Relationship between Electrode Potential, Gibb's Free Energy and Equilibrium Constant

For the reaction 

$2{\mathrm{Fe}}^{3+}\left(\mathrm{aq}\right)+2{\mathrm{I}}^{-}\left(\mathrm{aq}\right)\to 2{\mathrm{Fe}}^{2+}\left(\mathrm{aq}\right)+{\mathrm{I}}_2\left(\mathrm{s}\right)$, the magnitude of the standard molar free energy change, ${∆}_{\mathrm{r}}{\mathrm{G}}^{\mathrm{o}}\mathrm{m}=-$_______$\mathrm{KJ}$$(45/52).$

$$\begin{gathered} {{{\mathrm{E}}^0}_{\mathrm{Fe}}}^{2+}/\mathrm{Fe}\left(\mathrm{s}\right)=-0.440\mathrm{V} \\ {{{\mathrm{E}}^0}_{\mathrm{Fe}}}^{3+}/\mathrm{Fe}\left(\mathrm{s}\right) =-0.036\mathrm{V} \\ {{{\mathrm{E}}^0}_{{\mathrm{I}}_2}}_{/2{\mathrm{I}}^{-}}=0.539\mathrm{V} \\ \mathrm{F}=96500\mathrm{C} \end{gathered}$$

The standard reduction potential of ${\mathrm{TiO}}^{+2}$ and ${\mathrm{Ti}}^{+3}$ are given by

$$\begin{gathered} {\mathrm{TiO}}^{+2}+2{\mathrm{H}}^{+}+{\mathrm{e}}^{-}\to {\mathrm{Ti}}^{+3}+{\mathrm{H}}_2\mathrm{O} -- {\mathrm{E}}^{\circ }=0.10\mathrm{V} \\ {\mathrm{Ti}}^{+3}+3{\mathrm{e}}^{-}\to \mathrm{Ti} --- {\mathrm{E}}^{\circ }=-1.21\mathrm{V} \end{gathered}$$

Find the standard reduction potential of ${\mathrm{TiO}}^{+2} \mathrm{to} \mathrm{Ti}$.

Consider an electrochemical cell

$\mathrm{Pt}, {\mathrm{H}}_2/{\mathrm{H}}^{+}\parallel {\mathrm{Ag}}^{+}/\mathrm{Ag}$

Given, ${\mathrm{E}}_{{\mathrm{Ag}}^{+}/\mathrm{Ag}}^{\circ }=+0.80 \mathrm{V}$

The value of $∆{\mathrm{G}}^{\circ }$ for the cell represented above is $-\mathrm{x} \mathrm{kJ}$, then the value of $\mathrm{x}$ in nearest integer is.

If ${{\mathrm{E}}_1}^{°}$, ${{\mathrm{E}}_2}^{°}$ and ${{\mathrm{E}}_3}^{°}$are the standard electrode potentials for $\mathrm{Fe} | {\mathrm{Fe}}^{2+}, {\mathrm{Fe}}^{2+}| {\mathrm{Fe}}^{3+}$and $\mathrm{Fe} |{\mathrm{Fe}}^{3+}$ electrodes, respectively, derive a relation between ${{\mathrm{E}}_1}^{°}, {{\mathrm{E}}_2}^{°}$and ${{\mathrm{E}}_3}^{°}$.

Calculate the standard electrode potential of ${\mathrm{Cu}}^{+}/\mathrm{Cu}$ half cell. Given that the standard reduction potentials of ${\mathrm{Cu}}^{2+}/\mathrm{Cu}$ and ${\mathrm{Cu}}^{2+}/{\mathrm{Cu}}^{+}$ are $0.337 \mathrm{V}$ and $0.153 \mathrm{V}$respectively.

Derive the relationship between Gibb's free energy change and the cell potential.

