Question

A gas at $350K$ temperature and $15bar$ pressure has a molar volume that is 20% less than that for an ideal gas under the same conditions. The correct option about the gas and its compressibility factor $\left( Z \right)$ 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: Recall the formula for the compressibility factor and how it is related to the real and the ideal volumes of the given gas. Infer the nature of the forces based on the value of the compressibility factor.

Complete answer:
The compressibility factor here is denoted by $Z$ and is also sometimes described as the gas deviation factor. It shows us the correlation between the behaviour of an ideal gas and the deviation of the behaviour of a real gas. It is described as the ratio of the volume of a gas if it behaved like a real gas to the volume of the gas if it behaved like an ideal gas. The formula is shown as follows:
\[Z=\dfrac{{{V}_{real}}}{{{V}_{ideal}}}\]
In this problem, we can see that the volume of the gas if it behaved ideally is more than that of the gas if it behaved like a real gas. If we had the values to substitute, we will get a value that is less than 1 since the numerator will be less than the denominator. So now we can easily rule out options C and D since they state that the compressibility factor is greater than 1.
Now, we know that if the value of $Z$ is lesser than 1, the attractive forces are dominant. The gas will only have a lower volume in real conditions when the attraction between two molecules will be greater and will cause the gas to be more closely packed and hence reduce the overall volume of the gas.

From these inferences, we can say that the correct answer to this question is ‘A. $Z<1$ and attractive forces are dominant’

Note:
Note that the basic inference if the value of $Z$ is less than 1 is that the attractive forces are dominant and if the value is greater than 1, then the repulsive forces are dominant since this will imply that ${{V}_{real}}$ has a greater value than ${{V}_{ideal}}$. All the other information given in the question is extra information that will be required only if we want to calculate specific values.