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JEE Main 2025 · Chemistry · Electrochemistry · hard

A concentration cell is built from two silver electrodes at 298 K. One dips in a saturated solution of AgCl in pure water (Ksp=1.0×10^-10) and the…

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A concentration cell is built from two silver electrodes at 298 K298\ \mathrm{K}. One dips in a saturated solution of AgCl\mathrm{AgCl} in pure water (Ksp=1.0×10−10K_{sp}=1.0\times10^{-10}) and the other in 0.1 M0.1\ \mathrm{M} AgNO3\mathrm{AgNO_3}. Taking 2.303RTF=0.059 V\dfrac{2.303RT}{F}=0.059\ \mathrm{V}, the emf of the cell is
  1. A. 0.118 V0.118\ \mathrm{V}
  2. B. 0.177 V0.177\ \mathrm{V}
  3. C. 0.472 V0.472\ \mathrm{V}
  4. D. 0.236 V0.236\ \mathrm{V}
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Answer: (D) 0.236 V0.236\ \mathrm{V}

In saturated AgCl\mathrm{AgCl}, [Ag+]=Ksp=10−5 M[\mathrm{Ag^+}]=\sqrt{K_{sp}}=10^{-5}\ \mathrm{M}. For a concentration cell n=1n=1 and E=0.059log⁡[Ag+]conc[Ag+]dil=0.059log⁡0.110−5=0.059×4=0.236 VE=0.059\log\dfrac{[\mathrm{Ag^+}]_{\text{conc}}}{[\mathrm{Ag^+}]_{\text{dil}}}=0.059\log\dfrac{0.1}{10^{-5}}=0.059\times4=0.236\ \mathrm{V}. The saturated-AgCl\mathrm{AgCl} half cell is the anode (dilute side).
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