Question

A first order reaction with respect to reactant $A$ , has a rate constant $\text{6} \, \text{min}^{- 1} .$ If we start with $\left[\text{A}\right] = 0.5 \, \text{mol} \, \text{L}^{- 1}$ , when would $\left[\right.A\left]\right.$ reach the value $0.05 \, \text{mol} \, \text{L}^{- 1}$

• A. 0.384 min
• B. 0.15 min
• C. 3 min
• D. 3.84 min

Answer 1

Answer: (A)

We know that for first order kinetics
$k=\frac{2.303}{t}log\frac{a}{a - x}$
$\left(\text{a-x}\right) = 0.05 \, \text{mol} \, \left(\text{L}\right)^{- 1}$
$6=\frac{2.303}{t}log\frac{0.5}{0.05}$
or $\text{t} = \frac{2.303}{6} \text{log} \frac{0.5}{0.05} = \frac{2.303}{6} = 0.384 \, \text{min}$