Rate Laws

When you know what reactants are interacting to create another substance, it's useful to know how fast the reaction is happening. We use a rate law to help us determine, mathematically, how fast a reaction is proceeding. For a reaction like:

the rate law might look something like:

k is the rate constant for the reaction. The exponents are the orders of reaction ... the "order of the reaction with respect to H2" is 1, and the "order of the reaction with respect to O2" is 3. The overall order of the reaction is 4, the sum of the exponents.

Important Note

For an overall reaction, the exponents (orders of reaction) have NOTHING to do with the coefficients in the balanced chemical equation. They MUST be determined EXPERIMENTALLY.

So how do you figure them out?

Consider these initial rates of reaction, given the initial concentration of each of three reactants:

[A]₀	[B]₀	[C]₀	Initial Rate
1	1	1	2.0
1	1	2	2.0
1	2	2	8.0
4	1	1	4.0

We can figure out what each exponent is based on these values (the rate law).

We know that the rate law is something like:

COMPARE the FIRST and SECOND rows. The only difference is that [C] doubled. What happened to the rate? The rate didn't change! What must 2 be raised to, to result in no change to the rate? The answer is 0, because...

COMPARE the SECOND and THIRD rows. The only difference is that [B] doubled. What happened to the rate? The rate is 4 times what it was! What must 2 be raised to, to quadruple the rate? The answer is 2, because...

COMPARE the FIRST and FOURTH rows. The only difference is that [A] quadrupled. What happened to the rate? The rate is 2 times what it was. What must 4 be raised to, to double the rate? The answer is 1/2, because...

So, we've figured out individually what each exponent was:

which of course simplifies to:

We can also figure out what k is, since we have data:

From the first row, [A]=1, [B]=1, [C]=1, Rate = 2

So 2 = k(1)^0.5 (1)^2
so 2 = k

And so we have our final rate law!