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 A

Step 1: Understanding the Question:

• Assertion: equal volumes of all gases at the same T and P contain the same number of molecules (Avogadro's law). Reason: at constant temperature, mean molecular energies of the gases are equal.

Step 2: Detailed Explanation:

• (A) is correct (Avogadro's law).

• (R) is correct: the average translational kinetic energy is \( \tfrac{3}{2}kT \), which depends only on temperature.

• From kinetic theory, \( PV = \tfrac{2}{3} N \bar{E} \). At the same T the mean energy \( \bar{E} \) is the same for all gases, so equal P and V give equal N. Thus (R) explains (A).

Step 3: Final Answer:
The correct option is (A) Both (A) and (R) are correct and (R) is the correct explanation of (A).