Question

What percent of a sample of nitrogen must be allowed to escape if its temperature, pressure and volume are to be changed from ${273}^{o}C,3.00atm$, and $1.65L$ to $0^{o}C,0.75atm$ and $0.55L$.

• A. $16.67\%$
• B. $83.33\%$
• C. $75.00\%$
• D. $25.00\%$

Answer 1

The correct option is B $83.33\%$

According to puestion,

The initial condition of the system has

$T_1={220}^{\circ }C=493K,P_1=3\text{atm,}{V}_1=1.65l$

The final conditim of the system has

$T_2={110}^{\circ }C=383K,P_2=0.07atm,V_2=1\cdot OVL$

$\begin{array}{cc}PV& =nRT\\ \frac{M_2}{n_1}& =\frac{P_2{V}_2}{R{T}_2}\times \frac{R{T}_1}{P_1{V}_1}\\ & =\frac{0.07\times 1\times 493}{3\times 1.05\times 383}=0.1677\end{array}$

percentage of the fraction of moles $=0.1677\times 100$

$=16.77$

Now the percentage of sample left

$\begin{array}{cc}& =100-16.77\\ =& 83.33\%\end{array}$

Corect Answer - B