Measuring and Expressing Rates of Chemical Reactions | A-Level化学：化学反应速率的测定与表示

📚 Measuring and Expressing Rates of Chemical Reactions | A-Level化学：化学反应速率的测定与表示

In A-Level chemistry, the rate of a chemical reaction describes how quickly reactants are consumed or products are formed over time. Understanding how to measure and express this rate is a core skill, both for theoretical study and for practical investigations.

在A-Level化学中，化学反应速率描述的是反应物被消耗或产物生成随时间变化的快慢。理解如何测定和表示这一速率，既是理论学习也是实验探究的核心技能。

1. Defining Reaction Rate | 反应速率的定义

The rate of a reaction is defined as the change in concentration of a reactant or product per unit time. It is usually expressed in mol dm⁻³ s⁻¹, although other time units such as min⁻¹ or h⁻¹ may also be used depending on the experiment.

反应速率定义为反应物或产物浓度在单位时间内的变化量。其常用单位为 mol dm⁻³ s⁻¹，但根据实验情况，也可使用 min⁻¹ 或 h⁻¹ 等其他时间单位。

For a general reaction: A → B, the average rate can be calculated as the change in concentration of A or B divided by the time interval taken.

对于一般反应 A → B，平均速率可通过A或B的浓度变化量除以所经历的时间间隔来计算。

Average rate = − Δ[A] / Δt = + Δ[B] / Δt

The negative sign in front of Δ[A] ensures that the rate is a positive quantity, since the concentration of a reactant decreases over time.

Δ[A] 前面的负号是为了确保速率为正值，因为反应物浓度随时间减小。

2. Instantaneous Rate vs Average Rate | 瞬时速率与平均速率

The average rate is calculated over a finite time interval, while the instantaneous rate is the rate at a specific moment in time. The instantaneous rate is found by drawing a tangent to the concentration–time curve at the point of interest and measuring its gradient.

平均速率是在有限时间间隔内计算的，而瞬时速率是在某一具体时刻的速率。求瞬时速率的方法是在浓度-时间曲线上目标点处作切线，并测量其斜率。

In practice, initial rate is often used in kinetics experiments. The initial rate is the instantaneous rate at time t = 0, and it avoids complications arising from changing concentrations of reactants as the reaction progresses.

在实际操作中，动力学实验常使用初始速率。初始速率即 t = 0 时的瞬时速率，它可以避免反应进行过程中反应物浓度变化所带来的干扰。

When comparing the initial rates of reactions under different conditions, chemists can deduce the order of reaction with respect to each reactant and propose a rate equation.

通过比较不同条件下反应的初始速率，化学家可以推断出各反应物的反应级数，并写出速率方程。

3. Methods for Measuring Reaction Rates | 反应速率的测定方法

There are several experimental techniques for monitoring the progress of a reaction. The choice of technique depends on the physical or chemical properties of the reactants and products.

监测反应进程的实验方法有多种。方法的选择取决于反应物和产物的物理或化学性质。

Gas volume measurement: If a gas is produced, a gas syringe or measuring cylinder over water can record the volume of gas evolved at regular time intervals.
气体体积测量：如果反应产生气体，可用气体注射器或排水集气法用量筒定期记录释放气体的体积。
Mass loss measurement: If a gaseous product escapes, the total mass of the reaction vessel decreases over time. This method is simple but only suitable for reactions producing a gas.
质量损失测量：如果气态产物逸出，反应容器的总质量会随时间减小。该方法简便，但仅适用于有气体生成的反应。
Colorimetry: If a reactant or product is coloured, the intensity of colour can be measured using a colorimeter to determine concentration at intervals.
比色法：如果反应物或产物有颜色，可以使用比色计测量颜色强度，从而在不同时间确定浓度。
Titration: Samples are removed from the reaction mixture at known times and quenched, then titrated against a standard solution to find the concentration of a reactant or product.
滴定法：在已知时间点从反应混合物中取出样品并终止反应，然后用标准溶液滴定，以确定反应物或产物的浓度。
pH measurement: If H⁺ or OH⁻ ions are involved, a pH meter can provide continuous readings of pH, from which concentration changes can be calculated.
pH测量：如果反应涉及 H⁺ 或 OH⁻ 离子，可用pH计连续读取pH值，从而计算浓度变化。
Electrical conductivity: If the number or mobility of ions changes during the reaction, conductivity measurements can be used to follow the rate.
电导率测量：如果反应过程中离子数目或迁移率发生变化，可通过电导率测量来跟踪速率。

