Question

The Kinetics of the reaction 2 A -> 4X +Y is 1st order in A and overall 1st order. The half- life of this reaction is 2.4 hours at 30 degrees C.

A. Starting with 100g of A, how many grams will remain after period of 9.6 hours?

B. Starting with 300g of A, how many grams will remain after a period of 17 hours?

C. What period of time id required to reduce 4.2x10^11 molecules of A to 1.1 x 10^8 molecules?

Answer 1

Rate = k[A] The integrated rate law for the first order Reactions ln([A]_t) = -kt = ln[A]_0 Half life for first order reactions is ln(2)/t_1/2 = k k = ln(2)/2.4 hours = 0.289 hr^-1 (A) ln([A]^-_t) = -(0.289 hr^-1)(9.6 hr) + ln(100g) = -2.77 + 4.60 = 1.83 [A]_t = e^1.83 = 6.23 g remaining (B) ln[A]_t = -10.289 hr^-1)(17 hr) + ln(300 g) = 0.79 [A]_t = 2.209 remaining (C) ln([A]_t) - ln[A]_0 = -kt ln [A]_0/[A]_t = kt t = ln[[A]_0/[A]_t]/k = ln(4.2 times 10^10/1.1 times 10^8)/0.289 hr^-1 = 20.67 hr