AP EAMCET · Chemistry · States of Matter

Assertion (A) At \(300 \mathrm{~K}\), kinetic energy of \(16 \mathrm{~g}\) of methane is equal to the kinetic energy of 32 \(g\) of oxygen.Reason (R) At constant temperature, kinetic energy of one mole of all gases is equal.

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

Verified Solution

Answer & Solution

Correct Answer

(A) Both \((A)\) and \((R)\) are true and \((R)\) is the correct explanation of \((A)\)

Step-by-step Solution

Detailed explanation

Kinetic energy for one mole gas is given by equation, \[ \begin{aligned} & E=\frac{3}{2} k T \text { (where, } k=\text { Boltzman's constant) } \\ & \therefore \quad E \propto T \end{aligned} \] Thus at constant temperature kinetic energy of one mole of any gas is equal.

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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