Question

The rate of first order reaction is $1.5 \times 10^{-2}$ mol $L^{-1} \, min^{-1}$ at 0.5 M concentration of the reactant. The half-life of the reaction is

• A. 0.383 min
• B. 23.1 min
• C. 8.73 min
• D. 7.53 min

Answer 1

Answer: (B)

23.1 min

Answer 2

For the first order reaction, \hspace10mm Rate \, \big(\frac{dx}{dt}\big)=k [A] [A] = concentration of reactant k - rate constant Given that \hspace15mm \frac{dx}{dt}=1.5 \times 10^{-2} \, mol \, L^{-1} \, min^{-1} \hspace20mm k= ? and [A] = 0.5 M $\therefore \, \, 1.5 \times 10^{-2}=k \times 0.5$ \therefore \hspace15mm k=\frac{1.5 \times 10^{-2}}{0.5} \hspace20mm =3 \times 10^{-2} \, min^{-1} For first order reaction, half-life period, $t_{1/2}=\frac{0.693}{k}=\frac{0.693}{3 \times 10^{-2}}$ \hspace30mm = 23.1\, min