Calculation of Cell Potential for Cu (s)| Cu2 (aq) anode and Ag | Ag(s) cathode

Step 1: Write the Redox Reaction
The given cell has a Cu (s)| Cu2 (aq) anode and Ag | Ag(s) cathode. The redox reaction taking place in the cell is:

Cu(s) → Cu2+ (aq) + 2e- (oxidation)

Ag+ (aq) + e- → Ag(s) (reduction)

The overall reaction for the cell is:

Cu(s) + 2Ag+ (aq) → Cu2+ (aq) + 2Ag(s)

Step 2: Calculate the Standard Cell Potential
The standard cell potential, E°cell, can be calculated using the standard reduction potentials of the half-reactions involved in the cell. The standard reduction potentials for Cu2+ (aq) + 2e- → Cu(s) and Ag+ (aq) + e- → Ag(s) are -0.34 V and +0.80 V, respectively.

E°cell = E°reduction (cathode) - E°oxidation (anode)

E°cell = +0.80 V - (-0.34 V)

E°cell = +1.14 V

Step 3: Calculate the Q Value
The Q value for the cell can be calculated using the concentrations of Cu2+ (aq) and Ag+ (aq) under non-standard conditions. The Q value is given by:

Q = [Cu2+]^2/[Ag+]

Q = (0.300 M)^2/(0.0500 M)

Q = 1.80

Step 4: Calculate the Cell Potential under Non-Standard Conditions
The cell potential under non-standard conditions can be calculated using the Nernst equation:

Ecell = E°cell - (0.0592 V/n) log Q

where n is the number of electrons transferred in the cell reaction.

For this cell, n = 2

Ecell = 1.14 V - (0.0592 V/2) log(1.80)

Ecell = 1.14 V - (0.0296 V) log(1.80)

Ecell = 1.14 V - 0.019 V

Ecell = 1.12 V

Conclusion
The cell potential for the given cell under non-standard conditions is 1.12 V. The increase in the concentration of Cu2+ and decrease in the concentration of Ag+ shifts the reaction to the right, increasing the value of Q and decreasing the cell potential. The Nernst equation is used to calculate the cell potential under non-standard conditions.