The following mechanism has been proposed for the gas-phase reaction of chloroform (CHCl3) and chlorine. What rate law does this mechanism predict?

Question

Cl2 ⇌ 2Cl (fast, reversible)

Cl + CHCl₃ → HCl + CCl₃ (slow)

Cl + CCl₃ → CCl₄ (fast)

(Choose from the list below and enter your answers in alphabetical order, e.g. ABC ).

A) k

B) [CHCl₃]

C) [CCl₃]

D) [HCl]

E) [Cl₂]

F) [Cl]

G) [Cl]^1/2

H) [CHCl₃]^1/2

I) [CCl₃]^1/2

J) [HCl]^1/2

K) [Cl₂]^1/2

L) [Cl]²

M) [CHCl₃]²

N) [CCl₃]²

O) [HCl]²

P) [Cl₂]²

Answer 1

I can't make out what the answers are supposed to be, but the rate limiting step is the slow step and has the rate r = k[Cl][CHCl₃]

The first step is a fast equilibrium so K_eq = [Cl]²/[Cl₂] and [Cl] = sqrt(K_eq[Cl₂]

subbing in for [Cl] in reaction rate expression:

r = ksqrt(K[Cl₂])[CHCl₃]

so r = k'[Cl₂]^1/2[CHCl₃]