Because reaction orders cannot be deduced from a balanced chemical equation, chemists must use experimental methods to determine them. There are two main experimental approaches: the initial rates method and continuous monitoring.
🔑 Key Principle
The rate of reaction is proportional to the gradient of the concentration-time curve. The initial rate is found by measuring the gradient of a tangent drawn at \( t = 0 \).
1. The Initial Rates Method
In this method, several separate experiments are carried out. In each experiment, the initial concentrations of the reactants are varied, and the initial rate of the reaction is measured. Usually, we change the concentration of one reactant at a time while holding the others constant.
The rate at the very beginning of a reaction, at time \( t = 0 \), before any significant depletion of reactants has occurred. It represents the maximum rate of reaction.
| Experiment | Initial \( [A] \) / \( \text{mol dm}^{-3} \) | Initial \( [B] \) / \( \text{mol dm}^{-3} \) | Initial Rate / \( \text{mol dm}^{-3}\text{s}^{-1} \) |
|---|---|---|---|
| 1 | 0.100 | 0.100 | \( 2.0 \times 10^{-4} \) |
| 2 | 0.200 | 0.100 | \( 8.0 \times 10^{-4} \) |
| 3 | 0.200 | 0.200 | \( 1.6 \times 10^{-3} \) |
b) Write the rate equation.
c) Calculate the value of the rate constant \( k \) including units.
Part a): Finding the orders
- Order with respect to \( A \): Compare Experiment 1 and Experiment 2. Here, \( [B] \) is kept constant at 0.100 \( \text{mol dm}^{-3} \). \( [A] \) is doubled (\( \times 2 \)) from 0.100 to 0.200 \( \text{mol dm}^{-3} \). The rate increases from \( 2.0 \times 10^{-4} \) to \( 8.0 \times 10^{-4} \), which is a factor of four (\( \times 4 \)). Since \( 2^2 = 4 \), the reaction is second order with respect to \( A \).
- Order with respect to \( B \): Compare Experiment 2 and Experiment 3. Here, \( [A] \) is kept constant at 0.200 \( \text{mol dm}^{-3} \). \( [B] \) is doubled (\( \times 2 \)) from 0.100 to 0.200 \( \text{mol dm}^{-3} \). The rate increases from \( 8.0 \times 10^{-4} \) to \( 1.6 \times 10^{-3} \), which is a factor of two (\( \times 2 \)). Since \( 2^1 = 2 \), the reaction is first order with respect to \( B \).
Part b): The rate equation
\( \text{Rate} = k[A]^2[B] \)
Part c): Calculating \( k \)
Use the data from Experiment 1 to calculate \( k \):
\( k = \frac{\text{Rate}}{[A]^2[B]} = \frac{2.0 \times 10^{-4}}{(0.100)^2 \times (0.100)} = \frac{2.0 \times 10^{-4}}{0.0010} = 0.20 \)
Deduce units:
\( \text{Units of } k = \frac{\text{mol dm}^{-3}\text{ s}^{-1}}{(\text{mol dm}^{-3})^2 \times (\text{mol dm}^{-3})} = \text{dm}^6\text{mol}^{-2}\text{s}^{-1} \)
Therefore, \( k = 0.20\text{ dm}^6\text{mol}^{-2}\text{s}^{-1} \).
2. Continuous Monitoring Method
In this method, a single reaction is set up, and the concentration of a reactant or product is measured continuously or at regular time intervals as the reaction proceeds. Techniques to monitor reactions include:
- Gas collection: Measuring the volume of gas produced over time using a gas syringe.
- Colorimetry: Measuring the absorption of light over time for reactions that involve colored species.
- Electrical conductivity: Measuring the concentration of ions in solution over time.
- pH monitoring: Using a pH meter to follow changes in hydrogen ion concentration.
- Quenching and titration: Taking samples at intervals, stopping (quenching) the reaction instantly (e.g., by rapid cooling or dilution), and titrating to determine concentration.
For AQA exams, you must know specific examples of physical measurements. For instance, colorimetry is ideal for the reaction of propanone with iodine because iodine is a colored species that gets decolored as the reaction goes to completion.
Deducing Orders from Rate-Concentration Graphs
To use continuous monitoring to find reaction orders, we first plot a concentration-time graph. We then draw tangents at different times to determine the rate of reaction at various reactant concentrations. Finally, we plot a Rate-Concentration graph:
Using tangents to find instantaneous rates
The rate of reaction at any specific instant can be determined by drawing a tangent line to the concentration-time curve at that time. The gradient of the tangent is equal to the rate:
\( \text{Rate} = \left| \text{Gradient} \right| = \left| \frac{\Delta y}{\Delta x} \right| \)
Step 1: Plot the data
Plot a graph of concentration of the reactant (y-axis) against time (x-axis).
Step 2: Draw tangents and calculate gradients
Select at least three different concentrations of the reactant on the curve. At each point, draw a tangent to the curve. Find the gradient of each tangent (\( \Delta y / \Delta x \)) to determine the instantaneous rate at that concentration.
Step 3: Plot Rate vs. Concentration
Plot a second graph of Rate (y-axis) against Concentration (x-axis):
- If the graph is a horizontal straight line, the reaction is zero order.
- If the graph is a straight line passing through the origin, the reaction is first order.
- If the graph is a curve sloping upwards, plot Rate against Concentration squared (\( [\text{Reactant}]^2 \)). If this gives a straight line through the origin, the reaction is second order.
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