A reaction A B has the following time dependence for the concentration of [A] vs

Question

A reaction A B has the following time dependence for the concentration of [A] vs time. For t=(0 s, 5 s, 10 s, 15 s, 25 s) the concentration of [A]=(30.00 M, 14.32 M, 9.40 M, 7.00 M, 4.63 M). The initial concentration of [A] is the value at t=0 s.

(A)Calculate the values of the rate constant k assuming that the reaction is first order.
What is the value of k at 5 s? ________________s-1
What is the value of k at 10 s?________________ s-1
What is the value of k at 15 s? ________________s-1
What is the value of k at 25 s? ________________s-1

(B)Calculate the value of k assuming that the reaction is second order.

What is the value of k at 5 s? ________________M-1s-1
What is the value of k at 10 s? ________________M-1s-1
What is the value of k at 15 s? ________________M-1s-1
What is the value of k at 25 s? ________________M-1s-1

(C)Use your results from parts A and B above to decide what the order of the reaction is for your data. (Enter 1 or 2) ________________

(D)What is the concentration of [A] at time t=73 s? ________________M

Explanation / Answer

For the given reaction data for first order reaction kinetics,

(A) rate constants (k)

k at t = 5s = [ln(30) - ln(14.32)]/5 = 0.148 s-1

k at t = 10s = [ln(30) - ln(9.40)]/5 = 0.116 s-1

k at t = 15s = [ln(30) - ln(7)]/5 = 0.097 s-1

k at t = 25s = [ln(30) - ln(4.63)]/5 = 0.075 s-1

(B) value of k for second order kinetics

k at t = 5s = [(1/14.32) - (1/30)]/5 = 0.0073 M.s-1

k at t = 10s = [(1/9.40) - (1/30)]/10 = 0.0073 M.s-1

k at t = 15s = [(1/7) - (1/30)]/15 = 0.0073 M.s-1

k at t = 25s = [(1/4.63) - (1/30)]/25 = 0.0073 M.s-1

(C) The order for the reaction is second-order as the rate constant values remain unchanged for second order kinetics calculations in (B).

(D) concentration of [A] at t = 73s

(1/[A]) = (1/30)] + 0.0073 x 73

[A] = 1.77 M

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