Reaction rate measures the speed of a chemical change

The reaction rate measures how quickly reactants are used up or products are formed during a chemical reaction. It is defined as the change in the amount of reactants or products per unit time. Typically, it is expressed in units of mol dm^-3 s^-1.

Various methods can be used to monitor reaction rates

To measure a reaction rate, you need to observe a property that changes as the reaction proceeds. Several continuous monitoring methods are used:

1. Measuring gas volume

• If a gas is produced, it can be collected in a gas syringe.
• Record the volume of gas at regular intervals (e.g., every 15 seconds).
• Convert gas volume to moles using the ideal gas equation, then determine reactant concentration using stoichiometry.

2. Measuring mass change

• If a gas is released, the reaction system will lose mass.
• Measure the mass at regular intervals using a balance.
• Calculate moles of gas lost and remaining reactant concentration using mole calculations.

3. Tracking colour change

• A colorimeter measures the absorbance (light absorption) of a solution.
• More concentrated coloured solutions have higher absorbance.
• Create a calibration curve by plotting known concentrations against absorbance.
• During the reaction, measure absorbance of samples at regular intervals.
• Determine sample concentrations using the calibration curve by locating their absorbance on the y-axis and reading the corresponding concentration from the x-axis.

4. Monitoring pH changes

• If H⁺ ions are produced or consumed, the pH of the solution will change.
• Measure pH at regular intervals and calculate [H⁺] using the relationship: pH = $-$log[H⁺].

5. Performing titrations

• Take small samples of the reaction mixture at regular intervals.
• Titrate each sample with a standard solution.
• Calculate reactant or product concentration from titration data.

6. Measuring electrical conductivity

• Changes in the number of ions in solution affect electrical conductivity.
• Measure conductivity at regular intervals to track the progress of the reaction.

Rate equations relate reaction rate to reactant concentrations

A rate equation is a mathematical expression that shows how the rate of a chemical reaction depends on the concentrations of the reactants.

For a general reaction: A + B ➔ C + D

The rate equation takes the form:

Rate = k[A]^m[B]ⁿ

Where:

• Rate is the reaction rate (mol dm^-3 s^-1).
• k is the rate constant.
• [A] and [B] are the concentrations of reactants A and B (mol dm^-3).
• m and n are the orders of reaction with respect to A and B.

Reaction orders show how reactant concentrations affect the rate

The values of m and n in the rate equation are the reaction orders with respect to each reactant.

They indicate how changing the concentration of a reactant influences the reaction rate.

1. Zero order (m or n = 0) - The rate is independent of the reactant concentration. Doubling or tripling the concentration has no effect on the rate. [A]⁰ = 1, so zero order terms are often written without the concentration term.

2. First order (m or n = 1) - The rate is directly proportional to the reactant concentration. Doubling the concentration doubles the rate, tripling the concentration triples the rate.

3. Second order (m or n = 2) - The rate is proportional to the square of the reactant concentration. Doubling the concentration quadruples the rate (2² = 4), tripling the concentration increases the rate ninefold (3² = 9).

The overall order of the reaction is the sum of m and n.

Importantly, reaction orders can only be determined experimentally, not from balanced chemical equations.

The rate constant k relates reactant concentrations to rate at a given temperature

The rate constant, k, is a proportionality constant that relates the rate of a reaction to the concentrations of the reactants at a specific temperature.

• A larger k value indicates a faster rate of reaction.
• k remains constant for a given reaction at a fixed temperature.
• Increasing the temperature exponentially increases the value of k, as collisions between reactant molecules are more frequent and more energetic.

The units of k depend on the overall order of the reaction.

Determining reaction order from rate-concentration graphs

The shape of a rate-concentration graph can reveal the reaction order with respect to a particular reactant.

To construct a rate-concentration graph from experimental data, follow these steps:

1. Begin with a concentration-time graph for the reactant of interest.

2. Calculate the rate (gradient) at various points along the concentration-time curve.

• For linear plots, the gradient is constant and can be easily determined.
• For curved plots, draw tangent lines at selected points to determine the gradient at each point.

1. Plot the rate (y-axis) against the corresponding concentration (x-axis) for each point.

2. Fit a smooth curve or line through the resulting data points.

The shape of the resulting rate-concentration graph reveals the reaction order with respect to the reactant:

• Zero order - A horizontal line indicates that the reaction rate is independent of the reactant concentration. The rate equation is: rate = k

• First order - A straight line passing through the origin signifies that the reaction rate is directly proportional to the reactant concentration. The rate equation is: rate = k[X]

• Second order - A curved plot indicates that the reaction rate is proportional to the square of the reactant concentration. The rate equation is: rate = k[X]²

In these equations, k represents the rate constant, and [X] denotes the concentration of reactant X.

First order reactions have constant half-lives

The half-life (${\text{t}}_{\frac{1}{2}}$) of a reaction is the time taken for the concentration of a reactant to decrease to half of its initial value.

For first-order reactions:

• The half-life is independent of the initial concentration.
• Each successive half-life is the same duration.
• The half-life can be read directly from the concentration-time graph.

The rate constant (k) of a first-order reaction is related to its half-life (${\text{t}}_{\frac{1}{2}}$) by the equation:

$\text{k }=\frac{\ln (2)}{{\text{t}}_{\frac{1}{2}}}$

Worked example 1 - Calculating the rate constant from half-life data

The graph below illustrates the decomposition of hydrogen peroxide.

Determine the half-life at different concentration intervals and calculate the rate constant. Give your answer to 3 significant figures.

Step 1: Determine half-life

Half-life measurements:

• [H₂O₂] from 8 to 4 mol dm^-3: ${\text{t}}_{\frac{1}{2}}$ = 100 s
• [H₂O₂] from 4 to 2 mol dm^-3: ${\text{t}}_{\frac{1}{2}}$ = 100 s
• [H₂O₂] from 2 to 1 mol dm^-3: ${\text{t}}_{\frac{1}{2}}$ = 100 s The consistent half-life of 100 s, regardless of concentration, confirms that the reaction is first-order with respect to H₂O₂.

Step 2: Equation

$\text{k }=\frac{\ln (2)}{{\text{t}}_{\frac{1}{2}}}$

Step 3: Substitution and correct evaluation

$\text{k }=\frac{\ln (2)}{100}=6.93\times {10}^{-3}{\text{ s}}^{-1}$