Kinetics
Rate Equations
The rate of reaction is the change of concentration of a substance in a given time. Whether that be reactants disappearing or products appearing; the rate of reaction is affected by the temperature. However, the chemical equation does not tell us how fast things happen, for this we use a rate equation.
[A] means, the concentration of A. k is the rate constant and m and n are the order of the reaction, the values of m and n can only be found by experimentation and have nothing to do with the moles of substance. The addition of m and n gives you overall order.
Orders of Reaction
In a zero order reaction the rate=k since anything to the power of 0 is 1. Therefore the rate of reaction does not change over time and the [A] (for example) changes linearly.
In a first order reaction, the rate and concentration are proportional. This means that if the concentration is doubled, the rate will double.
And finally, in a second order reaction, if the concentration is doubled, the rate will increase by a factor of 4 (2^{2}). The speed at which the [A] changes is much faster in a second order reaction.
Determining the Rate
As we said above, the orders of a reaction can only be found by using experimental data, so now you will learn how to do that.
Here we need to find m and n in the equation: rate = k[A]^{m}[B]^{n}.
In order to do this you need to compare individual experiements. Look at experiment 1 and then experiment 2. [A] is doubled and [B] is the same, so we can deduce the order with respect to A. The rate increases by a factor of 4 which is 2^{2} so m is 2.
Now we do the same thing for n. I you compare experiments 2 and 3 the initial [B] is doubled, the initial rate stays the same so n is 0. Therefore the overall equation is: rate = k[A]^{2}[B]^{0}.
The overall order is 2, and this can be seen when comparing experiments 1 and 4, both concentrations are trebled, and the rate increases by a factor of 9.
Units of k
The units of k (the rate constant) vary according to the overall order of the equation. Fortuneately it follows an easy to follow pattern, so remembering the below table should be very easy.
Overall order (n+m) | Units of k |
---|---|
0 | mol dm^{-3}s^{-1} |
1 | s^{-1} |
2 | mol^{-1} dm^{3} s^{-1} |
3 | mol^{-2} dm^{6} s^{-1} |
4 | mol^{-3} dm^{9} s^{-1} |