Rate Law and Integrated Rate Law Problem {2013-07-03}

Under some set of conditions, ammonia gas and fluorine gas react to form nitrogen trifluoride gas and hydrogen gas at 8.73ºC. What is the correct rate law expression (including the rate law constant) given the following data:

Rxn #	[NH3]0	[F2]0	Rate (M/min)
1	0.274	0.218	1.841x10-2
2	0.274	0.436	7.362x10-2
3	0.822	0.436	2.209x10-1

The rate law expression for this reaction is:

Rate₀ = k[NH₃]₀^x [F₂]₀^y

Comparing Rxn #1 and #2:

y = 2, the reaction is 2^nd order with respect to fluorine concentration

Comparing Rxn #3 and #2:

x = 1, the reaction is 1^st order w.r.t. ammonia concentration

Plugging in values from Rxn #1 and solving for k...

1.841x10^-2 M/min = k (0.274M)¹ (0.218M)²

k = 1.42 M^-2min^-1

In Rxn #2, how much time must pass before [F₂] = 0.324M?

Plugging in to the 2^nd order integrated rate law expression...

t = 0.558 minutes

In Rxn #1, how much time must pass before [NH₃] = 0.217M?

Plugging in to the 1^st order integrated rate law expression...

t = 0.164 minutes