Question

Consider the reaction CHCl3(g) + Cl2(g) ⟶ CCl4(g) + HCl(g).

Use the following rate data to determine the order of the reaction with respect to Cl2

    [CHCl3] (M)                 [Cl2] (M)             Initial Rate (M/s)

    0.010                           0.010                           0.0035

    0.020                           0.010                           0.0070

    0.020                           0.020                           0.0099

1

2

1.4

0.5

Answer 1

The reaction is half-order in [Cl₂].

For the reaction A + B ⟶ products

The rate law is r = k [A]^m[B]^n

Consider two Experiments 1 and 2.

r₂/r₁ = {k[A]₂^m[B]₂^n}/{k[A]₁^m[B]₁^n}

r₂/r₁ = {[A]₂/[A]₁}^m × {[B]₂/[B]₁}^n

_______________________

Let A = CHCl₃ and B = Cl₂

You must find two experiments in which [B] changes but [A] does not.

Consider Experiments 3 and 2.

r₃/r₂ = (0.020/0.020)^m × (0.020/0.010)^n = 0.0099/0.0070

1.0^m × 2.0^n = 1.41

2.0^m = 1.41

mlog2 = log 1.41

m = log1.41/log2 = 0.50 ≈ ½

The reaction is half-order in [Cl₂].