Question

(a) Calculate the pressure exerted by $5moles$ of $C{O}_2$ in the one-liter vessel at ${47}^{\circ }C$ using van der Waals' equation. Also, report the pressure of the gas if it behaves ideally in nature. Given, that $a=3.592atmlitr{e}^{2}mo{l}^{-2},b=0.0427litremo{l}^{-1}$.
(b) If volume occupied by $C{O}_2$ molecules is negligible, then calculate the pressure exerted by one mol of $C{O}_2$ gas at $273K$.

Answer 1

$\left(a\right)$ $5$ moles of ${CO}_2$ in $1l$ vessel of $47°C.$

$n=5,v=1l,t=273.15+47=320.15k$

vanderwaal's equation of state, $a=3.592b=0.0427$

$(p+a\frac{n^2}{v^2}\left)\right(V-nb)=nrt$

$(p+3.592\times \frac{5^2}{1^2}\left)\right(1-5\times 0.0427)=5\times 0.0821\times 320.15$

$(p+89.8)=167.1$

$Pressure,P=77.297atm$

$\left(b\right)$ Volume occupied by $C{O}_2$ gas is negligible $(b=0).$

vander waal's equation for $1$ mole of gas is, $(p+\frac{a}{v^2}\left)\right(v-b)=nrt⟶(i\left)\right(p+\frac{a}{v^2}\left)\right(v)=nrtP=\frac{RT}{v}-\frac{a}{v^2}$

Using $R=0.0821,T=273K,v=22.4litre$ for $1$ mole of an ideal gas.

$P=\frac{0.0821\times 273}{22.4}-\frac{3.592}{{22.4}^2}=0.9934atm$