NEET · Chemistry · STD 11 - 5. Thermodynamics and thermochemistry

The work done during reversible isothermal expansion of one mole of hydrogen gas at \(25^{\circ} \mathrm{C}\) from pressure of \(20 \mathrm{atmosphere} \mathrm{to} 10 \mathrm{atmosphere}\) is (Given \(R=2.0 \mathrm{cal} \mathrm{K}^{-1} \mathrm{~mol}^{-1}\) )

A \(-413.14\) calories
B \(413.14\) calories
C \(100\) calories
D \(0\) calorie

Verified Solution

Answer & Solution

Correct Answer

(A) \(-413.14\) calories

Step-by-step Solution

Detailed explanation

\(W_{\text {rev, iso }} \)\( =-2.303 n R T \log \frac{P_i}{P_f} \) \( =-2.303 \times 1 \times 2 \times 298 \times \log 2 \)

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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Match List \(I\) with List \(II\).

List I (Complex)	List \(II\) (Type of isomerism)
\(A\). \(\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5\left(\mathrm{NO}_2\right)\right] \mathrm{Cl}_2\)	\(I\). Solvate isomerism
\(B\). \(\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5\left(\mathrm{SO}_4\right)\right] \mathrm{Br}\)	\(II\). Linkage isomerism
\(C\). \(\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]\left[\mathrm{Cr}(\mathrm{CN})_6\right]\)	\(III\). Ionization isomerism
\(D\). \(\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right] \mathrm{Cl}_3\)	\(IV\). Coordination isomerism

Choose the correct answer from the options given below:

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