Question

What percent of a sample of nitrogen must be allowed to escape if its temperature, pressure and volume are to be changed from ${220}^{0}C$, 3 atm and 1.65 litre to ${110}^{0}C$, 0.7 atm and 1.00 litre respectively?

• A. 81.8%
• B. 71.8%
• C. 76.8%
• D. 86.8%

Answer 1

The correct option is A 81.8%

Let us consider the problem:

Initial condition

$T_1={220}^{0}C=493$

$P_1=3atm$

$v_1=1.65L$

Final conditions

$T_2={110}^{0}C=383K$

$P_1=0.07atm$

$V_2=1.00L$

Therefore,

$n_1=\frac{p_1{v}_1}{R{T}_1}$

$=\frac{3\times 1.65}{R\times 493}$

similarly,

$n_2=\frac{0.7\times 1}{R\times 383}$

Hence

Fraction of the gas remaining ,

$\frac{n_2}{n_1}=\frac{0.7\times 1\times 493}{3\times 1.65\times 393}$

therefore

Fraction of gas escaped=$\mathrm{1.0.182}$

$=808$

$=81.8$

Hence the $81.8$ of nitrogen gas should be allowed to escape.