Final answer:
To find the Ksp of AgCl using the measured cell potential, we use the Nernst equation and the fact that [Ag+] equals Ksp when [Cl-] is at 1.0M, leading to the conclusion that Ksp will be equal to the concentration of Ag+ in the saturated solution.
Step-by-step explanation:
To calculate the Ksp of silver chloride using the given cell potential, we can start with Nernst equation:
E = E° - (RT/nF) * lnQ
Where:
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- E = cell potential under non-standard conditions
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- E° = standard reduction potential of the electrodes
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- R = universal gas constant (8.314 J/(mol*K))
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- T = temperature in Kelvin (298 K)
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- n = number of moles of electrons transferred (1 for Ag+/Ag)
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- F = Faraday's constant (96485 C/mol)
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- Q = reaction quotient ([Ag+] in the saturated AgCl solution)
The given cell potential (0.29V) is already adjusted for the Ag/AgCl reference electrode, so E° for Ag/AgCl is not required. Substituting the known values and isolating Q gives us the concentration of Ag+ ions in equilibrium with solid AgCl, which equals the Ksp when [Cl-] is at 1.0M, as is the case with a saturated solution.
After finding [Ag+] (which equals Ksp), we can use the relation:
Ksp = [Ag+][Cl-]
Since the concentration of Cl- is 1.0 M in a saturated solution of AgCl, Ksp will be equal to the concentration of Ag+.
Given the typical solubility of AgCl at 25 °C is 1.67 × 10-5 M, which gives us the Ksp under standard conditions.