Exam

NEET

Year

2004

Subject

Chemistry

Chapter

Chemical Kinetics

NEET 2004 · Chemistry · Chemical Kinetics

The rate of a first order reaction is 1.5 × 10^ -2 ~mol ~L^ -1...

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

Step-by-step solution

Let the reaction be $$\begin{aligned}& \mathrm{A} \stackrel{k}{\longrightarrow} \text{ Product }\\ & \text{ Rate }=k[\mathrm{~A}]\\ & 1.5 \times10^{-2} \mathrm{~mol} \mathrm{\textrm {L } ^ { - 1 } \mathrm{ min } ^ { - 1 } = k [ 0 . 5 ]}\\ & k=\frac{1.5 \times 10^{-2}}{0.5}\\ &=3 \times10^{-2} \mathrm{~min}^{-1}\\ & t_{1/2}=\frac{0.693}{k}\\ & \Rightarrow \quad t_{1/2}=\frac{0.693}{3 \times 10^{-2}}\\ &=0.231 \times10^2 \mathrm{~min}\\ & \Rightarrow \quad t_{1/2}=23.1 \mathrm{~min} \end{aligned}$$Related Theory Decay profiles for first-order reactions with large and small rate constants