Question

Thermal decomposition of a compound is of first order. If $50$ percent of a sample of compound is decomposed in $120$ mins, how long will it take for $90$ percent of compound to decompose?

• A. $299$ mins.
• B. $399$ mins.
• C. $99$ mins.
• D. $9.9$ mins.

Answer 1

Answer: (B)

$399$ mins.

According to half time period

$k=\frac{0.693}{t_{\frac{1}{2}}}$

$\Rightarrow \frac{0.693}{120}=5.77\times {10}^{-3}{min}^{-1}$

Here,

$(t_{\frac{1}{2}}=120mint)$

Now a first order reaction

$k=\frac{2.303}{t}\log \frac{1}{a-x}$

$a=100,x=90$

$\therefore 5.77\times {10}^{-3}=\frac{2.303}{t}\log \frac{100}{100-90}$

$t=\frac{2.303}{5.77\times {10}^{-3}}\log 10$

$=399min.$

This is the required answer.