Question

What percentage of a sample of nitrogen must be allowed to escape if its temperature, pressure and volume are to be changed from $600\text{K},3\text{atm}$ and $1.5$ litre to $400\text{K},0.7\text{atm}$ and $1.00$ litre respectively?

• A. 76.67%
• B. 40%
• C. 23.33%
• D. 60%

Answer 1

The correct option is A 76.67%

According to the given data,
Initial conditions: $P_1,V_1,T_1$
Final conditions: $P_2,V_2,T_2$

Calculating the number of moles of nitrogen at both the conditions
$n_1=\frac{3\times 1.5}{0.0821\times 600}$
$=0.0913$ moles
$n_2=\frac{0.7\times 1}{0.0821\times 400}$
$=0.0213$ moles

$\text{Hence, the fraction of the gas remaining is,}$
= $\frac{0.0213}{0.0913}$
= 0.2332
So percentage of gas escaped,
= $(1-0.2332)\times 100$ %
= 76.68%