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For the cell Pt | H2(g) | HCl(aq) | AgCl(s) | Ag(s), the standard cell potential is 0.23 V at 15 deg C and 0.21 V at 35 deg C. Taking standard reduction potential of Ag+/Ag as 0.80 V at 25 deg C and assuming the thermodynamic quantities are constant over 15-35 deg C, the molar solubility of AgCl in water at 25 deg C is closest to:

1. 1.0 * 10⁻⁵ mol/L
2. 1.0 * 10⁻¹⁰ mol/L
3. 1.0 * 10⁻⁴ mol/L
4. 2.0 * 10⁻⁵ mol/L

Correct answer: 1.0 * 10⁻⁵ mol/L

Solution

The cell potential varies linearly with temperature. Interpolating to 25 deg C gives E(cell) = 0.22 V, which is exactly the standard reduction potential of the AgCl + e- -> Ag + Cl- electrode (since the hydrogen electrode is the reference at 0 V). The Ag+/Ag couple has E = 0.80 V. The 0.58 V gap between the two silver couples is governed by the solubility product of AgCl, giving Ksp = 1*10⁻¹⁰ and hence a solubility of 1*10⁻⁵ mol/L.

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