The relationship between standard reduction potential of a cell and the equilibrium constant is shown by:

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 half-cell containing a $Pt$ rod immersed in a solution of $1 \ M$ $HA$,$O_{2(g)}$ is bubbled at $1 \ atm$. The standard reduction potential for water formation is $1.23 \ V$. Given a dissociation constant,$K_a = 1 \times 10^{-4}$ for $HA$,what is $E_{\text{Half-cell}}$ at $298 \ K$ in $V$?

Derive the Nernst equation for the following galvanic cell: $Ni_{(s)}|Ni_{(aq)}^{2+}\parallel Ag_{(aq)}^{+}|Ag_{(s)}$

Consider the following electrode processes of a cell: $Cl^{-} \rightarrow \frac{1}{2} Cl_2 + e^{-}$ and $MCl + e^{-} \rightarrow M + Cl^{-}$. If the $EMF$ of this cell is $-1.140 \ V$ and the $E^{\circ}$ value of the cell is $-0.55 \ V$ at $298 \ K$,the value of the equilibrium constant $(K_{sp})$ of the sparingly soluble salt $MCl$ is in the order of:

For the cell $Co | Co^{+2} (C_2) || Co^{+2} (C_1) | Co$,$\Delta G$ is negative if