If $E^{\circ}_{\text{cell}}$ is $1.049 \ V$ and the reaction involves the transfer of $2$ electrons,calculate the equilibrium constant $(K)$ of the cell.

Which of the following statements is true regarding the cell emf at $298 \ K$ for the cell $Ni_{(s)} | Ni^{2+}(0.01 \ M) || Ag^{+}(0.01 \ M) | Ag_{(s)}$?

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 $........$

Consider the following half-cell reaction: $Cr_2O_7^{2-}{_{\text{(aq)}}} + 14H^{+}{_{\text{(aq)}}} + 6e^{-} \rightarrow 2Cr^{3+}{_{\text{(aq)}}} + 7H_2O_{\text{(l)}}$. The reaction was conducted with the ratio $\frac{[Cr^{3+}]^2}{[Cr_2O_7^{2-}]} = 10^{-6}$. The $pH$ value at which the $EMF$ of the half-cell will become zero is $............$ (nearest integer value). [Given: standard half-cell reduction potential $E^{o}_{Cr_2O_7^{2-}, H^{+} / Cr^{3+}} = 1.33 \ V$,$\frac{2.303 RT}{F} = 0.059 \ V$]

For a cell having a standard $emf$ of $0.295 \ V$ at $25^o \ C$ involving a two-electron change,the equilibrium constant for the reaction is:

Calculate $E_{cell}$ for the following cell:
$Pt_{(s)} | H_{2(g)} | HA, 1 \ M \ (K_a = 10^{-7}) || HB, 1 \ M \ (K_a = 10^{-5}) | H_{2(g)} | Pt_{(s)}$ (in $V$)