Question

A reaction that is of the first order with respect to reactant A has a rate constant 6 min⁻¹. If we start with [A]₀ = 0.5 mol dm⁻³, when would [A] reach the value 0.05 mol dm⁻³?

Options

• 0.384 min

• 0.15 min

• 3 min

• 3.84 min

Answer 1

0.384 min

Explanation:

For first order kinetics, the integrated rate law is,

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

where, k = rate constant = 6 min⁻¹, t = time

[A]₀ = initial concentration = 0.5 mol dm⁻³

[A]_t = concentration at time t = 0.05 mot dm⁻³

6 = `2.303/"t" log  0.5/0.05`

or t = `2.303/(6  "min"^-1) log  0.5/0.05`

= `2.303/(6  "min"^-1)`

= 0.384 min