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_{(1)/(2)} = \text{20 min}\\`

`n = \frac{t}{t_{(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}`