A silver wire dipped in 0.1 M HCl solution saturated with AgCl at 25°C develops oxidation potential of –0.209 V. If = –0.799V, the Ksp of AgCl at 25°C is
Question
A silver wire dipped in 0.1 M HCl solution saturated with AgCl at 25°C develops oxidation potential of –0.209 V. If , the Ksp of AgCl at 25°C is
Solution
The question is asking for the solubility product constant (Ksp) of AgCl at 25°C. We can use the Nernst equation to solve this problem. The Nernst equation is:
E = E° - (RT/nF) * lnQ
where: E is the cell potential, E° is the standard cell potential, R is the gas constant, T is the temperature in Kelvin, n is the number of moles of electrons transferred in the redox reaction, F is the Faraday constant, and Q is the reaction quotient.
Given in the problem, we have E = -0.209 V, E° = -0.799 V, T = 25°C = 298 K, and n = 1 (since the reaction is Ag+ + e- -> Ag, only one electron is transferred).
We can plug these values into the Nernst equation:
-0.209 = -0.799 - (8.314 * 298 / (1 * 96485)) * lnQ
Solving for Q gives Q = [Ag+][Cl-] = 10^((E°-E)nF/RT) = 10^((0.799-(-0.209))96485/(8.314298)) = 1.7710^-10
Since the solution is saturated with AgCl, [Ag+] = [Cl-] = sqrt(Ksp). Therefore, Ksp = Q = 1.77*10^-10.
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