Question

For a first order reaction, the time taken to reduce initial concentration by a factor of $ 1/4$ is $ 10 $ minutes. The time required to reduce initial concentration by a factor of $ 1/16 $ will be

• A. $10\, minutes$
• B. $20\, minutes$
• C. $ 30\, minutes$
• D. $ 40\, minutes.$

Answer 1

Answer: (B)

Let initial concentration $(a) be 1.$ Then, final concentration $\left(a-x\right)=\frac{1}{4}$ ...(i) $\therefore t _{1/4}=\frac{2.303}{k} log \frac{1}{1/4}$
Similarly,$t _{1/16}=\frac{2.303}{k} log \frac{1}{1/16}$ ...(ii)
Dividing equation $(ii) by (i),$
$\frac{t_{1 /16}}{10}= \frac{log16}{log 4}$
$t_{1 /16} =10\times\frac{1.204}{0.6021} = 20\, minutes$