In order to find the rate law of a reaction you will need to know the order of the reaction and the reactant concentration. The order of the reaction can be determined by doing a rate experiment and varying the concentrations of the reactants. The order of the reaction is the exponent of the reactant’s concentration in the rate law expression. For example if the rate depends on the concentration of A raised to the second power then the reaction is second order in A. Once the order of the reaction is determined the next step is to find the rate constant. The rate constant has the units of concentration-1*time-1 for a first order reaction concentration-2*time-1 for a second order reaction etc. The rate constant can be found from the initial rates of the reaction at different concentrations. The rate law expression can then be determined by plugging in the values for the order and rate constant.
One example of how to determine the rate law of a reaction is the decomposition of N2O5 to NO2 and O2. The following table lists the initial rates and concentrations of N2O5 used in the experiments.
|Initial Concentration of N2O5 (M)|Initial Rate of Reaction (M/s)|
|———————————|——————————-|
|0.0400 |0.010 |
|0.0200 |0.005 |
|0.0100 |0.00250 |
|0.00500 |0.001250 |
From the table it can be seen that the initial rate of the reaction varies with the concentration of N2O5. The order of the reaction can be determined by plotting the initial rate of the reaction vs. the concentration of N2O5. The plot should be linear if the reaction is first order linear with a slope of 2 if the reaction is second order etc. In this case the plot is linear so the reaction is first order in N2O5. The next step is to find the rate constant. This can be done by taking the inverse of the slope of the plot. The slope is 0.010 M-1*s-1 so the rate constant is k = 100 M-1*s-1. The rate law expression for the decomposition of N2O5 is therefore rate = k[N2O5].
As another example consider the reaction A + B –> products. The following table lists the initial rates and concentrations of A and B used in the experiments.
|Initial Concentration of A (M) |Initial Concentration of B (M)|Initial Rate of Reaction (M/s)|
|——————————–|——————————-|——————————-|
|0.0100 |0.0200 |0.0010 |
|0.0200 |0.0100 |0.0040 |
|0.0100 |0.00500 |0.0010 |
|0.00500 |0.0100 |0.0020 |
From the table it can be seen that the initial rate of the reaction varies with the concentrations of both A and B. The order of the reaction can be determined by plotting the initial rate of the reaction vs. the concentrations of A and B. The plot should be linear if the reaction is first order linear with a slope of 2 if the reaction is second order etc. In this case the plot is linear so the reaction is first order in both A and B. The next step is to find the rate constant. This can be done by taking the inverse of the slope of the plot. The slope is 0.0010 M-1*s-1 so the rate constant is k = 1000 M-1*s-1. The rate law expression for the reaction A + B –> products is therefore rate = k[A][B].
In conclusion the rate law of a reaction can be determined by knowing the order of the reaction and the reactant concentration. The order of the reaction can be determined by doing a rate experiment and varying the concentrations of the reactants. The order of the reaction is the exponent of the reactant’s concentration in the rate law expression. The rate constant can be found from the initial rates of the reaction at different concentrations. The rate law expression can then be determined by plugging in the values for the order and rate constant.
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