4. Measuring Gas Volume | 测定气体体积

For reactions that evolve a gas, such as the reaction between magnesium and hydrochloric acid, the volume of hydrogen gas can be measured using a gas syringe.

对于放出气体的反应，例如镁与盐酸的反应，可用气体注射器测量氢气的体积。

Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g)

At regular time intervals, the volume of gas collected is recorded. A graph of volume of gas against time is plotted, and the rate at any time is the gradient of the tangent to the curve at that point.

每隔一定时间记录收集到的气体体积，绘制气体体积-时间曲线图。任意时刻的速率即为该点处曲线切线的斜率。

One advantage of this method is that the reaction can be monitored continuously without removing samples. However, the gas syringe must be airtight, and the reaction should be stirred to avoid local concentration differences.

该方法的优点是可以连续监测反应，无需取样。但气体注射器必须密封良好，且反应需要搅拌以避免局部浓度不均。

5. Measuring Mass Loss | 测定质量损失

When a gas escapes from the reaction vessel, the total mass decreases. By placing the reaction flask on a balance and recording the mass at intervals, the rate of gas evolution can be determined.

当气体从反应容器中逸出时，总质量减小。将反应烧瓶置于天平上，定时记录质量，即可确定气体产生的速率。

For example, in the reaction between calcium carbonate and hydrochloric acid, carbon dioxide gas is released.

例如，在碳酸钙与盐酸的反应中，会释放出二氧化碳气体。

CaCO₃(s) + 2HCl(aq) → CaCl₂(aq) + CO₂(g) + H₂O(l)

Mass loss is easy to measure and requires simple apparatus. However, the balance must be accurate, and if the gas is released too quickly, readings may be difficult to capture. Also, any gas that dissolves or reacts with the solution will not be measured.

质量损失法测量简便，所需仪器简单。但天平必须精确；如果气体释放过快，读数可能难以捕捉。此外，若气体溶解或与溶液反应，则无法被测定。

6. Using Colorimetry | 使用比色法

Colorimetry is used when at least one species in the reaction is coloured. The intensity of the colour is proportional to the concentration of the coloured species, according to the Beer–Lambert law.

当反应中至少有一种物质有颜色时，可使用比色法。根据朗伯-比尔定律，颜色强度与有色物质的浓度成正比。

A common example is the reaction between iodine and propanone, or the iodine clock reaction, where the appearance of a blue-black colour can be timed.

一个常见例子是碘与丙酮的反应，或碘钟反应，其中蓝黑色出现的时间可以被计时。

In practice, a colorimeter is calibrated using solutions of known concentration, and a calibration curve is plotted. Then, samples taken from the reaction mixture at known times are analysed to find their concentrations.

实际操作中，先用已知浓度的溶液校准比色计，绘制标准曲线。然后，在已知时间从反应混合物中取样分析，以确定其浓度。

Colorimetry is suitable for reactions with slow to moderate rates, because sampling and measurement take time. Fast reactions may require a continuous flow method or stopped-flow technique.

比色法适用于速率较慢或中等的反应，因为取样和测量需要时间。对于快速反应，可能需要连续流动法或停流技术。

7. Sampling and Titration | 取样与滴定

For reactions where direct continuous monitoring is difficult, samples can be withdrawn at intervals and analysed. The reaction in each sample is quenched by rapid cooling, dilution, or addition of a quenching agent that stops the reaction.

