Question

Half-life of first-order reaction \[\ce{X -> Y + Z}\] is 3 minutes. What is the time required to reduce the concentration of 'X' by 90 % of it's initial concentration?

Options

• 9.969 minutes

• 4.12 minutes

• 9.105 minutes

• 12.05 minutes

Answer 1

9.969 minutes

Explanation:

t_1/2 = 3 min

∴ k = `0.693/"t"_(1//2) = 0.693/3` = 0.231 min^-1

[A]₀ = Original amount of reactant = 100

[A]_t = Reactant remaining unreacted = 100 - 90 = 10

For first order reaction,

t = `2.303/"k" log_10  (["A"]_0)/(["A"]_"t")`

`= 2.303/(0.231 "min"^-1) log_10  100/10` = 9.969 min