Question

Method of Initial Rates Practice: You've been tasked with finding the rate constant, k, of a reaction that has the following rate law:

rate = k [E]^y [F]

Under conditions where [F]>>[E] such that [F] is a constant, you measured the rate of the reaction at four different initial concentrations of [E] and calculated the initial reaction rate of each reaction. The data are given below.

Trial	[E] (× 10-6 M)	[F] (M)	Initial Rate (× 10-6 M/s)
1	10.0	0.15	0.0482
2	8.0	0.15	0.0440
3	6.0	0.15	0.0310
4	4.0	0.15	0.0190

Using these data, determine the order of the reaction with respect to [E] and rate constant for the given reaction. The table below will help. Be sure to show a sample calculation to determine y and a sample calculation for k.

Would someone be able to explain this to me? I'm so confused. Thanks so much!

Trials Compared	Ratio of [E]	Ratio of Initial Rates	Calculated Reaction Order	Average y Rounded to the Nearest Integer		Trial	k (Units?)	Average k ± Std. Dev. (Units?)
1/2						1
1/3						2
1/4						3
2/3						4
2/4
3/4

Answer 1

Trial compared	Ratio of [E]	Ratio of rate	Calculated order	Average
1/2	1.25	1.0955	0.4086	0.98 = 1
1/3	1667	1.5548	0.8639
1/4	2.5	2.5368	1.016
2/3	1.33	1.41	1.205
2/4	2	2.316	1.211
3/4	1.5	1.63	1.206

The order of reaction is 1.

This is first order reaction.

Since [F] is constant the rate constant is K = k [F]

Therefore the equation becomes Rate = K [E]

Unit of rate constant is   s^-1

Trial	K	Average K
1	0.0048	0.005
2	0.0055
3	0.0052
4	0.0047

The average value of rate constant is 5 x 10^-3 s^-1

Sample calculation to find y:

Rate1/Rate2 = {kE₁^y F}/{kE2^y F}

y =[ log R1/R2]    / [log E1/E2] = log 1.0955/ log 1.25 = 0.4086

Sample calculation of K

Rate = K [E]

K = Rate / [E]

For trial 1 K = 0.0482 x 10^-6 /10 x 10^-6   = 0.00482 s^-1