# 5.2.6 Concentration-Time Graphs

### Concentration-Time Graphs

#### Order of reaction from concentration-time graphs

• In a zero-order the concentration of the reactant is inversely proportional to time
• This means that the concentration of the reactant decreases with increasing time
• The graph is a straight line going down

Concentration-time graphs of a zero-order reaction

• In a first-order reaction the concentration of the reactant decreases with time
• The graph is a curve going downwards and eventually plateaus

Concentration-time graphs of a first-order reaction

• In a second-order reaction the concentration of the reactant decreases more steeply with time
• The concentration of reactant decreases more with increasing time compared to in a first-order reaction
• The graph is a steeper curve going downwards

Concentration-time graphs of a second-order reaction

### Initial Rates Method

#### The Initial Rate Method

• The initial rate method is used to gather experimental data, to determine the order with respect to the reactants in the reaction
• The initial rate of a reaction is the rate right at the start of the reaction
• This is used because right at the start of the reaction, we know the exact concentration of the reactants used
• The method involves setting up a series of experiments
• When carrying out the experiments:
• The temperature must remain constant
• For each experiment, the concentration of only of the reactants is altered – the rest must remain constant
• The experiments are planned so that when the results are collected, they can be used to determine the order with respect to each reactant
• For each experiment, a concentration-time graph is drawn
• From each graph, the initial rate is calculated by drawing a tangent to the line at t = 0 and calculating the gradient
• The gradient at t = 0 is the initial rate for that reaction

#### General Example

• Let’s take the following general reaction as an example

2A + B + C → C + D

• We need to run a series of experiments at different concentrations of A, B and C, to determine how each affects the initial rate of the reaction
• Firstly, complete the experiment using the same concentration of A, B and C
• In another experiment, change the concentration of A but keep the concentrations of B and C the same as in experiment 1
• In a third experiment, change the concentration of B but keep the concentrations of A and C the same as in experiment 1
• And so on, until you have completed a series of experiments and collected the results
• Draw graphs for each experiment, draw a tangent at t=0 and calculate the gradient (the initial rate) for each graph
• Tabulate all of your results, and then use these to determine the order with respect to each reactant, to determine the rate equation for the reaction

A graph to show how to find the initial rate of a reaction (t=0)

Table of the results collected for the reaction

### Rate Constant & Zero Order Graphs

#### Finding the Rate Constant of a Zero Order Reaction

• As shown above, a zero order reaction will give the following concentration-time graph

Concentration-time graphs of a zero-order reaction

• The rate of the reaction isn’t changing – if you were to calculate the gradient at different points on the graph, you would achieve a constant value
• Since the order with respect to the reactant is 0, a change in the concentration of the reactant will have no effect on the rate of the reaction
• Therefore:

Rate = k

• The rate of the reaction is the gradient of the graph, meaning that the rate constant, k, for the reaction will also be the gradient of the graph
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