Question

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

• A. 120 min
• B. 299 min
• C. 399 min
• D. 320 min

Answer 1

The correct option is C 399 min

Half life of reaction = 120 min
We know that,
For first order reaction,
$k=\frac{0.693}{t_{1/2}}$

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

First order reaction equation,
$t=\frac{2.303}{k}log\frac{a}{a-x}$

For 90% decomposition,
If $a=100,x=90$
$(a-x)=10$

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

$t=\frac{2.303}{5.77\times {10}^{-3}}log10=\frac{2.303}{5.77\times {10}^{-3}}=399min$

Thus, option (c) is correct.