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!

alienation, transformation, consumption, and the relativity of truth.

you can choose any one of these, they are all important themes.

these themes reflect the distinct sensibilities of both the modernist and postmodern aesthetic movements. (from google, you should paraphrase)

hope this !

- melanie