Question

The rate constant of a first order reaction is $6.9 \times 10^{-3} \,s ^{-1}$. How much time will it take to reduce the initial concentration to its $1 / 8^{\text {th }}$ value?

• A. $100\, s$
• B. $200\, s$
• C. $300\, s$
• D. $400\, s$

Answer 1

Answer: (C)

$[ A ]=[ A ]_{0}\left(\frac{1}{2}\right)^{n}$
where $[A]_{0}=$ initial concentration
$\frac{1}{8}=1\left(\frac{1}{2}\right)^{n} ; n=3 $
$t_{1 / 2}=\frac{0.693}{6.9 \times 10^{-3}}=100 \sec$
$\therefore T=n \times t_{1 / 2}=3 \times 100=300 \sec$