Consider a concentration cell. Two Ag-electrodes are immersed in AgNO3 solutions

Question

Consider a concentration cell. Two Ag-electrodes are immersed in AgNO3 solutions of different concentrations. When the two compartments have an AgNO3-concentration of 1 M and 0.1 M, respectively, the measured voltage is 0.065 V (note: T in not necessarily = 25°C !).

a. What is the voltage, if the two compartments have AgNO3-concentration of 1 M and 0.01 M, respectively?

The electrochemical behavior of silver nanoclusters (Agn, with n the number of Ag atoms in the cluster) is investigated using the following electrochemical cells at 298 K:
I. Ag(s) | AgCl (saturated) || Ag+(aq, 0.01M) | Ag(s), E=0.170
II. (Pt electrode) Agn (s, nanocluster) | Ag+(aq, 0.01M) || AgCl (saturated) | Ag(s), with E = +1.030 V for Ag5 nanocluster and E = +0.430 V for Ag10 nanocluster
The standard reduction potential for Ag+ + e- Ag, is E0 = +0.800 V.

b. Use this data to calculate the solubility product of AgCl.

Explanation / Answer

Let the temperature be T.

Eocell = 0.065 V

[AgNO3] = 1 M and 0.1 M

We know that,

Eocell = RT/nF * ln Q

0.065 = RT/nF * ln (0.1 / 1) ..................(1)

when [AgNO3] is changed to 1 M and 0.01 M.

Eocell = RT/nF * ln (0.01 / 1) ..................(2)

From eq (1) and eq (2) -

0.065 / Eocell  = ln 0.1 / ln 0.01

0.065 / Eocell  = - 2.3025 / - 4.605

0.065 / Eocell  = 1 / 2

Eocell  = 2*0.065

Eocell  = 0.13 V

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