Question

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : At constant temperature and pressure, equal volumes of all gases contain the same number of molecules. Reason (R) : At constant temperature, the mean molecular energies of these gases will be equal. In the light of the above statements, choose the most appropriate answer from the options given below :

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

Mean molecular energy depends only on temperature ($T$), while the number of molecules depends on $P, V,$ and $T$.

Answer 1

The Correct Option is B

Concept:
• Avogadro's Law: Under the same conditions of temperature and pressure, equal volumes of all gases contain an equal number of molecules. This is the basis for Assertion (A).
• Kinetic Theory of Gases: The average kinetic energy (mean molecular energy) of a gas molecule depends only on the absolute temperature: $K.E._{avg} = \frac{3}{2}k_BT$.

Step 1: Evaluate Assertion (A).
Assertion (A) is a direct statement of Avogadro's Law, which is a fundamental principle of ideal gases. Thus, (A) is correct.

Step 2: Evaluate Reason (R).
Reason (R) states that at the same temperature, mean molecular kinetic energies are equal. According to the formula $E = \frac{3}{2}RT$ (per mole), if $T$ is constant, $E$ is constant regardless of the gas type. Thus, (R) is correct.

Step 3: Check for explanation.
While both are true, (R) describes the energetic state of molecules, whereas (A) describes the relationship between volume and quantity (molar volume). Avogadro's law is explained by the fact that gas molecules are point masses with negligible volume compared to the space between them, not specifically by their mean kinetic energy.