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. 399 min
• B. 410 min
• C. 250 min
• D. 120 min

Answer 1

Answer: (A)

First calculate the values of $K$
$K=\frac{0.693}{T12}=\frac{0.693}{120}=5.77\times10^{-3} min^{-1}$
Now we know that for a first order reaction
$K=\frac{2.303}{t}log\left(\frac{a}{a-x}\right)$
Here the initial concentration $a = 100$ and $n = 90$
$\therefore 5.77\times10^{-3}=\frac{2.303}{t}log \frac{100}{100-90}$
$t=\frac{2.303}{5.77\times10^{-3}}log \left(\frac{a}{a-x}\right)$
Solving, $t = 399$ minute