Gibbs energy and EMF

Consider the following two half-cell reactions along with the standard reduction potential given :
$$\ce{CO2 + 6H+ + 6e- -> CH3OH + H2O}\qquad E^\circ_\text{red}=0.02\ \mathrm V$$
$$\ce{1/2O2 + 2H+ + 2e- -> H2O}\qquad E^\circ_\text{red}=1.23\ \mathrm V$$
A fuel cell was set up using the above two reactions such that the cell operates under the standard condition of 1 bar pressure and 298 K temperature. The fuel cell works with 80% efficiency. If the work derived from the cell using 1 mol of $\ce{CH3OH}$ is used to compress an ideal gas isothermally against a constant pressure of 1 kPa, then the change in the volume of the gas, $\Delta V$ = ________ m³. (nearest integer)
Given : $F=96500$ C mol$^{-1}$

For a general redox reaction

Anode: $\mathrm{Red_1}\to\mathrm{Ox_1}^{n_1^+}+n_1e^-$

Cathode: $\mathrm{Ox_2}+n_2e^-\to\mathrm{Red_2}^{n_2^-}$

Which of the following statement is incorrect ?

Given at 298 K : $E^\ominus_{\ce{Fe^2+}/\ce{Fe}}=X$ Volt, $E^\ominus_{\ce{Fe^3+}/\ce{Fe}}=Y$ Volt

The $E^\ominus_{\ce{Fe^3+}/\ce{Fe^2+}}$ in Volt at 298 K is given by :

An electrochemical cell is fueled by the combustion of butane at 1 bar and 298 K. Its cell potential is $\dfrac{\boldsymbol{X}}{F}\times10^3$ volts, where $F$ is the Faraday constant. The value of $\boldsymbol{X}$ is _____.

Use: Standard Gibbs energies of formation at 298 K are: $\Delta_fG^\circ_{\ce{CO2}} = -394\ \mathrm{kJ\,mol^{-1}}$; $\Delta_fG^\circ_{\text{water}} = -237\ \mathrm{kJ\,mol^{-1}}$; $\Delta_fG^\circ_{\text{butane}} = -18\ \mathrm{kJ\,mol^{-1}}$

The reduction potential ($E^0$, in V) of $\ce{MnO4^-(aq)}/\ce{Mn(s)}$ is _____.

[Given: $E^0_{(\ce{MnO4^-(aq)}/\ce{MnO2(s)})} = 1.68$ V; $E^0_{(\ce{MnO2(s)}/\ce{Mn^2+(aq)})} = 1.21$ V; $E^0_{(\ce{Mn^2+(aq)}/\ce{Mn(s)})} = -1.03$ V]

The correct option(s) about entropy (S) is(are)

[R = gas constant, F = Faraday constant, T = Temperature]

The $\left(\dfrac{\partial E}{\partial T}\right)_P$ of different types of half cells are as follows :
$$\begin{array}{cccc}A&B&C&D\\1\times10^{-4}&2\times10^{-4}&0.1\times10^{-4}&0.2\times10^{-4}\end{array}$$
(Where E is the electromotive force)

Which of the above half cells would be preferred to be used as reference electrode ?

$$\mathrm{Cu(s)+Sn^{2+}(0.001M)\rightarrow Cu^{2+}(0.01M)+Sn(s)}$$
The Gibbs free energy change for the above reaction at 298 K is $x\times10^{-1}$ kJ mol$^{-1}$. The value of $x$ is ______. [nearest integer]

[Given : $E^\ominus_{\mathrm{Cu^{2+}/Cu}}=0.34$ V; $E^\ominus_{\mathrm{Sn^{2+}/Sn}}=-0.14$ V; $F=96500$ C mol$^{-1}$]

For the reaction taking place in the cell:
$$\mathrm{Pt(s)|H_2(g)|H^+(aq)\,||\,Ag^+(aq)|Ag(s)}$$
$E^\circ_{\rm cell}=+0.5332$ V.

The value of $\Delta_fG^\ominus$ is ______ kJ mol$^{-1}$. (in nearest integer)

For the given reactions

$$\mathrm{Sn^{2+}+2e^-\rightarrow Sn}$$
$$\mathrm{Sn^{4+}+4e^-\rightarrow Sn}$$

the electrode potentials are ; $E^\circ_{\mathrm{Sn^{2+}/Sn}}=-0.140$ V and $E^\circ_{\mathrm{Sn^{4+}/Sn}}=0.010$ V. The magnitude of standard electrode potential for $\mathrm{Sn^{4+}/Sn^{2+}}$ i.e. $E^\circ_{\mathrm{Sn^{4+}/Sn^{2+}}}$ is ______ $\times10^{-2}$ V. (Nearest integer)

For the given cell Zn(s) | Zn$^{2+}$ (C$_1$ M) || Zn$^{2+}$ (C$_2$ M) | Zn(s) the change in Gibbs energy (ΔG) will be zero when $\dfrac{C_1}{C_2}$ is equal to _______.

