For $Cr_2O_7^{2-} + 14H^{+} + 6e^- \longrightarrow 2Cr^{3+} + 7H_2O$,$E^0 = 1.33 \ V$. Given $[Cr_2O_7^{2-}] = 4.5 \ mmol$,$[Cr^{3+}] = 1.5 \ mmol$ and $E = 1.067 \ V$,calculate the $pH$ of the solution.

For a reaction,$A + B^{2+} \to B + A^{2+}; E^{\circ} = 0.2955 \ V$. Hence,the equilibrium constant of the reaction at $25 \ ^oC$ is:

If the concentration of a $Zn^{2+}$ solution is diluted $10$ times,what is the change in the potential of the $Zn/Zn^{2+}$ electrode?

Consider the cell
$Pt_{(s)} \mid H_2(g, 1\,atm) \mid H^{+}(aq, 1\,M) \parallel Fe^{3+}_{(aq)}, Fe^{2+}_{(aq)} \mid Pt_{(s)}$
When the potential of the cell is $0.712\,V$ at $298\,K$,the ratio $[Fe^{2+}] / [Fe^{3+}]$ is $.......$ (Nearest integer).
Given: $Fe^{3+} + e^- \longrightarrow Fe^{2+}$,$E^{\circ}_{Fe^{3+}/Fe^{2+}} = 0.771\,V$
$\frac{2.303 RT}{F} = 0.06\,V$

$Cu^{2+} + 2e^- \to Cu$. On increasing $[Cu^{2+}]$ concentration,electrode potential

The e.m.f. of the cell in which the following reaction $Zn_{(s)} + Ni^{2+}(a = 1.0) \rightleftharpoons Zn^{2+}(a = 10) + Ni_{(s)}$ occurs,is found to be $0.5105 \ V$ at $298 \ K$. The standard e.m.f. of the cell is ............ $V$.