Question

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

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

Answer 1

Answer: (A)

$81.8$%

Let $n_i$ and $n_f$ be initial & final moles of nitrogen respectively.

$\because PV=nRT$

$\therefore 3\times 1.65=n_i\times R\times 493$

$n_i=\frac{4.95}{493R}$

Similarly, $0.7\times 1=n_f\times R\times 383$

$\therefore n_f=\frac{0.7}{383R}$

$\therefore \%$ nitrogen escaped$=\frac{(n_i-n_f)}{n_i}\times 100$

$=\frac{(\frac{4.95}{493R}-\frac{0.7}{383R})}{\frac{4.95}{493R}}\times 100$

$=81.8\%$ $\because R=0.082057L.atm.K^{-1}.mo{l}^{-1}$

Hence, the correct option is $A$