Consider a 70% efficient hydrogen-oxygen fuel cell working under standard conditions at 1 bar and 298 K. Its cell reaction is

$$\ce{H2(g) + 1/2 O2(g) -> H2O(l)}.$$

The work derived from the cell on the consumption of $1.0\times10^{-3}$ mol of $\ce{H2(g)}$ is used to compress 1.00 mol of a monoatomic ideal gas in a thermally insulated container. What is the change in the temperature (in K) of the ideal gas?

The standard reduction potentials for the two half-cells are given below.

$$\ce{O2(g) + 4H+(aq) + 4e- -> 2H2O(l)},\quad E^0 = 1.23\ \text{V},$$

$$\ce{2H+(aq) + 2e- -> H2(g)},\quad E^0 = 0.00\ \text{V}.$$

Use $F = 96500\ \mathrm{C\,mol^{-1}}$, $R = 8.314\ \mathrm{J\,mol^{-1}\,K^{-1}}$.

Consider an electrochemical cell: $\mathrm{A(s)\,|\,A^{n+}(aq,\ 2\ M)\,||\,B^{2n+}(aq,\ 1\ M)\,|\,B(s)}$. The value of $\Delta H^\ominus$ for the cell reaction is twice that of $\Delta G^\ominus$ at 300 K. If the emf of the cell is zero, the $\Delta S^\ominus$ (in J K$^{-1}$ mol$^{-1}$) of the cell reaction per mole of B formed at 300 K is ____.

(Given: ln(2) = 0.7, $R$ (universal gas constant) = 8.3 J K$^{-1}$ mol$^{-1}$. $H$, $S$ and $G$ are enthalpy, entropy and Gibbs energy, respectively.)

For the following cell,

$$\mathrm{Zn(s)\,|\,ZnSO_4(aq)\,\|\,CuSO_4(aq)\,|\,Cu(s)}$$

when the concentration of $\mathrm{Zn^{2+}}$ is 10 times the concentration of $\mathrm{Cu^{2+}}$, the expression for $\Delta G$ (in $\mathrm{J\,mol^{-1}}$) is

[F is Faraday constant; R is gas constant; T is temperature; $E^o(cell) = 1.1$ V]

What is the standard reduction potential (E°) for $\ce{Fe^3+ -> Fe}$ ?

Given that :

$\ce{Fe^2+ + 2e- -> Fe}$ ; $E^\circ_{\ce{Fe^2+/Fe}}=-0.47$ V

$\ce{Fe^3+ + e- -> Fe^2+}$ ; $E^\circ_{\ce{Fe^3+/Fe^2+}}=+0.77$ V

All the energy released from the reaction $\mathbf X\to\mathbf Y$, $\Delta_rG^\circ=-193\ \mathrm{kJ\,mol^{-1}}$ is used for oxidizing $\ce{M+}$ as $\ce{M+ -> M^{3+} + 2e-}$, $E^\circ=-0.25$ V.

Under standard conditions, the number of moles of $\ce{M+}$ oxidized when one mole of X is converted to Y is

$[F=96500\ \mathrm{C\,mol^{-1}}]$

Given below are the half - cell reactions :

$\ce{Mn^2+ + 2e- -> Mn}$ ; $E^\circ=-1.18$ V

$2\left(\ce{Mn^3+ + e- -> Mn^2+}\right)$ ; $E^\circ=+1.51$ V

The $E^\circ$ for $\ce{3Mn^2+ -> Mn + 2Mn^3+}$ will be :

The standard reduction potential data at 25 °C is given below.

$E^\circ(\ce{Fe^{3+}},\ce{Fe^{2+}})=+0.77$ V; $E^\circ(\ce{Fe^{2+}},\ce{Fe})=-0.44$ V;
$E^\circ(\ce{Cu^{2+}},\ce{Cu})=+0.34$ V; $E^\circ(\ce{Cu+},\ce{Cu})=+0.52$ V;
$E^\circ[\ce{O2(g) + 4H+ + 4e- -> 2H2O}]=+1.23$ V; $E^\circ[\ce{O2(g) + 2H2O + 4e- -> 4OH-}]=+0.40$ V;
$E^\circ(\ce{Cr^{3+}},\ce{Cr})=-0.74$ V; $E^\circ(\ce{Cr^{2+}},\ce{Cr})=-0.91$ V

Match $E^\circ$ of the redox pair in List I with the values given in List II and select the correct answer using the code given below the lists:

The value of $\Delta G$ (kJ mol⁻¹) for the given cell is (take 1 F = 96500 C mol⁻¹)

For the above cell