对于难以直接连续监测的反应，可定时取出样品进行分析。每个样品中的反应可通过快速冷却、稀释或加入终止剂来淬灭，使反应停止。

For example, in the hydrolysis of an ester with a base, samples can be titrated with acid to determine the remaining concentration of alkali.

例如，在酯的碱性水解反应中，可用酸滴定样品以确定剩余碱的浓度。

This method is accurate and versatile, but it is time-consuming and requires care to ensure that the quenching process is rapid and complete. Only a small sample volume should be removed so that the overall reaction mixture is not significantly disturbed.

该方法准确且通用性较强，但耗时较长，并且需要确保淬灭过程迅速彻底。取出样品体积应尽量小，以免对整体反应混合物造成明显干扰。

8. Representing Data Graphically | 用图形表示数据

Once concentration or volume data are collected, they are plotted against time. A concentration–time graph shows how the concentration of a reactant decreases or a product increases over time.

收集到浓度或体积数据后，将其对时间作图。浓度-时间图显示反应物浓度随时间减小或产物浓度随时间增大。

For a zero-order reaction, the concentration–time graph is a straight line with a negative slope. For a first-order reaction, the graph is a downward curve, and the half-life is constant. For a second-order reaction, the half-life increases as concentration decreases.

对于零级反应，浓度-时间图是一条斜率为负的直线；对于一级反应，曲线向下弯曲，且半衰期恒定；对于二级反应，半衰期随浓度降低而增大。

From a concentration–time graph, the rate at any instant is found from the gradient of the tangent. This allows the initial rate to be determined, as well as rates at various concentrations to study the rate equation.

从浓度-时间图中，任意时刻的速率可通过切线的斜率求得。由此可以确定初始速率，也可以得到不同浓度下的速率，从而研究速率方程。

9. Rate Equations and Orders of Reaction | 速率方程与反应级数

The rate of a reaction can often be expressed by a rate equation of the form:

反应的速率通常可以用如下形式的速率方程表示：

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 is m + n.

其中，k 为速率常数，m 为关于A的反应级数，n 为关于B的反应级数，总反应级数为 m + n。

The orders m and n are determined experimentally. They are not necessarily related to the stoichiometric coefficients in the balanced equation.

反应级数 m 和 n 通过实验测定，它们不一定与配平方程式中的化学计量数一致。

To determine the order with respect to a reactant, the initial rate method can be used: the concentration of that reactant is changed while all others are held constant, and the resulting change in initial rate is observed. Alternatively, a continuous monitoring method can be used, and the half-life or integrated rate law is applied.

为测定某个反应物的级数，可使用初始速率法：在保持其他反应物浓度不变的情况下改变该反应物的浓度，观察初始速率的变化。或者，也可使用连续监测法，并应用半衰期或积分速率定律。

10. Practical Considerations and Errors | 实验注意事项与误差

Accurate rate measurement depends on careful control of experimental conditions. Temperature must be kept constant, because the rate constant k is highly sensitive to temperature changes.

准确测定速率依赖于对实验条件的严格控制。温度必须保持恒定，因为速率常数 k 对温度变化非常敏感。

Common sources of error include:

常见误差来源包括：

Heat loss or gain from the surroundings, leading to temperature fluctuations.
周围环境的热量散失或获得导致温度波动。
Incomplete mixing of reactants at the start of the reaction.
反应开始时反应物混合不充分。
Delays in recording readings, especially for fast reactions.
读数记录延迟，尤其是快速反应时。
Parallax error when reading volumes from a gas syringe or burette.
读取气体注射器或滴定管体积时产生视差误差。
Loss of volatile products or reactants from the reaction mixture.
反应混合物中挥发性产物或反应物的损失。

To minimise errors, thermostated water baths can be used, the reaction mixture should be stirred vigorously before timing begins, and readings should be taken quickly and consistently.

为减少误差，可使用恒温水浴，计时前应充分搅拌反应混合物，并快速、一致地读取数据。

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Measuring and Expressing Rates of Chemical Reactions | A-Level化学：化学反应速率的测定与表示