Question

A real gas at its critical points has the value of $\frac{R{T}_c}{8P_c}=0.2L/mol$. (Where R is the gas constant). If this gas follows the equation P(V − nb) = nRT at STP, then find the volume (in litres) of the container in which 3 moles of this gas is occupied at STP. (Assume T= $0^{\circ }C$ and P=1 atm at STP)

Answer 1

$\frac{R{T}_c}{8P_c}=\frac{R\frac{8a}{27Rb}}{8\frac{a}{27b^2}}=b=0.2L/mol$
At STP, 1 mole of an ideal gas occupies 22.4 L.
Since (V-nb) is the volume occupied at an ideal condition. So, for 3 moles, we have,
$V-3b=22.4\times 3V=67.2+0.2\times 3$
$V=67.8L$