Concentration-Time Graphs and Initial Rates Revision Notes | A Level AQA Chemistry

1. Why Concentration-Time Graphs Matter

Rate equations tell you how concentration affects rate, but to build a rate equation in the first place, you need experimental data. Concentration-time graphs are the raw material: they capture the entire story of a reaction from start to finish in a single curve.

Picture a beaker of hydrogen peroxide decomposing. At the start, the concentration is high and the curve drops steeply. As the reaction proceeds, concentration falls, collisions become less frequent, and the curve flattens. Every feature of that shape carries quantitative information about rate.

The central skill this lesson develops is extracting a numerical rate from that curve at any chosen moment, and in particular at time zero. That initial rate value is what you feed into rate-equation calculations and order-determination experiments.

2. Reading Rate from a Concentration-Time Graph

Rate is defined as the change in concentration divided by the change in time. On a concentration-time graph, that ratio is the gradient. A steep gradient means a fast rate; a shallow gradient means a slow rate.

The curve is not a straight line, so the gradient changes continuously. You cannot use a simple rise-over-run calculation across the whole graph; you must draw a tangent at the exact point of interest. A tangent is a straight line that touches the curve at precisely one point and does not cross it at that point.

Notice how the curve above is steepest at t = 0 and progressively flattens. The gradient at any point on this curve gives the rate at that moment. To find the rate at, say, t = 60 s, you would draw a tangent at that point and calculate its gradient.

2a. Calculating the Gradient of a Tangent

Once you have drawn your tangent, extend it to form a large triangle. Read off the coordinates of two widely spaced points on the tangent line (not on the curve itself), then apply the gradient formula. Using a large triangle reduces the percentage error in your reading.

Worked example: Finding the Rate at t = 60 s from a Tangent

A tangent is drawn to a concentration-time graph at t = 60 s. The tangent passes through the points (10 s, 0.70 mol dm⁻³) and (110 s, 0.30 mol dm⁻³). Calculate the rate of reaction at t = 60 s.

1. $t_1 = 10 \text{ s},\ [A]_1 = 0.70 \text{ mol dm}^{-3}$ $t_2 = 110 \text{ s},\ [A]_2 = 0.30 \text{ mol dm}^{-3}$ — These are points on the tangent line, not on the curve. Always read from the tangent.
2. $\Delta[A] = 0.30 - 0.70 = -0.40 \text{ mol dm}^{-3}$ — The negative sign confirms concentration is decreasing, as expected for a reactant.
3. $\Delta t = 110 - 10 = 100 \text{ s}$ — Use the same two points as in step 1.
4. $\text{gradient} = \frac{-0.40}{100} = -0.0040 \text{ mol dm}^{-3} \text{ s}^{-1}$ — The gradient is negative because [A] is falling with time.
5. $\text{rate at } t = 60 \text{ s} = 0.0040 \text{ mol dm}^{-3} \text{ s}^{-1}$ — Rate is always positive. Take the modulus of the gradient. [M1] correct method; [A1] correct value with units.

Answer: Rate at t = 60 s = 0.0040 mol dm⁻³ s⁻¹

3. The Initial Rate: Why t = 0 is Special

The initial rate is the rate at the very start of the reaction, when t = 0. At this moment, the concentrations of all reactants are known precisely because you set them yourself when preparing the reaction mixture. This makes the initial rate uniquely useful for building rate equations.

To find the initial rate, draw a tangent to the concentration-time curve at t = 0. This tangent touches the curve at its steepest point (the very beginning) and extends as a straight line away from the origin region. The gradient of this tangent gives the initial rate.

Once you have the initial rate for several experiments with different starting concentrations, you can compare those rates to determine the order of reaction with respect to each reactant. This is the foundation of the initial rates method in rate-equation analysis.

Worked example: Determining the Initial Rate from a Concentration-Time Graph

A reaction is monitored and the following data are recorded. The tangent drawn at t = 0 passes through the point (0 s, 1.20 mol dm⁻³) and the point (80 s, 0.00 mol dm⁻³). Calculate the initial rate.

1. $t_1 = 0 \text{ s},\ [A]_1 = 1.20 \text{ mol dm}^{-3}$\n$t_2 = 80 \text{ s},\ [A]_2 = 0.00 \text{ mol dm}^{-3}$ — The tangent at t = 0 starts at the initial concentration. Extend it far enough to form a large, readable triangle.
2. $\Delta[A] = 0.00 - 1.20 = -1.20 \text{ mol dm}^{-3}$ — Concentration decreases, so the change is negative.
3. $\Delta t = 80 - 0 = 80 \text{ s}$ — Time interval between the two tangent points.
4. $\text{gradient} = \frac{-1.20}{80} = -0.015 \text{ mol dm}^{-3} \text{ s}^{-1}$ — Divide the change in concentration by the change in time.
5. $\text{initial rate} = 0.015 \text{ mol dm}^{-3} \text{ s}^{-1}$ — Take the modulus. [M1] tangent at t = 0; [M1] correct gradient method; [A1] 0.015 mol dm⁻³ s⁻¹.

