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. $10minutes$
• B. $20minutes$
• C. $30minutes$
• D. $40minutes.$

Answer 1

Answer: (B)

Let initial concentration $(a)be1.$ 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 $(ii)by(i),$
$\frac{t_{1/16}}{10}=\frac{log16}{log4}$
$t_{1/16}=10\times \frac{1.204}{0.6021}=20minutes$