Question

$200ml$ of $O_2$ gas maintained at $700mm$ pressure and $250ml$ of $N_2$ gas maintained at $720mm$ pressure are put together in one-litre flask.If the temperature is kept constant, the final pressure of the mixture in mm is:

• A. $450$
• B. $320$
• C. $632$
• D. $316$

Answer 1

The correct option is B $320$

According to Boyle's law, at constant temperature,

$PV=\text{constant}$

$\therefore PV=P^{\prime }{V}^{\prime }$

whereas,

$P$ and $V$ are partial pressure and volume of the gas respectively and $P^{\prime }$ is the partial pressure of the same gas at different volume.

Therefore,

For $N_2$	For $O_2$
$P=700\text{mmHg}$ $V=200mL$ $P^{\prime }=p_{N_2}$ $V^{\prime }=1L=1000mL$ From ${eq}^n\left(1\right)$, we have $700\times 200=p_{N_2}\times 1000$ $\Rightarrow p_{N_2}=140\text{mmHg}$	$P=720\text{mmHg}$ $V=250mL$ $P^{\prime }=p_{O_2}$ $V^{\prime }=1L=1000mL$ From ${eq}^n\left(1\right)$, we have $720\times 250=p_{O_2}\times 1000$ $\Rightarrow p_{O_2}=180\text{mmHg}$

According to Dalton's law of partial pressure, total pressure of the mixture is equal to the sum of partial pressure of the individual gases.

$\therefore p_{mix.}=p_{N_2}+p_{O_2}$

$\Rightarrow p_{mix.}=(140+180)\text{mmHg}=320\text{mmHg}$

Hence, the final pressure of the mixture in mm will be $320$.