Answer: Initial rate = 0.015 mol dm⁻³ s⁻¹

4. The Continuous Monitoring Method

To draw a concentration-time graph, you need concentration data at many time points throughout the reaction. The continuous monitoring method achieves this by measuring a physical property of the reaction mixture repeatedly without stopping or sampling the reaction.

The key advantage over sampling methods is that you never interrupt the reaction. Each measurement is taken on the same, undisturbed reaction mixture, so the concentration-time profile is continuous and complete. This gives you enough data points to draw a smooth curve and place tangents accurately at any time, including t = 0.

• Gas volume: collect gas produced in a syringe or inverted burette; volume increases as reaction proceeds
• Mass loss: place the reaction vessel on a balance; mass decreases as gas escapes
• Colorimetry/spectrophotometry: measure absorbance of a coloured reactant or product at a fixed wavelength; Beer-Lambert law relates absorbance to concentration
• Conductivity: monitor changes in ion concentration in solution using a conductivity probe
• Pressure: use a manometer for gas-phase reactions where the number of moles of gas changes

Notice that the continuous monitoring method produces a full curve, not just a single data point. This is its defining strength: you can extract the rate at any time, compare rates at different stages of the same reaction, and identify whether the reaction follows first-order or second-order kinetics from the shape of the curve alone.

5. Interpreting the Shape of Concentration-Time Curves

The shape of a concentration-time graph carries information about the order of reaction. For a first-order reaction, the concentration decreases exponentially and the half-life is constant throughout. For a zero-order reaction, concentration decreases linearly with time, giving a straight line with a constant negative gradient.

At A Level, you are most commonly asked to identify first-order behaviour from a constant half-life, or to compare the steepness of tangents at different points on the same curve. The continuous monitoring method gives you the data to do both.

6. Connecting Initial Rates to Rate Equations

Earlier in this topic you met the rate equation: rate = $k[A]^m[B]^n$. The initial rate method feeds directly into this equation. By running several experiments with different initial concentrations and measuring the initial rate from the tangent at t = 0 in each case, you can compare rates and deduce the orders $m$ and $n$.

The logic is straightforward: if you double the initial concentration of A while keeping everything else constant, and the initial rate doubles, then the reaction is first order with respect to A. If the rate quadruples, it is second order. If the rate is unchanged, it is zero order. The concentration-time graph is the experimental tool that generates the initial rate values you need to make these comparisons.

Worked example: Using Initial Rates from Concentration-Time Graphs to Determine Order

Three experiments are run with different initial concentrations of reactant A. The initial rate is determined from the tangent at t = 0 in each case. Experiment 1: [A]₀ = 0.10 mol dm⁻³, initial rate = 2.0 × 10⁻³ mol dm⁻³ s⁻¹. Experiment 2: [A]₀ = 0.20 mol dm⁻³, initial rate = 4.0 × 10⁻³ mol dm⁻³ s⁻¹. Experiment 3: [A]₀ = 0.40 mol dm⁻³, initial rate = 8.0 × 10⁻³ mol dm⁻³ s⁻¹. Determine the order with respect to A.

1. $\frac{[A]_2}{[A]_1} = \frac{0.20}{0.10} = 2$ (concentration doubled) $\frac{\text{rate}_2}{\text{rate}_1} = \frac{4.0 \times 10^{-3}}{2.0 \times 10^{-3}} = 2$ (rate doubled) — Doubling [A] doubles the rate. This is consistent with first-order behaviour.
2. $\frac{[A]_3}{[A]_2} = \frac{0.40}{0.20} = 2$ (concentration doubled) $\frac{\text{rate}_3}{\text{rate}_2} = \frac{8.0 \times 10^{-3}}{4.0 \times 10^{-3}} = 2$ (rate doubled) — The same pattern holds: doubling [A] always doubles the rate.
3. If rate $\propto [A]^m$ and doubling [A] doubles rate: $2^m = 2 \Rightarrow m = 1$ — The exponent m = 1 confirms first-order dependence on A.
4. Order with respect to A = 1 (first order) — [B1] correct order stated with supporting reasoning from the data.

Answer: The reaction is first order with respect to A.

7. Exam Technique and Common Pitfalls

Questions on concentration-time graphs appear in both multiple-choice and extended-answer formats. The most common marks are awarded for: correctly identifying the tangent method, showing a large triangle with labelled coordinates, and quoting the rate with correct units. Each of these is a separate mark-winning action.

For 'evaluate' questions about the continuous monitoring method, a complete answer addresses both strengths and limitations. The key strength is that a full concentration-time profile is obtained from a single experiment, allowing rate determination at any point. The key limitation is that the method requires a measurable physical property that changes proportionally with concentration; if no such property exists, a different method must be used.

Concentration-time graphs and the initial rates they generate are the experimental foundation of the entire rate equations topic. Every order determination, every rate constant calculation, and every mechanistic inference ultimately traces back to the gradient of a tangent on one of these curves.