Nernst Equation

Write the Nernst equation for the following cell reaction:
$\mathrm{Zn}\left(\mathrm{s}\right)+{\mathrm{Cu}}^{2+}\left(\mathrm{aq}\right)\to {\mathrm{Zn}}^{2+}\left(\mathrm{aq}\right)+\mathrm{Cu}\left(\mathrm{s}\right)$
How will the ${\mathrm{E}}_{\mathrm{cell}}$ be affected when concentration of ${\mathrm{Zn}}^{2+}$ ions is increased

Write the Nernest equation.

If the ${\mathrm{Pb}}^{2+}$ concentration is maintained at $1.0 \mathrm{M}$, what is the$\left[{\mathrm{Cu}}^{2+}\right]$ concentration when the cell potential drops to zero? ${\mathrm{E}}_{\mathrm{cell}}^{\mathrm{o}}=0.473\mathrm{V}$,

${\mathrm{Pb}}_{\left(\mathrm{s}\right)}\mid {\mathrm{Pb}}^{2+}\mid \mid {\mathrm{Cu}}^{2+}\mid \mid {\mathrm{Cu}}_{\left(\mathrm{s}\right)}$

Calculate the EM.F. of the half-cell given below: 
$\mathrm{Pt}, {\mathrm{H}}_2\mid \mathrm{H}\mathrm{C}\mathrm{l}$ at $1$ atmosphere pressure and $0.1 \mathrm{M}$. Given, ${\mathrm{E}}^{\circ }(\mathrm{O}.\mathrm{P})=2 \mathrm{V}$.

 A cell is prepared by dipping a zinc rod in $1\mathrm{M}$ zinc sulphate solution and a silver electrode in $1\mathrm{M}$ silver nitrate solution. The standard electrode potentials given are:
${\mathrm{E}}_{{\mathrm{Zn}}^{2+}/\mathrm{Zn}} =-0.76\mathrm{V}, {\mathrm{E}}_{{\mathrm{Ag}}^{+}/\mathrm{Ag}} =+0.80\mathrm{V}$
What is the effect of increase in concentration of ${\mathrm{Zn}}^{2+}$ on the ${\mathrm{E}}_{\mathrm{Cell}}$.

Equilibrium constant is related to ${{\mathrm{E}}^{°}}_{\mathrm{Cell}}$ but not to ${\mathrm{E}}_{\mathrm{Cell}}$. Explain why?

For the reaction, $2 \mathrm{AgCl} \left(\mathrm{s}\right) + {\mathrm{H}}_2 \left(\mathrm{g}\right) (1 \mathrm{atm}) )\to 2 \mathrm{Ag} (\mathrm{s}) + 2 {\mathrm{H}}^{+} (0.1 \mathrm{M}) + 2 {\mathrm{Cl}}^{-} (0.1 \mathrm{M})$
$∆\mathrm{G}°=-43600 \mathrm{J}$ at $25°\mathrm{C}$. Calculate the e.m.f. of the cell $(\log {10}^{-\mathrm{n}} =- \mathrm{n})$.

Calculate the emf of the following cell at $298 \mathrm{K}$:
$\mathrm{Mg} \left(\mathrm{s}\right) | {\mathrm{Mg}}^{2+} (0.1 \mathrm{M}) || {\mathrm{Cu}}^{2+} (0.01 \mathrm{M}) |\mathrm{Cu} \left(\mathrm{s}\right)$
[Given $\mathrm{E}{°}_{\mathrm{Cell}}= + 2.71 \mathrm{V}, 1 \mathrm{F} = 96500 \mathrm{C} {\mathrm{mol}}^{-1}$] 

