A student wishes to calculate the experimental value of Ksp for AgI. S/he follow

Question

A student wishes to calculate the experimental value of Ksp for AgI. S/he follows the procedure in Part 3 and finds Ecell to be 0.839 V. S/he does not perform Part 2; instead, s/he uses the theoretical slope of the Nernst plot for an Ag/Ag+ concentration cell, as instructed by her/his TA; this value is ?0.0591 V.

(a) What is the concentration of Ag+(aq) in the saturated solution of AgI (i.e., [Ag+?]dilute)? ([Ag+?]conc = 1.0???10?1 M.)

(b) Using [I ??] = 0.20 M, calculate the experimental Ksp.

This has been asked here before, but I didn't understand the answer.

Explanation / Answer

Ecell = 0.839 V

E°cell = -0.0591 V

Nernst Equation:

E°cell = -RT/nF x ln(K)

E°cell = -0.0592 / n x log([Ag+][I-])

0.839 = - 0.0591 - 0.05916 / 1 log Ksp

Ksp = 6.58 x 10^-16

AgI(s) -----------------> Ag+(aq) + I-(aq)

Ksp = [Ag+][I-]

[Ag+] = [I-]

6.58 x 10^-16 = [Ag+]^2

[Ag+] = 2.56 x 10^-8 M

b)

Ksp = [Ag+][I-]

       = 2.56 x 10^-8 x 0.20

       = 5.13 x 10^-9

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