Final answer:
The rate law predicted by the mechanism for the reaction between CHCl₃(g) and Cl₂(g) is rate = k[CHCl₃][Cl], where the rate-determining step is the slow reaction involving CHCl₃ and a Cl atom.
Step-by-step explanation:
The proposed mechanism for the reaction between CHCl₃(g) and Cl₂(g), producing CCl₄(g) and HCl(g), involves a fast equilibrium in which Cl₂ dissociates into two Cl atoms, followed by a slow reaction where CHCl₃ and a Cl atom form HCl and CCl₃, and finally a fast reaction in which CCl₃ reacts with another Cl atom to produce CCl₄. The rate-determining step is the slow step, which dictates the overall rate of reaction.
The rate law for this reaction would be written based on the slow step, which involves CHCl₃ and Cl. Since the concentration of Cl generated in the fast equilibrium step is not directly included in the rate law (due to its rapid formation and consumption), it's often expressed in terms of the reactants of the overall reaction.
Therefore, the rate law is predicted to be rate = k[CHCl₃][Cl], where k is the rate constant for the slow step. In practice, the actual concentration of Cl might be substituted by expressions involving other reactants, if Cl is assumed to be in a pre-equilibrium with those reactants.