Question

At a certain temperature, the half-life of the first order decomposition of 2,4-cyclohexadienone (shown below) is 2.11 hr 2,4-cyclohexadienone phenol Answer the following questions about the decomposition of 2,4-cyclohexadienone and report all answers to three significant figures. 1. If the initial concentration of 2,4-cyclohexadienone is 8.04×10-2 M, calculate the time (in hr) required for the concentration of 2,4-cyclohexadienone to decrease to 38.4 % of the initial concentration. Submit Answer Tries o/s 2. If the initial concentration of 2,4-cyclohexadienone is 8.04×10-2 M, calculate the concentration (in M) after 1.35 hr. Submit Answer Tries o/3

Answer 1

1)

Given:

Half life = 2.11 hr

use relation between rate constant and half life of 1st order reaction

k = (ln 2) / k

= 0.693/(half life)

= 0.693/(2.11)

= 0.3284 hr-1

we have:

[A]o = 8.04*10^-2 M

[A] = 38.4 % of 8.04*10^-2 M = 3.087*10^-2 M

k = 0.3284 hr-1

use integrated rate law for 1st order reaction

ln[A] = ln[A]o - k*t

ln(3.087*10^-2) = ln(8.04*10^-2) - 0.3284*t

-3.478 = -2.521 - 0.3284*t

0.3284*t = 0.9571

t = 2.914 hr

Answer: 2.91 hr

2)

use integrated rate law for 1st order reaction

ln[A] = ln[A]o - k*t

ln[A] = ln(8.04*10^-2) - 0.3284*1.35

ln[A] = -2.521 - 0.3284*1.35

ln[A] = -2.964

[A] = e^(-2.964)

[A] = 5.161*10^-2 M

Answer: 5.16*10^-2 M