Question

In the corrections made to ideal gas equation for real gases, the reductions in pressure due to forces of attractions between the molecules is directly proportional to:
A.$\dfrac{n}{V}$
B.$\dfrac{{{n^2}}}{{{V^2}}}$
C.$V - nb$
D.$nb$

Answer 1

We have to know that an equation that is involving the relationship between the pressure, volume, temperature, and amount of real gases is known as van der Waals equation of gases. We have to remember that ideal gas equation is also referred as general gas equation which is represented by,
$PV = nRT$
Where,
P-Pressure of the system
V=Volume of the system
N=no. of moles
R= Gas constant
T= Temperature of the system

Complete step by step answer:
Pressure correction:
Let us consider that the real gas exerts a pressure P. The molecules which exert the force on the container would get attracted by molecules present on the immediate layer that are assumed not to be exerting pressure.
It could be seen that the pressure exerted by the real gas will be less than the pressure exerted by an ideal gas. The real gas experiences attractions by its molecules in the opposite direction. Thus, if a real gas exerts a pressure P, then an ideal gas will exert a pressure equal to $P + p$ (p represents the pressure lost by the gas molecules because of attractions).
This small pressure p would be directly proportional to the extent of attraction present between the molecules which are striking the container wall and the molecules that are attracting these.
Thus, $p \propto \dfrac{n}{v}$ (Concentration of molecules that are striking the walls of container)
$P \propto \dfrac{n}{v}$ (Concentration of molecules that are attracting these molecules) $\to p \propto \dfrac{{{n^2}}}{{{v^2}}}$
So we can write that,
$P = a\dfrac{{{n^2}}}{{{v^2}}}$
Here, the proportionality constant that depends on gas nature is represented as “a”.
So, the reduction in pressure because of the intermolecular force of attraction is proportional to $\dfrac{{{n^2}}}{{{V^2}}}$ .
Therefore, the option (B) is correct.
We can substitute the values of ideal volume and ideal pressure in ideal gas equation $PV = nRT$, the modified equation is written as,
$\left( {P + a\dfrac{{{n^2}}}{{{V^2}}}} \right)\left( {v - nb} \right) = nRT$
Here the pressure is represented by P.
The molar volume is represented by V.
The temperature of the given sample of the gas is written by T.
The gas constant is R.
Van der waals constant is represented by a and b.
n represents the moles of the gas.
Therefore, the option B is correct.

Note:
Now we can discuss about the some of the merits of van der Waals equation are,
-Predicts the behaviour of gases better than the ideal gas equation.
-Applicable to gases as well for all fluids.
Some of the demerits of van der Waals equation are,
-We can get more accurate results of all real gases only above critical temperature by this equation.
-The equation completely fails in the conversion phase of gas to the liquid below a critical temperature.