Question

Determine the rate law, including the values of the orders and rate law constant, for the following reaction using the experimental data provided.
A + B yields products

Trial [A] [B] Rate
1 0.30 M 0.25 M 1.2 × 10-2 M/min
2 0.30 M 0.50 M 4.8 × 10-2 M/min
3 0.60 M 0.50 M 9.6 × 10-2 M/min

Answer 1

Answer:

Rate = (0.64 M²/min) [A]¹[B]²

Explanation:

1) Determination of the orders of A & B:

• The rate law of the reaction = k [A]ᵃ[B]ᵇ

where, k is the rate law constant,

a is the order of the reaction with respect to reactant A,

b is the order of the reaction with respect to reactant B.

This is initial rate method problem:

From trial 1 & 2:

• Reactant [A] has the same concentration in both trials, but [B] has different concentrations and the rate of the reaction changes, so the reaction rate depends on [B].

• From trial 1, Rate₁ = k [A₁]ᵃ[B₁]ᵇ, [1.2 × 10⁻² M/min] = k [0.30 M]ᵃ[0.25 M]ᵇ

• From trial 2, Rate₂ = k [A₂]ᵃ[B₂]ᵇ, [4.8 × 10⁻² M/min] = k [0.30 M]ᵃ[0.50 M]ᵇ

By dividing Rate₁ / Rate₂:

Rate₁ / Rate₂ = k [A₁]ᵃ[B₁]ᵇ / k [A₂]ᵃ[B₂]ᵇ

[1.2 × 10⁻² M/min] / [4.8 × 10⁻² M/min] = k [0.30 M]ᵃ[0.25]ᵇ / k [0.30 M]ᵃ[0.50 M]ᵇ

0.25 = [0.50]ᵇ

Taking log for both sides; log(0.25) = b log(0.5)

b = log(0.25) / log(0.5) = 2.

The reaction is second order with respect to reactant B.

By the same way for reactant A:

From trial 2 & 3:

• Reactant [B] has the same concentration in both trials, but [A] has different concentrations and the rate of the reaction changes, so the reaction rate depends on [A].

• From trial 2, Rate₂ = k [A₂]ᵃ[B₂]ᵇ, [4.8 × 10⁻² M/min] = k [0.30 M]ᵃ[0.50 M]ᵇ

• From trial 2, Rate₃ = k [A₃]ᵃ[B₃]ᵇ, [9.6 × 10⁻² M/min] = k [0.60 M]ᵃ[0.50 M]ᵇ

By dividing Rate₂ / Rate₃:

Rate₂ / Rate₃ = k [A₂]ᵃ[B₂]ᵇ / k [A₃]ᵃ[B₃]ᵇ

[4.8 × 10⁻² M/min] / [9.6 × 10⁻² M/min] = k [0.30 M]ᵃ[0.50 M]ᵇ / k [0.60 M]ᵃ[0.50 M]ᵇ

0.50 = [0.50]ᵃ

Taking log for both sides; log(0.50) = a log(0.5)

a = log(0.50) / log(0.50) = 1.

The reaction is first order with respect to reactant A.

• The rate law of the reaction will be: Rate = k [A]¹[B]²

• The overall order of the reaction is third order reaction.

2) Determining the rate law constant:

• Taking data of trial 1:

Rate = k [A]¹[B]²

[1.2 × 10⁻² M/min] = k [0.30 M]¹[0.25 M]²

k = [1.2 × 10⁻² M/min] / [0.30 M]¹[0.25 M]² = 0.64 M²/min.

So, the rate law will be: Rate = (0.64 M²/min) [A]¹[B]²