Question

In a first order reaction, a substance is reduced to $\frac{1}{3^{rd}}$ in $100$ seconds. In how much time will it be reduced to $\frac{1}{9^{th}}$ ?

• A. $150s$
• B. $400s$
• C. $100s$
• D. $200s$

Answer 1

Answer: (D)

According to first order kinetic equation,
$K=\frac{2.303}{t}{\left(log\right)}_{10}\left(\frac{a}{a-x}\right)$
where $a=$ initial concentration
$x=$ change in the concent-
ration after time ${}^{\prime }{t}^{\prime }$
$k=\frac{2.303}{100}lo{g}_{10}\left[\frac{a}{\frac{a}{3}}\right]$
$k=\frac{2.303}{100}{\left(log\right)}_{10}\mathrm{3...}\left(1\right)$
$\frac{1}{9}$ part will be left at time t
$K=\frac{2.303}{t}{\left(log\right)}_{(10)}\left[\frac{a}{\frac{a}{9}}\right]$
$K=\frac{2.303}{t}lo{g}_{10}9$
$K=\frac{2.303}{100}log{3}^2$
$=\frac{2.303}{100}\cdot 2log3$
From equations $(i)$ and $(ii)$
$\frac{2.303}{100}lo{g}_{10}3=\frac{2.303}{t}lo{g}_{10}{3}^2$
$\frac{1}{100}=\frac{2}{t};t=200sec$