Chemical Kinetics

 22) 2ClO₂(aq) + 2OH^-(aq) ClO₃^-(aq) + ClO₂^-(aq) + H₂O(l)

       (a) Rate = k[ClO₂]^m[OH^-]ⁿ

             Rate1/Rate2 = 0.0248 M/s/0.00276 M/s = k x (0.060 M)^m x (0.030)ⁿ/k x (0.020 M)^m x (0.030)ⁿ

             8.99 = (0.060 M/0.020 M)^m = 3.00^m

             m = 2

             Rate2/Rate3 = 0.00276 M/s/0.00828 M/s = k x (0.020 M)^m x (0.030)ⁿ/k x (0.020 M)^m x (0.090)ⁿ

             0.333 = (0.030 M/0.090 M)ⁿ = 0.333 ⁿ

             n = 1

             Rate = k[ClO₂]²[OH^-]

       (b) Rate = k[ClO₂]²[OH^-]

             0.0248 M/s = k x (0.060 M)² x 0.030 M

             k = 0.0248 M/s/(0.060² x 0.030 M³) = 230 M^-2s^-1

       (c) [ClO₂] = 0.010 M          [OH^-] = 0.015 M

             Rate = k[ClO₂]²[OH^-]

             Rate = 2.3 x 10² M^-2s^-1 x (0.010 M)² x 0.015 M

             Rate = 3.4 x 10^-4 M/s