Question

Assertion- $C{{H}_{4}}$ and $C{{O}_{2}}$ have the value of Z (Compressibility factor) less than one.
Reason- Z < 1 is due to repulsive forces among the molecules.
(A) Both assertion and reason are true, reason is the correct explanation of assertion.
(B) Both assertion and reason are true, reason is the incorrect explanation of assertion.
(C) Assertion is true but reason is false
(D) Assertion and reason both are false
(E) Assertion is false but reason is true

Answer 1

Hint: The compressibility factor tells us about the deviation of a real gas from ideal behavior. The value of compressibility factor Z for an ideal gas is 1. Any value of Z other than 1 shows non-ideal behavior.

Complete step by step solution:
Let’s look at the answer:
First let us see the assertion statement. $C{{H}_{4}}$and $C{{O}_{2}}$have the value of Z (Compressibility factor) less than one.
*We know that the attraction forces in both these gases are more. Therefore, the value of Z will be less than 1. So, the assertion statement is true.
Now, let’s look at the reason. It states that Z<1 is due to repulsive forces among the molecules.
*The deviation of a gas from ideal behavior is due the types of forces present in the gas. In an ideal gas it is assumed that no forces of attraction or repulsion are present. This is in accordance to one of the postulates of the kinetic theory of gases.
*If the repulsive forces dominate then the value of Z will be greater than 1. And if the attractive forces dominate then the value of Z will be less than 1. And if no repulsive or attractive forces are present then the value of Z will be equal to 1.
Now, it is given that Z<1 is due to repulsive forces among the molecules which is incorrect.
Hence, the assertion is correct but the reason is incorrect.
Hence, the answer is option (C).

Note: A gas can be easily liquefied if Z < 1 as the volume of the gas will be less than the ideal volume. Whereas a gas is difficult to liquefy > 1 as the volume occupied by the gas is more than ideal volume,
Formula for Z
$Z=\dfrac{PV}{nRT}$