Question

The half-life model is often used as a representation of a first order reaction because half-life is inversely proportional to the rate constant and half-life is independent of concentration.
Based on this knowledge, calculate the half-life for a first order reaction whose rate constant is $2.31\times {10}^{-2}{\sec }^{-1}$.

• A. $30.0sec$
• B. $0.0300sec$
• C. $180.sec$
• D. $0.180sec$

Answer 1

Answer: (A)

$30.0sec$

Consider a reaction which is $1^{st}$ order,

$A⟶B\therefore Rate\left(R\right)=K\left[A\right]\therefore \frac{-d\left[A\right]}{dt}=K\left[A\right]\therefore {\int }_{A_o}^{\frac{A_o}{2}}\frac{-d\left[A\right]}{\left[A\right]}{\int }_{t_o}^{t_{1/2}}Kdt\therefore \frac{-ln\left[\frac{A_o}{2}\right]}{A_o}=K{t}_{1/2}\therefore t_{1/2}=\frac{1}{K}\ln 2\therefore t_{1/2}=\frac{0.693}{K}=\frac{0.693}{2.31\times {10}^{-2}{sec}^{-1}}\therefore t_{1/2}=30sec$