What is the delta G naught for the cell in question 1 at 298 K?

Question 1: Which is spontaneous, the oxidation of copper to Cu2+ or the reduction of Cu2+ to Cu?

Work:
OX: Cu --> Cu2+ + 2e-
RE: 2e- + Cu2+ --> Cu
Overall: Cu + Cu2+ --> Cu + Cu2+

Delta G knaught = -RTln(Keq)
= -(8.314)(298)ln(1)
= 0?
R=8.314 J/Kmol
T=298 K
Keq= [Cu2+]/[Cu2+] = 1

The problem I am having is with the Keq. I think its one, but that would make the entire delta G knaught 0? I am just a bit confused.

You have no concns listed so you can't get Keq that way.

Use dGo = -nEoF
You will need to look up the value of Eo for the reaction. Obviously the one with Eo a positive number will give you a negative dGo and that is the one that is spontaneous. If you want Keq, you can get that AFTER you know dGo by
dGo = -RTlnK.

To determine the spontaneity of a reaction, you can compare the standard free energy change, delta G naught, to zero. If delta G naught is negative, the reaction is spontaneous, while if delta G naught is positive, the reaction is non-spontaneous.

In this case, you're trying to find the delta G naught for the cell in question 1 at 298 K, where the oxidation of copper to Cu2+ and the reduction of Cu2+ to Cu are taking place.

The overall reaction can be represented as:
Cu + Cu2+ → Cu + Cu2+

To calculate delta G naught for this reaction, you need to know the standard Gibbs free energy change, delta G naught, for each half-reaction (oxidation and reduction) involved.

Using the equation:
delta G naught = -RTln(K)
R = 8.314 J/(mol*K) (ideal gas constant)
T = 298 K (temperature)
K = equilibrium constant (also known as Keq)

For the oxidation half-reaction:
Cu → Cu2+ + 2e-
The delta G naught value can be calculated using the given equation:
delta G naught (OX) = -RTln(KOX)

For the reduction half-reaction:
2e- + Cu2+ → Cu
The delta G naught value can be calculated using the given equation:
delta G naught (RE) = -RTln(KRE)

To find the equilibrium constant (Keq), you need to use the Nernst equation, which is based on the concentrations of the species involved.

Keq = [Cu2+]/[Cu]
Since there is no specific concentration or molarity given in the question, it is assumed that both the concentration of Cu2+ and Cu are 1 M (molar) at standard conditions.

Hence, [Cu2+]/[Cu] = 1/1 = 1.

Therefore, Keq = 1.

Now, plug the value of Keq into the delta G naught equation for each half-reaction.

delta G naught (OX) = -(8.314 J/(mol*K))(298 K)ln(1) = 0 J/mol
delta G naught (RE) = -(8.314 J/(mol*K))(298 K)ln(1) = 0 J/mol

Since both delta G naught values are zero, it means that both the oxidation and reduction reactions are at equilibrium under standard conditions at 298 K. This indicates that the reaction is not spontaneous in either direction.

Therefore, the answer to your question is that the oxidation of copper to Cu2+ and the reduction of Cu2+ to Cu are not spontaneous at 298 K.