By how much will the potential of the half-cell $Cu^{2+}/Cu$ change if the solution is diluted to $100$ times at $298 \ K$?

For a $Daniel$ cell $Zn | ZnSO_{4(0.01 \ M)} || CuSO_{4(1 \ M)} | Cu$ at $298 \ K$,the cell potential is $E_1$. When the concentrations of $ZnSO_4$ and $CuSO_4$ are changed to $1 \ M$ and $0.01 \ M$ respectively,the cell potential becomes $E_2$. Determine the relationship between $E_1$ and $E_2$.

The cell potential for the following cell
$Pt \mid H_{2(g)} \mid H^{+}_{(aq)} \parallel Cu^{2+}(0.01 \, M) \mid Cu_{(s)}$
is $0.576 \, V$ at $298 \, K$. The $pH$ of the solution is $......$ (Nearest integer)

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$(s)$.

$E^0 = \frac{RT}{nF} \ln K_{eq}$. This is called

The e.m.f. of the cell $Ag | Ag^{+}(0.1 \ M) || Ag^{+}(1 \ M) | Ag$ at $298 \ K$ is ........... $V$.