Calculate the e.m.f. of the cell at $298 \mathrm{K}$ in which the following reaction takes place:
$\mathrm{Ni} \left(\mathrm{s}\right) +2 {\mathrm{Ag}}^{+} \left(\mathrm{aq}\right) \left[0.002 \mathrm{M}\right]\to {\mathrm{Ni}}^{2+} \left(\mathrm{aq}\right) [0.160 \mathrm{M}] + 2 \mathrm{Ag} \left(\mathrm{s}\right)$
(Given $\mathrm{E}{°}_{\mathrm{Cell}}=1.05 \mathrm{V}$)

The standard reduction potentials for two reactions are given below:
$$\begin{gathered} \mathrm{AgCl} \left(\mathrm{s}\right) + {\mathrm{e}}^{-} \to \mathrm{Ag} \left(\mathrm{s}\right) + {\mathrm{Cl}}^{-} \left(\mathrm{aq}\right), \mathrm{E}° = 0.22 \mathrm{V} \\ {\mathrm{Ag}}^{+} \left(\mathrm{aq}\right)+{\mathrm{e}}^{-} \to \mathrm{Ag}\left(\mathrm{s}\right), \mathrm{E}°=0.80\mathrm{V} \end{gathered}$$
Calculate the solubility product of $\mathrm{AgCl}$ under standard conditions of temperature ($298 \mathrm{K}$).

What will be the EMF of the following electrode concentration cell at $25°\mathrm{C}$.
$\mathrm{Hg}—\mathrm{Zn} \left({\mathrm{C}}_1\mathrm{M}\right) | {\mathrm{Zn}}^{2+} (\mathrm{CM}) | \mathrm{Hg}—\mathrm{Zn} \left({\mathrm{C}}_2\mathrm{M}\right)$
if the concentrations of zinc amalgam are $2 \mathrm{g} \mathrm{per} 100 \mathrm{g}$of mercury and $1 \mathrm{g} \mathrm{per} 100 \mathrm{g}$ of mercury in the anodic and the cathodic compartments respectively.
 

For the cell reaction, $\mathrm{Sn} \left(\mathrm{s}\right) + {\mathrm{Pb}}^{+2} \left(\mathrm{aq}\right) \to {\mathrm{Sn}}^{2+}\left(\mathrm{aq}\right) + \mathrm{Pb} \left(\mathrm{s}\right),$
$$$\mathrm{E}{°}_{{\mathrm{Sn}}^{2+}|\mathrm{Sn}}=-0.136 \mathrm{V}, \mathrm{E}{°}_{{\mathrm{Pb}}^{2+}|\mathrm{Pb}}=-0.126 \mathrm{V}.$
Calculate the ratio of concentration of ${\mathrm{Pb}}^{2+}$ to ${\mathrm{Sn}}^{2+}$ ion at which the cell reaction will be reversed?

EMF of Daniell cell was found using different concentrations of ${\mathrm{Zn}}^{2+}$ion and ${\mathrm{Cu}}^{2+}$ ion. A graph was then plotted between ${\mathrm{E}}_{\mathrm{Cell}}$ and $\log \frac{\left[{\mathrm{Zn}}^{2+}\right]}{\left[{\mathrm{Cu}}^{2+}\right]}$. The plot was found to be linear with intercept on ${\mathrm{E}}_{\mathrm{Cell}}$ axis equal to $1.10 \mathrm{V}$. Calculate for $\mathrm{Zn} | {\mathrm{Zn}}^{2+} (0.1 \mathrm{M}) || {\mathrm{Cu}}^{2+} ( 0.01 \mathrm{M}) | \mathrm{Cu}$

Two students use same stock solution of ${\mathrm{ZnSO}}_4$ and a solution of ${\mathrm{CuSO}}_4$ The emf of one cell is $0.03 \mathrm{V}$ higher than the other. The concentration. of ${\mathrm{CuSO}}_4$ in the cell with higher emf value is $0.5 \mathrm{M}$. Find out the concentration of ${\mathrm{CuSO}}_4$ in the other cell $\left(\raisebox{1ex}{$2.303 \mathrm{RT}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{F}$}\right.=0.06\right)$.

