Question

1. For the following second order reaction, the half-life is 52.4 and the [A]₀ = 3.04. Calculate the rate constant. 2 A →→ 3 B

2. Consider the following reaction.

aA +bB →→ cC

whose first and second half-lives are 20.9 and 20.9 minutes respectively. If the rate constant is equal to 0.03316 and [A]₀ = 10.66, calculate the [A] at t = 19.85 minutes.

Answer 1

1)

Given:

Half life = 52.4

use relation between rate constant and half life of 2nd order reaction

k = 1/([A]o*half life)

= 1/(3.04*52.4)

= 6.278*10^-3

Answer: 6.278*10^-3

2)

Since half life in constant, this is 1st order reaction.

we have:

[A]o = 10.66 M

t = 19.85 min

k = 3.316*10^-2 min-1

Given:

[A]o = 10.66 M

use integrated rate law for 1st order reaction

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

ln[A] = ln(10.66) - 3.316*10^-2*19.85

ln[A] = 2.366 - 3.316*10^-2*19.85

ln[A] = 1.708

[A] = e^(1.708)

[A] = 5.519 M

Answer: 5.52 M