Electrochemical Cell and Gibbs Energy — Prelims Questions

For a reaction $2\text{Ag}^+\text{(aq)} + \text{Cu(s)} \rightarrow 2\text{Ag(s)} + \text{Cu}^{2+}\text{(aq)}$, the standard cell potential ($E^\circ_{cell}$) is $+0.46 \text{ V}$. What is the standard Gibbs Free Energy change ($\Delta G^\circ$) for this reaction? (Given: $F = 96485 \text{ C/mol}$)

A galvanic cell is constructed with two half-cells: $\text{Zn}^{2+}|\text{Zn}$ and $\text{Cu}^{2+}|\text{Cu}$. The standard electrode potentials are $E^\circ_{\text{Zn}^{2+}|\text{Zn}} = -0.76 \text{ V}$ and $E^\circ_{\text{Cu}^{2+}|\text{Cu}} = +0.34 \text{ V}$. Calculate the equilibrium constant ($K$) for the cell reaction at 298 K. (Given: $R = 8.314 \text{ J/mol·K}$, $F = 96485 \text{ C/mol}$)

For the reaction $\text{Fe}^{2+}\text{(aq)} + \text{Ag}^+\text{(aq)} \rightarrow \text{Fe}^{3+}\text{(aq)} + \text{Ag(s)}$, the standard electrode potentials are $E^\circ_{\text{Fe}^{3+}|\text{Fe}^{2+}} = +0.77 \text{ V}$ and $E^\circ_{\text{Ag}^+|\text{Ag}} = +0.80 \text{ V}$. What is the standard cell potential ($E^\circ_{cell}$) and the spontaneity of the reaction under standard conditions?

For the cell reaction $\text{Ni(s)} + 2\text{Ag}^+\text{(0.01 M)} \rightarrow \text{Ni}^{2+}\text{(0.1 M)} + 2\text{Ag(s)}$, the standard cell potential ($E^\circ_{cell}$) is $1.05 \text{ V}$. Calculate the cell potential ($E_{cell}$) at 298 K. (Given: $\log 10 = 1$)