Question

Calculate the pressure exerted by 5 mol of $CO_{2}$ in one litre vessel at 47°C using van der Waal's equation. Also report the pressure of gas if it behaves ideally in nature. Given that a = 3.592 atm $ltr^{2}$ $mol^{-2}$. b = 0.042 litre $mol^{-1}$. And If volume occupied by $CO_{2}$ molecules is negligible, then also calculate the pressure exerted by one mol of $CO_{2}$ gas at 273K.

Answer 1

In the following question in order to calculate the pressure exerted by 5 moles of carbon dioxide 1 liter vessel at 40 degree Celsius we need to use the Van der Waals equation which is given by,

$(\frac{p+an^2}{v^2}) (v-nb) = nRT$

Pressure exerted by 5 moles,

$P=\frac{nRT}{V-nb} -\frac{an^2}{v^2}$

$=\frac{5(0.0821)(320)}{1-5(0.042)} -\frac{3.2592\times 5^2}{1^2}$

P=76.47 atm

Pressure exerted by 1 mole,

$P=\frac{1(0.0821)(320)}{1-1(0.042)}-\frac{3.592\times 1^2}{1^2}$

P=23.83 atm

As we can see the pressure exerted in the two cases is as follows pressure exerted by 5 moles = 70 6.4 ma pressure exerted by 1 mole = 23.83 atm