If the kinetic energy and RMS speed of a gas at a certain temperature are 4.0 kJ mol-1 and 5.0×104 cm s-1, respectively. The molecular weight of the gas is

AP EAMCET · Chemistry · States of Matter

If the kinetic energy and $RMS$ speed of a gas at a certain temperature are $4.0 kJ {mol}^{- 1}$ and $5.0 \times 10^{4} cm s^{- 1}$ , respectively. The molecular weight of the gas is

A $16$
B $32$
C $64$
D $44$

Verified Solution

Answer & Solution

Correct Answer

(B) $32$

Step-by-step Solution

Detailed explanation

As the kinetic energy expression used the RMS speed of the gas as:12Mv2rms=5.0×10412M(5.0×104×10-2)2rms=4×103M=0.032 Kg mole-1 Therefore, molecular weight is 0.032 Kg per mole or 32 g per mole.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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