等于速率常数 k。对于二级反应，图形是一条向上弯曲的抛物线，表明速率随浓度增加得更快。
Plotting rate against [A]² for a second-order reaction produces a straight line through the origin, which can be used to confirm the order. These graphs are useful because their gradients link directly to k.
对于二级反应，以速率对 [A]² 作图会得到一条过原点的直线，可用于确认级数。这些图形非常有用，因为它们的斜率与 k 直接相关。
7. Half-Life and First-Order Kinetics | 半衰期与一级动力学
For a first-order reaction, the half-life is given by t½ = ln 2 / k = 0.693 / k. This value is independent of the initial concentration, which means that successive half-lives in a first-order reaction are all equal.
对于一级反应，半衰期由 t½ = ln 2 / k = 0.693 / k 给出。该数值与初始浓度无关，这意味着在一级反应中连续的各半衰期都相等。
tial concentration, so a constant half-life is a diagnostic test for first-order kinetics.
对于零级反应，t½ = [A]₀ / 2k；对于二级反应，t½ = 1 / k[A]₀。两者都取决于初始浓度，因此恒定的半衰期是判断一级动力学的特征检验。
In exam questions, you may be asked to read successive half-lives from a concentration-time graph. If they are constant, the reaction is first order, and each half-life equals 0.693 divided by k.
在考试题中，你可能需要从浓度-时间图上读出连续的半衰期。如果它们相等，则反应为一级，且每个半衰期等于 0.693 除以 k。
8. Temperature Dependence and the Arrhenius Equation | 温度依赖性与阿伦尼乌斯方程
The rate constant k increases with temperature according to the Arrhenius equation: k = Ae−Eₐ/RT. In this equation, A is the pre-exponential factor, Eₐ is the activation energy in J mol⁻¹, R is the gas constant 8.31 J K⁻¹ mol⁻¹, and T is the absolute temperature in kelvin.
速率常数 k 随温度升高而增大，遵循阿伦尼乌斯方程：k = Ae−Eₐ/RT。式中 A 为指前因子，Eₐ 为活化能，单位为 J mol⁻¹，R 为气体常数 8.31 J K⁻¹ mol⁻¹，T 为开尔文温度。
Taking natural logarithms gives ln k = ln A − Eₐ/(RT). A plot of ln k against 1/T is a straight line with gradient −Eₐ/R and y-intercept ln A. This allows Eₐ and A to be determined experimentally.
取自然对数可得 ln k = ln A − Eₐ/(RT)。以 ln k 对 1/T 作图得到一条直线，斜率为 −Eₐ/R，截距为 ln A。由此可以通过实验测定 Eₐ 和 A。
Because the relationship is exponential, a small temperature rise can cause a large increase in k and therefore in the rate of reaction, especially when the activation energy is high.
由于该关系呈指数形式，温度的小幅升高就可能使 k 大幅增大，从而使反应速率
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