# Rates of Reaction

> Chemistry · CIE A-Level AS
> Source: https://www.owlsprep.com/study/cie-9701-u8-rates-of-reaction/

This sub-topic introduces the core definition of reaction rate, explains how to calculate rate from experimental data and concentration-time graphs, and covers common experimental methods for CIE AS Chemistry.

**Prerequisites:** [Concentration and mole calculations](https://www.owlsprep.com/study/cie-9701-u1-moles-calculations/)

## Learning objectives

- Define the term rate of reaction correctly
- Distinguish between average, instantaneous and initial rate
- Calculate rate of reaction from experimental and graphical data
- Describe common experimental methods for measuring reaction rate

## Definition and Measurement of Reaction Rate

**Rate of Reaction** — The rate of reaction is the change in concentration of a reactant or product per unit of time. The negative sign for reactants accounts for their decreasing concentration over time, ensuring rate is positive.

*Notation:* $r = -\frac{d[\text{reactant}]}{dt} = \frac{d[\text{product}]}{dt}$

*Example:* For the reaction $CaCO_3 + 2HCl \rightarrow CaCl_2 + CO_2 + H_2O$, rate can be measured as the increase in mass of $CO_2$ produced per second.

Rate is always determined experimentally by tracking a measurable change in a property of the reaction mixture over time. The property must change proportionally with the concentration of a reactant or product to give an accurate measure of rate.

**Worked example:** A 5.0 g lump of calcium carbonate reacts with excess hydrochloric acid. After 2 minutes, 0.88 g of $CO_2$ is collected. Calculate the average rate of reaction in g s⁻¹ of $CO_2$ produced.

1. Convert total reaction time to seconds, identify total mass of $CO_2$ produced:
2. $$\Delta m(CO_2) = 0.88 \text{ g}, \Delta t = 2 \times 60 = 120 \text{ s}$$
3. Calculate average rate as mass change divided by time change:
4. $$\text{Average rate} = \frac{\Delta m}{\Delta t} = \frac{0.88}{120} = 7.3 \times 10^{-3} \text{ g s}^{-1}$$

> **Exam tip:** CIE examiners always award a mark for correct units of rate, never forget to include units matching the question.

*Calculator:* allowed

## Average vs Instantaneous Rate

There are three key types of rate you need to distinguish for CIE:

- **Average rate**: Rate calculated over a time interval between two points
- **Instantaneous rate**: Rate at a single specific point in time
- **Initial rate**: Instantaneous rate at $t=0$, when the reaction just starts

**Worked example:** A concentration-time graph for a reactant A has a tangent at $t=20$ s that passes through (0 s, 1.0 mol dm⁻³) and (40 s, 0.4 mol dm⁻³). Calculate the instantaneous rate at 20 s.

1. Instantaneous rate equals the absolute value of the gradient of the tangent to the curve at the point of interest:
2. $$\text{Gradient} = \frac{\Delta [A]}{\Delta t} = \frac{0.4 - 1.0}{40 - 0} = \frac{-0.6}{40} = -0.015$$
3. Rate is always positive, so take the absolute value of the gradient:
4. $$\text{Rate} = |-0.015| = 0.015 \text{ mol dm}^{-3} \text{ s}^{-1}$$

**Check your understanding**

Test your understanding of core definitions:

1. Which of the following correctly defines initial rate?

   - The average rate of the first 10 seconds of reaction
   - The instantaneous rate at $t=0$ when reactants are mixed
   - The maximum rate reached during the reaction
   - The rate when half the reactant is consumed

   *Answer:* The instantaneous rate at $t=0$ when reactants are mixed

   *Why:* Initial rate is specifically the rate at the moment the reaction starts, which is widely used for kinetics experiments.

*Calculator:* allowed

## Common Experimental Methods for Rate Measurement

CIE AS frequently asks to describe a suitable method to measure the rate of a given reaction. The method you choose depends on the change in properties that occurs during the reaction.

- **Gas evolution reactions**: Collect gas in a gas syringe and measure total volume at different time intervals, or measure mass loss of the reaction mixture over time
- **Reactions with coloured species**: Use a colorimeter to measure absorbance, which is proportional to the concentration of the coloured species over time
- **Precipitation reactions (e.g. sodium thiosulfate + HCl)**: Time how long it takes for a cross under the reaction flask to disappear, then use $\frac{1}{\text{time}}$ as a measure of relative initial rate
- **Reactions changing $H^+$ concentration**: Use a pH meter to track pH changes over time and calculate $[H^+]$

**Worked example:** Describe how to measure the relative rate of the reaction between magnesium and different concentrations of hydrochloric acid, which produces hydrogen gas.

