Orders

The order with respect to a reactant is about how the concentration of the reactant affects the rate of the reaction. Of course if we increase the concentration of a reactant (and there are no other limiting factors) then we would expect the rate of reaction to increase because there would be more collisions happening per second. However when we talk about orders we are asking by how much does increasing the concentration increase the rate of reaction.

Rate ∝ [A]x. Where ‘x’ is the the order with respect to A. What this means is that the ‘x’ will be a number, probably 0, 1, or 2.

If x=0 then the order is 0. Rate ∝ [A]0. This means that the rate is unaffected by changing the concentration of A.

For first order, rate ∝ [A]1. So the rate increases in the same ratio as the concentration, for example if the concentration doubles, the rate also doubles.

For second order,rate ∝ [A]2. So the rate increases at a higher ratio than the concentraion. If the concentration doubles (so is multiplied by 2), then the rate will get 22=4 times bigger. If the concentration tripled, the rate would get 32=9 times bigger.

The rate equation for a reaction A + B → C is given by rate = k[A]m[B]n where m is the order of reaction with respect to A and n is the order of reaction with respect to B. The purpose of this equation is to show the relationship between the rate of reaction and the concentration of the reactants. The rate constant, k is the constant that links the rate of reaction with the concentrations of the reactants.

The overall order for a reaction is the sum of the individual orders of the reactants. So, if rate = k[A]2[B]2[C]3 then the overall order would be 2+2+3=7.

The units of rate constants are determined by the overall order of the rate reaction. This is because you have to rearrange the rate equation to make k the subject of the formula.

When the overall order is zero, rate = k[A]0 so k = rate and the units will be mol dm-3 s-1.

First order, rate = k[A] so k = rate/[A] and the units are mol dm-3 s-1/mol dm-3 which cancels to s-1.

Second order, rate = k[A]2 (or rate = k[A][B]) so k = rate/[A]2 and the units are mol dm-3 s-1/(mol dm-3)2 which cancels to dm3 mol-1 s-1.

And third order, rate = k[A]2[B] (or rate = k[A]3 or k[A][B][C]) so k = rate/[A]2[B] and the units are mol dm-3 s-1/(mol dm-3)2(mol dm-3) which cancels to dm6 mol-2 s-1.