A reactant decomposes with a half-life of 129 s when its initial concentration is 0.380 M. When the initial concentration is 0.504 M, this same reactant decomposes with the same half-life of 129 s. A. What is the value and unit of the rate constant (k) for this reaction? B. What is the order of the reaction? a. 0. b. 1. c. 2

A) The rate constant is 0.0078 s^-1

B) The order of the reaction is 1

Explanation:

A) Rate constant (k) = Rate : final concentration

Rate = change in concentration/half-life

Initial concentration of reactant = 0.38 M

Half-life is the time taken for the reactant to decompose to half of its initial concentration = 129 s

Final concentration = 1/2 * 0.38 = 0.19 M

Change in concentration = 0.38 - 0.19 = 0.19 M

Rate = 0.19/129 = 0.0015 M/s

Rate constant (k) = 0.0015 M/s : 0.19 M = 0.0078 s^-1

B) Rate = kC^n

n is the order of the reaction

0.0015 = 0.0078*0.19^n

0.19^n = 0.0015/0.0078

0.19^n = 0.19

Log 0.19^n = Log 0.19

nLog 0.19 = Log 0.19

n = Log 0.19/Log 0.19 = 1