Electrochemistry - Voltaic Cell

[iharuyuki]

A voltaic electrochemical cell consists of a silver electrode in contact with 200 mL of 0.1 M AgNO3 and a magnesium electrode in contact with 300 mL of a 0.1 M Mg(NO3)2 solution. We have the following data: Ag+ + e- --> Ag (E° = 0.8 V) Mg2+ + 2e- --> Mg (E° = -2.372 v)

a) Calculate the value of E for the cell at 25°C
b) A current is drawn from the cell until 1.2 g of silver has been deposited at the silver electrode. Calculate the value of E for the cell at this stage.
c) Determine E for the cell once the cell has reached equilibrium.

a a) 3.142 V; b) 2.958 V; c) zero
b a) 3.172 V; b) 3.122 V; c) 3.122 V
c a) 3.172 V; b) 3.122 V; c) 3.172 V
d a) 3.142 V; b) 2.958 V; c) 2.958 V

Attempt at solution:
Overall reaction:
2Ag+ + Mg(s) -> 2 Ag(s) + Mg2+ E0cell = 3.172

Q = [Mg2+]/[Ag+]^2 solid phase components not included

For part a) Nerst equation with E0cell = 3.172 V and finding Q with the given concentrations above yields E25C = 3.142V So b and c are eliminatedI'm not quite sure how to proceed from there. Is it possible for Ecell at equilibrium to be 0? If not, A is eliminated as well.

Thank you for the help, and sorry if I've broken any etiquette. It's my first time posting here.

 

[Adrmay]

Yes, it is possible for the cell potential at equilibrium to be zero. This occurs when the reaction has reached its equilibrium point and no further net reaction can occur. To solve for part b), we need to calculate the number of moles of silver that has been deposited. Using the molar mass of silver (107.87 g/mol), we can calculate the number of moles of silver deposited as 1.2g/107.87g/mol = 0.011 mol. We then need to calculate the new concentrations of Ag+ and Mg2+ in the cell. The new concentration of Ag+ will be 0.1M - 0.011mol/0.3L = 0.0989M and the new concentration of Mg2+ will be 0.1M + 0.011mol/0.3L = 0.1009M. Using these new concentrations in the Nernst equation with E0cell = 3.172V, we can calculate E = 3.122V. For part c), since the reaction has reached its equilibrium point, the cell potential is zero.