Question

A.) Two moles of ammonia gas are enclosed in a five litre flask at 27oC. Calculate the pressure exerted by the ammonia gas assuming that i) The gas behaves as a ideal gas; ii) The gas behaves as a real gas. ( a=3.592 , b= 0.0426)

B.) Using the van der waal’s equation , calculate the preesure exerted by one mole of carbon dioxide. When it occupies a volume of 0.05 litre at 100 degree C, given that a=3.592 ,b=0.0426 and R=0.0821 litre atmosphere/degree mole.

Answer 1

$\LARGE\underline{\blue{\mathrm{Answer}}}:-$

$\huge\bf{(A)}$

$\underline{\sf{Given}}:-$

• Number of moles (n) = 2 moles
• Volume of gas (V) = 5 L
• Temperature of gas (T) = 27°C = 300K

(i)For ideal gas ,the pressure exerted:

$\large\boxed{\mathrm{PV = nRT}}$

$\implies P\times V = n\times R\times T$

$\implies P\times 5L = 2\times 0.082 L-atm/mol-K \times 300K$

$\implies\bf{ P = 9.84\: atm}$

(ii)For real gas , the pressure exerted is :

$\large\boxed{\mathrm{(P+ \frac{a {n}^{2} }{ {V}^{2} } )(V-nb)=nRT}}$

$\footnotesize\implies (P+ \frac{3.592\times {2}^{2} }{ {5}^{2} } )(5 - 2\times 0.0426)=2\times 0.082 \times 300$

$\implies\bf{ P \approx 9.435 \:atm}$

$\huge\bf{(B)}$

$\underline{\sf{Given}}:-$

• Number of moles of Carbon-dioxide(n) = 1 mole
• Volume (V)= 0.05 L
• Temperature (T) = 100°C = 373 K
• additional pressure (a) = 3.592
• reduced volume (b) = 0.0426
• Gas constant (R) = 0.0821 L-atm/mol-K

Using Van der waals Equation, we get

$\sf{(P + \frac{a {n}^{2} }{ {V}^{2} } )(V - nb) = nRT}$

$\footnotesize\implies (P+ \frac{3.592\times {1}^{2} }{ {0.05}^{2} } )(0.05 - 1\times 0.0426)=1\times 0.082 \times 373$

$\implies \bf{P \approx 2,701.48 \:atm}$