Reaction Kinetics: Rate Laws

Using the method of initial rates, we take the ratio of rates between reactions 2 and 1 to determine the order of the reaction in permanganate.

By taking the ratios of the rates of experiments 3 and 1 we can obtain the order of the reaction in chlorite.

Finally, by taking the ratios of the rates of experiments 4 and 1 we can obtain the order of the reaction in H⁺.

Now that we know the order of the reaction in permanganate is 2, chlorite is 1, and H⁺ is 1/2, we can use the rate and concentration data in experiment 1 to calculate the rate constant.

Starting with the integrated rate law for a zero order reaction, we rearrange the variables so we can make the substitution that [A] / [A]_o = 0.5 when t = t_1/2, we derive the following equation:

The graph of ln [HN₃] versus time is linear:

That means the reaction is a first order decay process with a rate law rate = k [NaN₃]. The value of k is the negative of the value of the slope, so k = 0.056 s^-1.