[CopperSmurf]

I have a value of E I measured and the E° of the Ag E° reference. I know that Ag is being reduced and I have Cl^- ions floating in there to form a AgCl precipitate. I used the Ag/AgCl electrode to measure everything.

I also got E = E° - 2.303RT/(nF) * log(activity of Cl^-) that I used in earlier calculations.

I always thought of the solubility product as the equilibrium constant K. Can activity be used instead of concentrations? And if so, I'm not sure how this applies to the E and E° to find the solubility product.

[Borek]

Reaction quotient should always contain activities.

[CopperSmurf]

So then I think it should be:
K_sp = 1 / (activity of Cl^- x activity of Ag⁺)
but I don't have the concentration or the activity of the silver ion. How does E^o come into play?

[Borek]

What are you trying to do?

[CopperSmurf]

My ultimate goal is to calculate the solubility product of AgCl experimentally.
I've made standard solutions of KCl and made a calibration curve and measured an unknown. I have the activity and concentration of the chloride ion but I don't have the activity of the silver ion (because the silver came from the Ag/AgCl electrode). I also graphed E vs log of the activity of the chloride. I've also asked for help from the instructor and she hinted at the the idea of using the values for E^o and the value of E^o for the reduction of silver metal to calculate the solubility product. The problem is, I don't see how it's done (no matter how simple it may be).

Ag⁺  + Cl^- --> AgCl _s
AgCl_s + electron ---> Ag_s + Cl^-
E = E^o - 2.303RT/(nF)*log(activity of chloride)

[Borek]

E = E₀ + RT/F ln a_Ag⁺

If silver electrode is covered with solid AgCl, activity of Ag⁺ near the electrode surface is

a_Ag⁺ = K_sp/a_Cl^-

Put it into the Nernst equation. ln(K_sp) is constant. Do you see how the E₀ of Ag/Agcl electrode depends on the E₀ of the Ag/Ag⁺ electrode and K_sp?

[CopperSmurf]

I see it now.
Thank you again Borek!