Question

A gas at 350K and $15bar$ has molal volume $20\% $ smaller than that of an ideal gas under the same conditions. The correct option about the gas and its compressibility factor $(Z)$ is:
A. $Z > 1$ and attractive forces are dominant
B. $Z > 1$ and repulsive forces are dominant
C. $Z < 1$ and attractive forces are dominant
D. $Z < 1$ and repulsive forces are dominant

Answer 1

Hint: In Ideal situation gas molecules are assumed to have no force attraction between themselves, but we know that is not true. Forces of attraction or forces of repulsion exist in real gases and hence the volume of a real gas varies from the volume that would be in case for an ideal gas

The formulae to calculate compressibility factor is $Z = \dfrac{{{V_{REAL}}}}{{{V_{IDEAL}}}}$ .
If the value of $Z < 1$ then attractive forces are dominant and if the value of $Z > 1$ then repulsive forces are dominant.

Complete step by step answer:
When we consider an ideal gas, we consider all the gas atoms as spherical in size. They have no intermolecular forces of attraction and they behave as if they are independent of each other. These are all assumptions.

We know that in real life do not behave independently and there is interaction between gases which cannot be assumed. Hence, we compare the assumed value of physical properties than an ideal gas should have with the observed physical properties of the real gases, the deviation tells us how the gas is behaving in nature.

When we talk about the compressibility factor, we consider how compressible the gases are, which is a factor of the volume these gases occupy.
If a gas occupies more volume than an ideal gas, it means that the molecules are further apart in real situations as compared to the hypothetical situation when they had no interaction with each other and hence we can say there are repulsive forces at play.
If a Gas occupies less space than an ideal gas, it means the gas molecules are closer now than they would have been if there was no interaction between the molecules and hence there are attractive forces.

From the information in the question
we know; ${V_{real}} = 20\% {V_{ideal}}$
Substituting this value in the formula
$Z = \dfrac{{{V_{REAL}}}}{{{V_{IDEAL}}}}$
we get, $Z = \dfrac{{20\% {V_{ideal}}}}{{{V_{ideal}}}}$
$Z = 0.2 \Rightarrow Z < 1$

So, Option C is correct.

Note: All these measurements have to be taken while keeping all the other factors constant.
For example, Mole fraction, Temperature, Pressure. If any one of these values changes, the values for an ideal gas will also vary.
The compressibility factor tells us how much the gas is deviating from ideal gas behaviour. This compressibility factor can be used when modifying ideal gas law for applying in real gases.