Question

$N_2O_5$ decomposes to $NO_2$ and $O_2$ and follows first order kinetics. After $50$ minutes, the pressure inside the vessel increases from $50\, mm\, Hg$ to $87.5\, mm\, Hg.$ The pressure of the gaseous mixture after $100$ minute at constant temperature will be :

• A. $175.0 \,mm\,Hg$
• B. $116.25 \,mm\,Hg$
• C. $136.25 \,mm\,Hg$
• D. $106.25\, mm\,Hg$

Answer 1

Answer: (D)

The decomposition reaction is



We know $a=50\, mm\, Hg$

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

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

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

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

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

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

$k t=2.303 \log 2$

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

At $100\, min\, k t=2.303 \log \left(\frac{a}{a-y}\right)$

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

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

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

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

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

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

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

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

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

$= 50+\frac{3}{2} \times 37.5=106.25\, mm\, Hg$