The following data were measured for the reaction BF3 (g) + NH3 (g) →F3BNH3 (g) : Experiment [BF3] (M) [NH3] (M) Initial Rate (M/s) 1 0.250 0.250 0.2130 2 0.250 0.125 0.1065 3 0.200 0.100 0.0682 4 0.350 0.100 0.1193 5 0.175 0.100 0.0596 Part A What is the rate law for the reaction?

A. rate=k[BF3]2[NH3]

B. rate=k[BF3][NH3]

C. rate=k[BF3][NH3]2

D. rate=k[BF3]2[NH3]2

The right answer is "B": rate = k[BF3][NH3]

Explanation:

Let's begin writting the generic rate law

rate = k[BF3]ᵃ[NH3]ᵇ

I will rewrite the data provided for clarification:

Experiment [BF₃] (M) [NH₃] (M) initial rate (M/s)

1 0.250 0.250 0.2130

2 0.250 0.125 0.106

3 0.200 0.100 0.0682

4 0.350 0.100 0.1193

5 0.175 0.100 0.0596

For experiments 1 and 2 the reaction rate laws can be written as follows:

v₁ = k ([BF3]₁) ᵃ ([NH3]₁) ᵇ (The subscripts indicate the number of experiment)

v₂ = k ([BF3]₂) ᵃ ([NH3]₂) ᵇ

we can write [BF3]₁ and [NH3]₁ in terms of [BF3]₂ and [NH3]₂ respectively:

[BF3]₁ = [BF3]₂

[NH3]₁ / [NH3]₂ = 0.250 M / 0. 125 M = 2. Then:

[NH3]₁ = 2[NH3]₂

Then, replacing in v₁:

v₁ = k ([BF3]₂) ᵃ (2[NH3]₂) ᵇ

If we divide v₁ / v₂:

v₁ / v₂ = k ([BF3]₂) ᵃ (2[NH3]₂) ᵇ / k ([BF3]₂) ᵃ ([NH3]₂) ᵇ (distributing the exponent):

v₁ / v₂ = k ([BF3]₂) ᵃ 2ᵇ ([NH3]₂) ᵇ / k ([BF3]₂) ᵃ ([NH3]₂) ᵇ (cancelating terms that are equal)

v₁ / v₂ = 2ᵇ (applying ln in both sides of the equation)

ln (v₁ / v₂) = ln 2ᵇ (applying logarithmic property)

ln (v₁ / v₂) = b ln 2

ln (v₁ / v₂) / ln 2 = b

b = ln ((0.2130 M/s) / (0.106 M/s)) / ln 2 = 1

The same could be done using experiment 4 and 5 (I choose them because [BF₃]₄ = 2 [BF₃]₅ and it makes calculation easier, but you can choose every combination you want):

v₄ = k ([BF3]₄) ᵃ ([NH3]₄) ᵇ

v₅ = k ([BF3]₅) ᵃ ([NH3]₅) ᵇ

[BF3]₄ = 2 [BF3]₅ and [NH3]₄ = [NH3]₅

Replacing in the equation v₄:

v₄ = k (2[BF3]₅) ᵃ ([NH3]₅) ᵇ = k 2ᵃ ([BF3]₅) ᵃ ([NH3]₅) ᵇ

v₅ = k ([BF3]₅) ᵃ ([NH3]₅) ᵇ

v₄ / v₅ = k 2ᵃ ([BF3]₅) ᵃ ([NH3]₅) ᵇ / k ([BF3]₅) ᵃ ([NH3]₅) ᵇ

v₄ / v₅ = 2ᵃ

ln (v₄ / v₅) = a ln 2

ln (v₄ / v₅) / ln 2 = a

ln ((0.1193 M/s) / (0.0596 M/s)) / ln 2 = a = 1

The right answer is "B".

Have a nice day!