Question

The half-life period of a first-order reaction is 15 minutes. The amount of substance left after one hour will be:

• A. $\frac{1}{4}$ of the original amount
• B. $\frac{1}{8}$ of the original amount
• C. $\frac{1}{16}$ of the original amount
• D. $\frac{1}{32}$ of the original amount

Answer 1

Answer: (C)

$\frac{1}{16}$ of the original amount

For first order reaction,

$\frac{A_t}{A_0}=e^{-kt}$

$t_{1/2}=\frac{0.69}{k}$

$k=0.046mi{n}^{-1}$

$\frac{A_t}{A_0}=e^{-0.046\times 60}$

$\frac{A_t}{A_0}=\frac{1}{16}$

$A_t=\frac{A_0}{16}$

Hence, option A is correct.