For the cell $Zn_{(s)} | Zn^{2+} (0.1 \ M) || Fe^{2+} (0.01 \ M) | Fe_{(s)}$ at $298 \ K$,$E_{cell} = 0.2905 \ V$. What is the equilibrium constant $(K_c)$ for the reaction $Zn_{(s)} + Fe^{2+}_{(aq)} \rightleftharpoons Zn^{2+}_{(aq)} + Fe_{(s)}$?

$E_{1}, E_{2}, E_{3}$ are the $EMF$ values of three galvanic cells with the reaction $Zn(s) + Cu^{2+}(aq) \rightarrow Zn^{2+}(aq) + Cu(s)$ at $298 \ K$ with different concentrations: $(I) [Zn^{2+}] = 1 \ M, [Cu^{2+}] = 0.1 \ M$; $(II) [Zn^{2+}] = 1 \ M, [Cu^{2+}] = 1 \ M$; $(III) [Zn^{2+}] = 0.1 \ M, [Cu^{2+}] = 1 \ M$. Compare the $EMF$ values.

At $298 \ K$,a $1 \ L$ solution containing $10 \ mmol$ of $Cr_2O_7^{2-}$ and $100 \ mmol$ of $Cr^{3+}$ shows a $pH$ of $3.0$. Given: $Cr_2O_7^{2-} \rightarrow Cr^{3+}; E^0 = 1.330 \ V$ and $\frac{2.303 RT}{F} = 0.059 \ V$. The potential for the half-cell reaction is $x \times 10^{-3} \ V$. The value of $x$ is $........$

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

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

At $298 \ K$,if the $emf$ of the cell corresponding to the reaction,$Zn_{(s)} + 2H^+_{(aq)} \rightarrow Zn^{2+}(0.01 \ M) + H_{2(g)}(1 \ atm)$ is $0.28 \ V$,then the $pH$ of the solution at the hydrogen electrode is (Given: $\frac{2.303 \ RT}{F} = 0.06 \ V$,$E^o_{Zn^{2+}|Zn} = -0.76 \ V$)