Question

At relatively high pressure, Vander Waals equation reduced to:
A.$PV = RT$
B.$PV = RT + a/V$
C.$PV = RT + Pb$
D.$PV = RT - a/{V^2}$

Answer 1

Hint: Firstly we have to know about real and Vander Waal gases and their expressions and then we can estimate the expression at high pressure or low volume .Vander Waal gas equation is a modified version of the ideal gas equation.

Complete step by step answer:
Gases is a state of matter that has no fixed shape and no fixed volume. Gases have low density than other state of matter such as solid and liquid.
Ideal gas is a theoretical gas composed of many randomly moving point particle that are not subject to interparticle interaction. The ideal gas concept is useful because it obey the ideal gas law, a simplified equation of state.
Generally , a gas behaves more like an ideal gas at higher temperature and lower pressure as the potential energy due to intermolecular forces becomes less significant compared with the particle kinetic energy. The ideal gas equation may be given as:
$PV = nRT$
P=pressure
V= volume
n= number of moles
R= gas constant
T= temperature
The ideal gas model ignores the interaction between them. These become important at low temperature and high pressure so more detailed models are needed. One such model is described by van der waal equation:
$\left( {p + {n^2}a/{V^2}} \right)\left( {V - nb} \right) = nRT$
a= parameter that gives a measure of attraction forces between the particle
b=parameter proportional to volume of particle.
Now, comes to the solution part:
We have,$\left( {p + a{n^2}/{V^2}} \right)\left( {V - nb} \right) = nRT$
For n=1 mole
$\left( {p + a/{V^2}} \right)\left( {V - b} \right) = RT$
At high pressure, which means pressure increases and the part of $a/{V^2}$ <<<$p$ is negligible.
Then, $p\left( {V - b} \right) = RT$
$ \Rightarrow pV - pb = RT$
$ \Rightarrow pV = pb + RT$ .
Hence, the correct option is C.

Note: The constant b is an indication of molecular volume, it could be used to estimate radius of an atom or molecule, modeled as a sphere.
Constants provide a correction for the intermolecular forces.