Question

Substance A undergoes a first order reaction A  B with a half- life of 20 min at 25 °C. If the initial concentration of A ([A]◦ ) in a sample is 2.7 M, what will be the concentration of A after 60 min?

Answer 1

The concentration of A will be 0.34 mol·L⁻¹ after 60 min.

In a first-order reaction, the formula for the amount remaining after n half-lives is

$\text{[A]} = \frac{\text{[A]}_{0}}{2^{n}}$

If $t_{\frac{1}{2}} = \text{20 min}$

$n = \frac{t}{t_{\frac{1}{2}}} = \frac{\text{60 min}}{\text{20 min}}= \text{3.0}$

∴ $\text{[A]} = \frac{\text{2.7 mol/L}}{2^{3.0}} = \frac{\text{2.7 mol/L}}{8.0} = \textbf{0.34 mol/L}$