Question

What percentage of the 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 1.65litre to ${110}^{0}C$, 0.7 atm and 1.00 liter respectively?

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

Answer 1

The correct option is A $81.8\%$

$\begin{array}{c}\text{Let}{n}_i\text{and}{n}_f\text{be initial}\&\text{final moles of nitrogen}\\ \text{respectively.}\\ \because PV=nRT\\ \therefore 3\times 1.65=n_i\times R\times 493\\ \therefore n_i=\frac{4.95}{4.93R}\end{array}$

$\begin{array}{c}\text{Similarly,}\\ \begin{array}{cc}0.7\times 1& =n_f\times R\times 383\\ \therefore n_f& =\frac{0.7}{383R}\therefore \%\text{nitrogen}\end{array}\end{array}$

$\begin{array}{cc}\text{escaped}& =\frac{({\eta }_i-n_f)}{n_i}\times 100\\ & \Rightarrow \frac{(\frac{4.95}{493R}-\frac{0.7}{383R})}{\frac{4.95}{493R}}\times 100\\ & \Rightarrow 81.8\%\end{array}$