Question

$N_2{O}_5$ decomposes to $N{O}_2$ and $O_2$ and follows first order kinetics. After $50$ minutes, the pressure inside the vessel increases from $50mmHg$ to $87.5mmHg.$ The pressure of the gaseous mixture after $100$ minute at constant temperature will be :

• A. $175.0mmHg$
• B. $116.25mmHg$
• C. $136.25mmHg$
• D. $106.25mmHg$

Answer 1

Answer: (D)

The decomposition reaction is



We know $a=50mmHg$

At $t=t_{\text{50min }}.a-x+2x+\frac{1}{2}x=87.5$

$a+\frac{3}{2}x=87.5$

$\frac{3}{2}x=87.5-50=37.5$

$\Rightarrow x=\frac{37.5\times 2}{3}=25$

For first order reaction, $kt=2.303\log \left(\frac{a}{a-x}\right)$

At $50min,kt=2.303\log \left(\frac{50}{50-25}\right)$

$kt=2.303\log 2$

$\Rightarrow k=\frac{2.303\times 0.3010}{50}$

At $100minkt=2.303\log \left(\frac{a}{a-y}\right)$

$100\times \frac{2.303\times 0.3010}{50}$

$=2.303\log \left(\frac{50}{a-y}\right)$

$2\times 0.3010=\log \left(\frac{50}{a-y}\right)$

$\frac{50}{a-y}=4$

$a-y=\frac{50}{4}=12.5$

$50-y=12.5\Rightarrow y=37.5$

Therefore, total pressure at $100min$ can be calculated as

Total pressure $=a-y+2y+\frac{1}{2}y$

$=a+\frac{3}{2}y$

$=50+\frac{3}{2}\times 37.5=106.25mmHg$