The $emf$ of the following three galvanic cells:
$1. Zn|Zn^{2+} (1 \ M)||Cu^{2+} (1 \ M)|Cu$
$2. Zn|Zn^{2+} (0.1 \ M)||Cu^{2+} (1 \ M)|Cu$
$3. Zn|Zn^{2+} (1 \ M)||Cu^{2+} (0.1 \ M)|Cu$
are represented by $E_1, E_2, E_3$. Which of the following statements is true?

For the reduction of silver ions by copper metal,the standard cell potential at $25\,^{\circ}C$ is $0.46\,V$. What is the value of the standard Gibbs energy $(\Delta G^{\circ})$? $(F = 96500\,C\,mol^{-1})$

The standard $emf$ of a galvanic cell involving $2$ moles of electrons in its redox reaction is $0.59 \ V$. The equilibrium constant for the redox reaction of the cell is

In the cell $Pt_{(s)} | H_2(g, 1 \, bar) | HCl_{(aq)} | AgCl_{(s)} | Ag_{(s)} | Pt_{(s)}$,the cell potential is $0.92 \, V$ when a $10^{-6} \, m$ $HCl$ solution is used. The standard electrode potential of the $(AgCl/Ag, Cl^-)$ electrode is ............. $V$ $\{ \text{Given, } \frac{2.303RT}{F} = 0.06 \, V \text{ at } 298 \, K \}$

Which of the following relations represents the correct relation between standard electrode potential and equilibrium constant?
$I$. $\log K = \frac{nF E^o}{2.303 RT}$
$II$. $K = e^{\frac{nF E^o}{RT}}$
$III$. $\log K = -\frac{nF E^o}{2.303 RT}$
$IV$. $\log K = 0.4342 \frac{nF E^o}{RT}$
Choose the correct statement$(s)$.

For the cell $Fe | Fe^{+2} (x \, M) || Cu^{+2} (0.01 \, M) | Cu$,if $E_{cell} = 0.78 \, V$,$E^{\circ}_{Fe^{+2} | Fe} = -0.44 \, V$,and $E^{\circ}_{Cu^{+2} | Cu} = +0.34 \, V$,determine the value of $x$.