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 (22). 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 22 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-3s-1 |
| 1 | s-1 |
| 2 | mol-1 dm3 s-1 |
| 3 | mol-2 dm6 s-1 |
| 4 | mol-3 dm9 s-1 |