A ( g ) → 2   B (   g ) + C ( g ) is a first order reaction. The initial pressure of the…

The final pressure of each component can be calculated as follows,

$$\begin{gathered} \mathrm{A}\left(\mathrm{g}\right)\to 2 \mathrm{B}( \mathrm{g})+\mathrm{C}\left(\mathrm{g}\right) \\ \mathrm{intial} 800 0 0 \\ \mathrm{At} \mathrm{time}=\mathrm{t} 800-\mathrm{p} 2\mathrm{p} \mathrm{p} \end{gathered}$$

$800 + 2\mathrm{p} = 1600$

$2\mathrm{p} = 800$

$\mathrm{p}= 400$

The first order reaction rate constant can be calculated as follows,

$\mathrm{K}=\frac{2.303}{10}\log \frac{800}{400}=\frac{2.303\times \log 2}{10}$

For $30$ min,

$\mathrm{K}=\frac{2.303}{30}\log \frac{\left(800\right)}{(800-\mathrm{y})}$

$\frac{2.303\times \log 2}{10}=\frac{2.303}{30}\log \left(\frac{800}{800-\mathrm{y}}\right)$

$\Rightarrow \left(\frac{800}{800-\mathrm{y}}\right)=8$

$100 = 800 – \mathrm{y}$

$\mathrm{y} = 700$

Total pressure after $30$ min

$(800 – \mathrm{y}) + \left(2\mathrm{y}\right) + \left(\mathrm{y}\right)$

$= 800 + 2\mathrm{y}$

$= 800 + 1400$

$= 2200 \mathrm{mm} \mathrm{Hg}$