1. Set up the experiment: place a conical flask containing HCl of known concentration on a balance, add a fixed mass of magnesium ribbon, and quickly place cotton wool in the neck of the flask.
2. Start a stopwatch, and record the mass of the flask and contents every 10 seconds for 2 minutes. The mass loss equals the mass of hydrogen gas produced.
3. Repeat with the same mass of magnesium and different concentrations of HCl. Plot mass loss vs time graphs for each experiment, and calculate initial rate from the gradient of the tangent at t=0 to compare rates.

> **Exam tip:** When describing an experimental method, always mention: what variable you measure, what instrument you use, and how you record data over time.

*Calculator:* allowed

## Calculating Rate from Graphical Data

> **tip**
>
> Average rate between two points is always $\frac{\text{change in y-value}}{\text{change in x-value}}$. Instantaneous rate at any point is always the gradient of the tangent to the curve at that point.

**Worked example:** The total volume of gas produced at 10 s is 22 cm³, and at 30 s it is 58 cm³. Calculate the average rate of reaction between 10 s and 30 s.

1. Calculate the change in volume and change in time between the two points:
2. $$\Delta V = 58 - 22 = 36 \text{ cm}^3, \Delta t = 30 - 10 = 20 \text{ s}$$
3. Divide change in volume by change in time to get average rate:
4. $$\text{Average rate} = \frac{36}{20} = 1.8 \text{ cm}^3 \text{ s}^{-1}$$

*Calculator:* allowed

## Common pitfalls

- **Wrong:** Forgetting to include units for the calculated rate
  - Why it fails: CIE always allocates one mark for correct units, and most candidates miss this mark through carelessness
  - Correct: Always write units matching the quantities given in the question, common units include mol dm⁻³ s⁻¹, g s⁻¹ and cm³ s⁻¹
- **Wrong:** Calculating instantaneous rate as the gradient between two points on a curve
  - Why it fails: The gradient between two points gives average rate over the interval, not instantaneous rate at a single point
  - Correct: Always draw a tangent to the curve at the point of interest, then calculate the gradient of the tangent for instantaneous rate
- **Wrong:** Reporting a negative value for rate when using reactant concentration data
  - Why it fails: Rate is defined as a positive quantity by convention, negative values show you have not accounted for decreasing reactant concentration
  - Correct: Always take the absolute value of the gradient when calculating rate from a reactant concentration-time graph
- **Wrong:** Claiming 1/time is the actual initial rate in the disappearing cross experiment
  - Why it fails: 1/time is only proportional to initial rate, it is not the actual rate with units of concentration per time
  - Correct: State that initial rate $\propto \frac{1}{\text{time}}$, so 1/time can be used to compare relative rates between different experiments

## Cheatsheet

| Quantity | Definition | Calculation | Common Units |
| --- | --- | --- | --- |
| Average rate | Change per unit time over an interval | $\frac{\Delta [\text{species}]}{\Delta t}$ | mol dm⁻³ s⁻¹, g s⁻¹, cm³ s⁻¹ |
| Instantaneous rate | Rate at a specific time | Gradient of tangent to concentration-time graph | Same as average rate |
| Initial rate | Instantaneous rate at $t=0$ | Gradient of tangent at $t=0$ | Same as average rate |
| Relative rate | Comparison of reaction rates | $\frac{1}{\text{time (disappearing cross)}}$ | s⁻¹ |

## What's next

Understanding the definition of reaction rate and how to measure it experimentally is the foundation for all further topics in reaction kinetics. Next, you will explore how different factors (concentration, temperature, surface area, catalysts) affect reaction rate, then learn how to determine order of reaction and construct rate equations from initial rate data. These topics make up a large proportion of AS and A-Level CIE Chemistry exam marks, so building a strong foundation here is critical for high scores.

- [Collision Theory](https://www.owlsprep.com/study/cie-9701-u8-collision-theory/)
- [Catalysis](https://www.owlsprep.com/study/cie-9701-u8-catalysis/)
- [Periodicity](https://www.owlsprep.com/study/cie-9701-u9-overview/)

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