JEE Mains · Chemistry · STD 12 - 2. Electrochemistry

જો સંકેતો તેમના સામાન્ય અર્થ ધરાવતા હોય, તો નીચેનામાંથી કયું સમીકરણ નિર્બળ વિદ્યુતવિભાજ્ય માટે સાંદ્રતાના સંદર્ભમાં મોલર વાહકતામાં થતો ફેરફાર દર્શાવવા માટે સાચું છે?

A \(\Lambda_{\mathrm{m}}^2 \mathrm{C}-\mathrm{K}_{\mathrm{a}} \Lambda_{\mathrm{m}}^{\circ 2}+\mathrm{K}_{\mathrm{a}} \Lambda_{\mathrm{m}} \Lambda_{\mathrm{m}}^{\circ}=0\)
B \(\Lambda_{\mathrm{m}}-\Lambda_{\mathrm{m}}^{\circ}+\mathrm{AC}^{\frac{1}{2}}=0\)
C \(\Lambda_{\mathrm{m}}-\Lambda_{\mathrm{m}}^{\circ}-\mathrm{AC}^{\frac{1}{2}}=0\)
D \(\Lambda_{\mathrm{m}}^2 \mathrm{C}+\mathrm{K}_{\mathrm{a}} \Lambda_{\mathrm{m}}^{\circ 2}-\mathrm{K}_{\mathrm{a}} \Lambda_{\mathrm{m}} \Lambda_{\mathrm{m}}^{\circ}=0\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\Lambda_{\mathrm{m}}^2 \mathrm{C}-\mathrm{K}_{\mathrm{a}} \Lambda_{\mathrm{m}}^{\circ 2}+\mathrm{K}_{\mathrm{a}} \Lambda_{\mathrm{m}} \Lambda_{\mathrm{m}}^{\circ}=0\)

Step-by-step Solution

Detailed explanation

\( \mathrm{HA}(\mathrm{aq}) \rightleftharpoons \mathrm{H}^{+}(\mathrm{aq})+\mathrm{A}^{-}(\mathrm{aq}) \) \( \mathrm{K}_{\mathrm{a}}=\frac{\alpha^2 \mathrm{C}}{1-\alpha} \) \( \alpha^2 \mathrm{C}+\mathrm{K}_{\mathrm{a}} \alpha-\mathrm{K}_{\mathrm{a}}=0 \)…

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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