The e.m.f. of the cell $\mathrm{Cd}\left(\mathrm{s}\right)/{\mathrm{CdCl}}_2\left(0.1 \mathrm{M}\right)\parallel \mathrm{AgCl}\left(\mathrm{s}\right)/\mathrm{Ag}\left(\mathrm{s}\right)$ ) in which the cell reaction is $\mathrm{Cd}\left(\mathrm{s}\right)+2\mathrm{AgCl}\left(\mathrm{s}\right)\stackrel{ }{\to }2\mathrm{Ag}\left(\mathrm{s}\right)+{\mathrm{Cd}}^{2+}\left(\mathrm{aq}\right)+2{\mathrm{Cl}}^{-}\left(\mathrm{aq}\right)$ is $0.6915 \mathrm{V}$ at $0^{°} \mathrm{C}$ and $0.6753 \mathrm{V}$ at ${25}^{°} \mathrm{C}$. Calculate the enthalpy change of the reaction at ${25}^{°} \mathrm{C}$. 

Which one of the following statement is always true about the spontaneous cell reaction in a galvanic cell?

For the reduction of silver ions with copper metal, the standard cell potential was found to be $+0.46 \mathrm{V}$ at ${25}^{°} \mathrm{C}$. The value of standard Gibbs energy $△{\mathrm{G}}^{\circ }$ will be ($\mathrm{F}=96500 \mathrm{C} {\mathrm{mol}}^{-1}$)

The standard emf of a galvanic cell involving $3$ moles of electrons in a redox reaction is $0.59 \mathrm{V}$. The equilibrium constant for the reaction of the cell is

The cell in which the following reaction occurs:

$2{\mathrm{Fe}}^{3+}\left(\mathrm{aq}\right)+2{\mathrm{I}}^{-}\left(\mathrm{aq}\right)\stackrel{ }{\to }2{\mathrm{Fe}}^{2+}\left(\mathrm{aq}\right)+{\mathrm{I}}_2\left(\mathrm{s}\right)$ has ${{\mathrm{E}}^{\circ }}_{\mathrm{cell}}=0.236 \mathrm{V}$ at $298 \mathrm{K}$. Calculate the standard Gibbs energy of the cell reaction. 

($1\mathrm{F}=96500 \mathrm{C} {\mathrm{mol}}^{-}$)

${\mathrm{Cr}}_2{{\mathrm{O}}_7}^{2-}+14{\mathrm{H}}^{+}+6{\mathrm{e}}^{-}\stackrel{ }{\to }2{\mathrm{Cr}}^{3+}+7{\mathrm{H}}_2\mathrm{O}; {\mathrm{E}}^{\circ }=1.33 \mathrm{V}$

$3\times \left[2{\mathrm{I}}^{-}\stackrel{ }{\to }{\mathrm{I}}_2+2{\mathrm{e}}^{-}\right], {\mathrm{E}}^{\circ }=-0.54 \mathrm{V}$

Find out the value of the equilibrium constant and Gibbs free energy change in the reaction given above.

The emf (${{\mathrm{E}}^{\circ }}_{\mathrm{cell}}$) of the cell reaction, $3{\mathrm{Sn}}^{4+}+2\mathrm{Cr}\stackrel{ }{\to }3{\mathrm{Sn}}^{2+}+2{\mathrm{Cr}}^{2+}$ is $0.89 \mathrm{V}$. Calculate $△{\mathrm{G}}^{\circ }$for the reaction. ($\mathrm{F}=96500 \mathrm{C} {\mathrm{mol}}^{-1}$)
 

For the equilibrium, $2{\mathrm{H}}_2\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\stackrel{ }{\rightleftharpoons }2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)$ at ${25}^{\circ } \mathrm{C}$ $△{\mathrm{G}}^{\circ }$ is $-474.78 \mathrm{kJ} {\mathrm{mol}}^{-1}$. Calculate $\mathrm{logK}$ for it. (($\mathrm{R}=8.314 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}$)
 

Determine the values of equilibrium constant ($\mathrm{K}$) and $△{\mathrm{G}}^{\circ }$ for the following reaction :

