Use this information to write a rate law for this reaction, and calculate the value of the rate constant k.

Question

Some measurements of the initial rate of a certain reaction are given in the table below.

[N2]	[H2]	initial rate of reaction
1.87 M	1.78 M	25.0 M/s
1.87 M	0.403 M	1.28 M/s
3.98 M	1.78 M	113. M/s

Use this information to write a rate law for this reaction, and calculate the value of the rate constant k.

Round your value for the rate constant to 2 significant digits. Also be sure your answer has the correct unit symbol. 

rate = k

k =

Answer 1

Trial 2 vs. trial 1: [N₂] is constant; [H₂] increases 4.42x. Rate increases 19.5x. 2nd order in H₂.

Trial 1 vs. trial 3: [H₂] is constant; [N₂] increases 2.1x. Rate increases 4.5x. 2nd order in N₂.

Rate law:

Rate = k[N₂]²[H₂]²

Using values in trial 1, compute the value of k:

25.0 M/s = k[1.87 M]² [1.78 M]²

25.0 M/s = 11.1 M⁴k

k = 2.3 M^-3s^-1

Answer 2

assume a reaction rate of the form r = k[N₂]^b[H₂]^m

Take the ratio of r₂/r₁ = ( [H₂]₂/[H₂]₁)^m because k's and [N₂]'s cancel

so 1.28/25 = (.403/1.78)^m or .0512 = (.2264)^m Solving for m, you get 2 Usually, you can just see the power, but the formal way to do it is m = ln(.0512)/ln(.2264)

Use r₃/r₁ = ([N₂]₂/[N₂]₁) the same way to find n

In order to find k, use any line of data in the reaction rate with the powers obtained above and solve for k.