What is the 'rate law' for this reaction?

A rate law is the term used to describe a mathematical equation that equates the rate (speed) of a reaction with the concentration of the reactants. For the reaction

2G + B --> G₂B

The rate law is;

rate = k[G]²

So how did we get this rate law for the reaction we observed?

The answer is; by looking at the reactants in the slow step of the mechanism.

The mechanism for this reaction is;

Step 1: G + G --> G₂ (slow)

Step 2: G₂ + B --> G₂B (fast)

In the slow step of this mechanism two G atoms collide to form G₂, since there are two G atoms the coefficient for the reactant in the slow step becomes the exponent for that species in the rate law.

Let's consider some additional possible mechanisms for this reaction, and what the rate law would be.

Mechanism X:

Step 1: G + B --> GB (slow)

Step 2: GB + G --> G₂B (fast)

The rate law for this possible mechanism would be: rate = k[G]¹[B]¹

See how the coefficients for the reactants in the slow step of the mechanism are the same as the exponents in the rate law.