Question

In the van der Waal’s equation of gases, the kinetic equation for gas is modified with respect to:
A.Repulsive forces
B.Attractive forces between gaseous molecules
C.Actual volume of the gas
D.Pressure of the molecules

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 Waal’s equation of gases.

Complete step by step answer:
We can say the equation is fundamentally a modified version of the Ideal Gas Law that describes that gas contains point masses which undergo elastic collisions perfectly.
This equation can be obtained by assuming a real gas and 'changing ' it to an ideal gas.
Volume correction:
We know that for an ideal gas $PV = nRT$
Now in a real gas, we cannot ignore the molecular volume and thus let us consider that 'b' is the volume excluded (out of the volume of container) for the moving gas molecules per mole of a gas.
So, because of n moles of a gas the volume excluded would be taken as $nb$, a real gas present in a container of volume V has only available volume of $\left( {V - nb} \right)$ and this could be thought of as an ideal gas present in container of volume $\left( {V - nb} \right)$.
Therefore, the ideal volume is given as,
${V_i} = V - nb$
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 will be directly proportional to the extent of attraction present between the molecules that are striking the container wall and the molecules that are attracting these.
Thus, $p\alpha \dfrac{n}{v}$ (Concentration of molecules that are striking the walls of container)
$P\alpha \dfrac{n}{v}$ (Concentration of molecules that are attracting these molecules)$\to p\alpha \dfrac{{{n^2}}}{{{v^2}}}$
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”.
The increased attractions between the molecules of gas is reflected by the higher value of “a”.
So, the ideal pressure is written as,
${P_i} = P + \dfrac{{a{n^2}}}{{{v^2}}}$
Here n represents the moles of real gas.
V=volume of the gas
The proportionality constant that depends on gas nature is represented as “a”.
We can substitute the values of ideal volume and ideal pressure in ideal gas equation, 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 waal’s constant is represented by a and b.
n represents the moles of the gas.
We can see in the van der Waal’s equation of gases, we can modify the kinetic equation for gas with respect to the actual volume of the gas and pressure of the molecules.

So, the correct answer is Option C,D .

Note:
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.