Determine Rate Law: Initial Rates

Question

The following initial rate data are for the reaction of UO₂⁺ with hydrogen ion in aqueous solution:

2 UO₂⁺ + 4 H⁺U⁴⁺ + UO₂²⁺ + 2 H₂O

Experiment	[UO2+]o, M	[H+]o, M	Initial Rate, M s-1
1	3.85×10-3	0.346	8.41×10-4
2	7.70×10-3	0.346	3.36×10-3
3	3.85×10-3	0.692	1.68×10-3
4	7.70×10-3	0.692	6.73×10-3

Complete the rate law for this reaction in the box below.

Use the form k[A]^m[B]ⁿ , where '1' is understood for m or n and concentrations taken to the zero power do not appear. Don't enter 1 for m or n.

Rate =

From these data, the rate constant is _________M^-2s^-1.

Answer 1

Compare expt. 1 and 2: [UO₂] doubles and [H⁺] is constant. Rate increases 4x which means the reaction is 2nd order in UO₂.

Compare expt. 2 and 4: [H⁺] doubles and [UO₂] is constant. Rate increases 2x which means the reaction is 1st order in H⁺.

Rate = k[UO₂]²[H⁺]

To find the rate constant, choose any experiment, and solve for k. We'll use experiment 4:

6.73x10^-3 Ms^-1 = k [7.7x10^-3 M]²[0.692 M]

k = 6.73x10^-3 Ms^-1 / [7.7x10^-3 M]²[0.692 M]

k = 164 M^-2s^-1

(check the math to be sure)