Question

The thermal decomposition of a compound is of first order. If a sample of the compound decomposes $50\%$ in $120$ min, in what time will it undergo $90\%$ decomposition?

• A. Nearly $ 240\min $
• B. Nearly $480\min $
• C. Nearly $ 450\min $
• D. Nearly $400\min $

Answer 1

Answer: (D)

The first order reaction is
$\Rightarrow k=\frac{2.303}{t} \log _{10}\left(\frac{a}{a-x}\right)$
For $50 \%$ decomposition,
$t=120\, \min a=100 (a-x)=100-50=50 \,k$
$=\frac{2.303}{120} \log _{10} \frac{100}{50}$ or
$k=\frac{2.303}{120} \log _{10} 2 k=\frac{2.303 \times 0.3010}{120}$
or $k=\frac{0.6931}{120}$
For $90\%$ decomposition $t=?$
$s a=100(a-x)=100-90=10$
$k=\frac{2.303}{t} \log _{10} \frac{a}{(a-x)} \frac{0.6931}{120}$
$=\frac{2.303}{t} \log _{10} \frac{100}{10} t$
$=\frac{2.303 \times 120}{0.6931}$
$t=398.76 \,\min$