Find the solubility product of${\mathrm{Ag}}_2{\mathrm{CrO}}_4$ in water at $298 \mathrm{K}$ if the e.m.f. of the cell $\mathrm{Ag}/{\mathrm{Ag}}^{+}\left(\mathrm{saturated} {\mathrm{Ag}}_2{\mathrm{CrO}}_4 \mathrm{soln}.\right) \left|\right| {\mathrm{Ag}}^{+}(0.1 \mathrm{M})/\mathrm{Ag}$ is $0.164 \mathrm{V}$ at $298 \mathrm{K}$.

The EMF of a cell corresponding to the reaction
$\mathrm{Zn} \left(\mathrm{s}\right) + 2{\mathrm{H}}^{+} \left(\mathrm{aq}\right) )\to {\mathrm{Zn}}^{2+}(0.1 \mathrm{M}) + {\mathrm{H}}_{2 }(\mathrm{g}, 1 \mathrm{atm})$ is $0.28 \mathrm{volt}$ at $25°\mathrm{C}$.
Write the half-cell reactions and calculate the $\mathrm{pH}$ of the solution at the hydrogen electrode.

$\mathrm{E}{°}_{{\mathrm{Zn}}^{2+}|\mathrm{Zn}}=-0.76 \mathrm{volt}, \mathrm{E}{°}_{{\mathrm{H}}^{+}|{\mathrm{H}}_2}=0$

Calculate the stability constant of the complex $[\mathrm{Zn} {\left({\mathrm{NH}}_3\right)}_4{]}^{2+}$ formed in the reaction
${\mathrm{Zn}}^{2+} +4{\mathrm{NH}}_3\rightleftharpoons {\left[\mathrm{Zn}{\left({\mathrm{NH}}_3\right)}_4\right]}^{2+}$
Given that $\mathrm{E}{°}_{{\mathrm{Zn}}^{2+}|\mathrm{Zn}}=-0.76 \mathrm{V}$ and $\mathrm{E}{°}_{ [\mathrm{Zn} {\left({\mathrm{NH}}_3\right)}_4{]}^{2+}|\mathrm{Zn}, 4{\mathrm{NH}}_3}=-1.03 \mathrm{V}$.

Write short notes on Nernst equation.

In the button cell widely used for watches and other devices, the following reaction takes place:

$\mathrm{Zn} \left(\mathrm{s}\right) + {\mathrm{Ag}}_2\mathrm{O} \left(\mathrm{s}\right) + {\mathrm{H}}_2\mathrm{O} \left(\mathrm{l}\right)\to {\mathrm{Zn}}^{2+} \left(\mathrm{aq}\right) + 2 \mathrm{Ag} \left(\mathrm{s}\right) + 2 {\mathrm{OH}}^{-} \left(\mathrm{aq}\right)$

Give the cell representation and determine the value of ${\mathrm{K}}_{\mathrm{c}}$ for the above reaction using the following data:

$$\begin{gathered} {\mathrm{Ag}}_2\mathrm{O} \left(\mathrm{s}\right) + {\mathrm{H}}_2\mathrm{O} \left(\mathrm{l}\right) + 2 {\mathrm{e}}^{-} \to 2 \mathrm{Ag} \left(\mathrm{s}\right) + 2 {\mathrm{OH}}^{-} \left(\mathrm{aq}\right) (\mathrm{E}° = 0.344 \mathrm{V}) \\ {\mathrm{Zn}}^{2+} \left(\mathrm{aq}\right) + 2 {\mathrm{e}}^{-}\to \mathrm{Zn} \left(\mathrm{s}\right) (\mathrm{E}° =- 0.76 \mathrm{V}) \end{gathered}$$

Write Nernst equation for the general electrochemical change of the following type at $25°\mathrm{C}$.

$\mathrm{aA}+\mathrm{bB}\stackrel{{\mathrm{ne}}^{-}}{\to }\mathrm{cC}+\mathrm{dD}$