Question

Consider the following:
Statement-I: If thermal energy is stronger than intermolecular forces, the substance prefers to be in gaseous state.
Statement-II: At constant temperature, the density of an ideal gas is proportional to its pressure.
The correct answer is

• A. Statement-I is correct, but Statement-II is not correct.
• B. Statement-I is not correct, but Statement-II is correct.
• C. Both Statement-I and Statement-II are correct.
• D. Both Statement-I and Statement-II are not correct.

Hint:

Gaseous state favored when thermal energy $>$ intermolecular forces. Ideal gas law: $P \propto \rho$ at constant T.

Answer 1

The Correct Option is C

Statement I: When thermal energy overcomes intermolecular forces, molecules can escape the condensed phases (liquid and solid) and enter the gaseous state. So, this statement is correct. Statement II: The ideal gas law is $PV = nRT$. Density ($\rho$) is mass ($m$) divided by volume ($V$), so $\rho = \frac{m}{V}$. Also, $n = \frac{m}{M}$, where $M$ is the molar mass. Substituting, we get $PV = \frac{m}{M}RT$, or $P = \frac{m}{V} \frac{RT}{M}$, which means $P = \rho \frac{RT}{M}$. At constant temperature, $P \propto \rho$. So, this statement is correct.