Even when a mechanism is consistent with the rate law , later experimentation may it to be incorrect or only one of several alternative. As an example, the reaction between hydrogen and iodine has the following rate law: rate=k[H]^3[I]2.

The long accepted mechanism proposed a single
Biomolecular step, that is, the overall reaction was though to be elementary:
H2(g)+i2(g)-> 2HI (g)
In the 1960's, however, spectroscopy evidence showed the presence of free I atom during the reaction kineticists have since proposed a three step mechanism:
(1) I ^2(g)<-> 2i (g) [fast]
(2) H^2(g)+I(g)->H^2I (g)[fast]
(3)H^2i (g)+I(g)-> 2HI (g) [slow]
Show that this mechanism is consistent with the rate law.

To show that the proposed mechanism is consistent with the given rate law, we need to determine how the rate law expression is derived from the individual steps in the mechanism.

The rate law for the reaction between hydrogen (H2) and iodine (I2) is given as rate = k[H]^3[I]^2. This means that the rate of the reaction depends on the concentrations of both H2 and I2, with their exponents being 3 and 2, respectively.

Let's analyze each step in the proposed mechanism and see how it contributes to the overall rate law:

Step 1: I2(g) ⇌ 2I(g) (fast)
This step involves the dissociation of the I2 molecule into two iodine atoms. Since it is a fast step, we assume it to be at equilibrium, meaning the forward and backward reactions occur at similar rates. However, this step does not involve any H2, so it does not directly affect the rate law expression.

Step 2: H2(g) + I(g) → H2I(g) (fast)
This step corresponds to the combination of H2 and I to form a molecule of H2I. Again, since it is a fast step, we assume it is at equilibrium. However, the concentration of H2I does not appear in the rate law expression, so this step's rate does not contribute to the overall rate law.

Step 3: H2I(g) + I(g) → 2HI(g) (slow)
This step represents the slowest step in the mechanism. Here, the H2I reacts with an I atom (free I) to form two molecules of HI. The rate-determining step is the slowest step, which means this step determines the overall rate of the reaction. Importantly, the concentration of HI appears in the rate law expression, and since this step directly produces HI, it contributes to the overall rate law.

Overall, the key step in the proposed mechanism that influences the rate law is Step 3. This step involves the formation of HI, which is reflected in the rate law expression as [HI]^2. Therefore, the proposed mechanism is consistent with the given rate law rate = k[H]^3[I]^2, as the step involving the production of HI aligns with the rate law expression.