$\mathrm{Ni}\left(\mathrm{s}\right)+2{\mathrm{Ag}}^{+}\left(\mathrm{aq}\right)\stackrel{ }{\to }{\mathrm{Ni}}^{2+}\left(\mathrm{aq}\right)+2\mathrm{Ag}\left(\mathrm{s}\right); {\mathrm{E}}^{\circ }=1.05 \mathrm{V}$ ($1\mathrm{F}=96500 \mathrm{C} {\mathrm{mol}}^{-1}$)

For the cell, $\mathrm{Mg}\left(\mathrm{s}\right)/{\mathrm{Mg}}^{2+}\left(\mathrm{aq}\right)\parallel {\mathrm{Ag}}^{+}\left(\mathrm{aq}\right)/\mathrm{Ag}\left(\mathrm{s}\right)$, calculate the equilibrium constant of the cell reaction at ${25}^{°} \mathrm{C}$ and maximum work that can be obtained by operating the cell.

${{\mathrm{E}}^{\circ }}_{{\mathrm{Mg}}^{2+}/\mathrm{Mg}}=-2.37 \mathrm{V}$ and ${{\mathrm{E}}^{\circ }}_{{\mathrm{Ag}}^{+}/\mathrm{Ag}}=+0.80 \mathrm{V}, \mathrm{R}=8.31\mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}$

Calculate the standard free energy change taking place in ${\mathrm{H}}_2/{\mathrm{O}}_2$ fuel cell in which the following reactions occur:

(i) ${\mathrm{O}}_2+4{\mathrm{H}}^{+}+4{\mathrm{e}}^{-}\stackrel{ }{\to }2{\mathrm{H}}_2\mathrm{O}; {\mathrm{E}}^{\circ }=1.229 \mathrm{V}$

(ii) $2{\mathrm{H}}_2\stackrel{ }{\to }4{\mathrm{H}}^{+}+4{\mathrm{e}}^{-}; {\mathrm{E}}^{\circ }=0.000 \mathrm{V}$

Estimate the minimum potential difference needed to reduce ${\mathrm{Al}}_2{\mathrm{O}}_3$ at ${500}^{°} \mathrm{C}$. The free energy change for the decomposition reaction 

$\frac{2}{3}{\mathrm{Al}}_2{\mathrm{O}}_3\stackrel{ }{\to }\frac{4}{3}\mathrm{Al}+{\mathrm{O}}_2$ is $△\mathrm{G}=+960 \mathrm{kJ}, \mathrm{F}=96500 \mathrm{C} {\mathrm{mol}}^{-1}$

Calculate the standard free energy change and maximum work obtainable for the reaction, $\mathrm{Zn}\left(\mathrm{s}\right)+{\mathrm{Cu}}^{2+}\left(\mathrm{aq}\right)\stackrel{ }{\rightleftharpoons }\mathrm{Cu}\left(\mathrm{s}\right)+{\mathrm{Zn}}^{2+}\left(\mathrm{aq}\right)$. Given,  ${{\mathrm{E}}^{°}}_{{\mathrm{Cu}}^{2+}/\mathrm{Cu}}=+0.34 \mathrm{V}$, ${{\mathrm{E}}^{°}}_{{\mathrm{Zn}}^{2+}/\mathrm{Zn}}=-0.76 \mathrm{V}$, $\mathrm{F}=96500 \mathrm{C} {\mathrm{mol}}^{-1}$. Also calculate the equilibrium constant for the reaction.
 

Calculate the standard free energy change and maximum work obtainable for the reaction, $\mathrm{Zn}\left(\mathrm{s}\right)+{\mathrm{Cu}}^{2+}\left(\mathrm{aq}\right)\stackrel{ }{\rightleftharpoons }\mathrm{Cu}\left(\mathrm{s}\right)+{\mathrm{Zn}}^{2+}\left(\mathrm{aq}\right)$. Given,  ${{\mathrm{E}}^{°}}_{{\mathrm{Cu}}^{2+}/\mathrm{Cu}}=+0.34 \mathrm{V}$, ${{\mathrm{E}}^{°}}_{{\mathrm{Zn}}^{2+}/\mathrm{Zn}}=-0.76 \mathrm{V}$, $\mathrm{F}=96500 \mathrm{C} {\mathrm{mol}}^{-1}$ .