Question

Which of the following statements are correct about half-life period?

• A. It is proportional to initial concentration for zero order
• B. Average life $=1.44\times$ half life; for first order reaction
• C. Time of 75% reaction is thrice of half-life period in first order reaction
• D. 99.9% reaction takes place in 100 minutes for the case when rate constant is $0.0693mi{n}^{-1}$ for first order reaction

Answer 1

Answer: (A), (B), (D)

99.9% reaction takes place in 100 minutes for the case when rate constant is $0.0693mi{n}^{-1}$ for first order reaction
It is proportional to initial concentration for zero order
Average life $=1.44\times$ half life; for first order reaction

For zero-order:

$t_{1/2}=\frac{[A{]}_0}{2k}$

For first order:
Average life is when $\left[A\right]=1/e[A{]}_0$
$t_{avg}=1/k$ and $t_{1/2}=\frac{0.69}{k}$
or $t_{avg}=1.44\times t_{1/2}$

For 75% reaction $\left[A\right]=0.25[A{]}_0$
Rate law: $\frac{A_t}{A_0}=e^{-kt}$
$0.25=e^{-0.69t/t_{1/2}}$
$t=2t_{1/2}$

For x% reaction, $\left[A\right]=(1-x/100)[A{]}_0$ and $t=100min$ and $k=0.0693mi{n}^{-}1$
$1-x/100=e^{-6.93}$
$x/100=0.999$
$x=99.9$%

Therefore A, B, D are correct