Final answer:
The rate law for the overall reaction is controlled by the slowest step, which is step 2 in the proposed mechanism. Since Cl is an intermediate formed in a pre-equilibrium step, its concentration can be related to the concentration of the initial reactants, leading to a rate law of rate = k'[Cl2]^(1/2)[CHCl3], where k' is a constant that includes the equilibrium of Cl formation from Cl2.
Step-by-step explanation:
To determine the rate law for the overall reaction given the proposed mechanism Cl2(g) + CHCl3(g) → HCl(g) + CCl4(g), you should look at the slowest step of the mechanism as it will be the rate-determining step.
The proposed mechanism is:
-
Since step 2 is the slowest step, it will control the overall reaction rate. Therefore, the rate law is derived from this step and can be written as:
rate = k[Cl][CHCl3]
However, since Cl is an intermediate, its concentration is not initially present in the reaction mixture. We have to express its concentration in terms of reactants that are present at the start of the reaction. In this scenario, the concentration of Cl is governed by the pre-equilibrium established in the fast step 1, which means the concentration of Cl is proportional to the square root of the concentration of Cl2. This detail is standard for reactions where an intermediate is formed from the dissociation of a diatomic molecule.
Thus, the rate law accounting for the intermediate Cl is:
rate = k'[Cl2]1/2[CHCl3]
Where k' is a new rate constant that includes the equilibrium constant for the formation of Cl from Cl2.