Nernst equation

An electrochemical cell, consist of the following two redox couples, $\ce{M^{x+}}$(aq)/M(s) $[E^\ominus_{red}=+0.15\ \mathrm V]$ and $\ce{Fe^{3+}}$(aq)/Fe(s) $[E^\ominus_{red}=-0.036\ \mathrm V]$. The cell EMF ($E_\text{cell}$) is recorded to be 0.2057 V. If the reaction quotient of the electrochemical reaction is found to be $10^{-2}$, then the value of $x$ is ________. (Nearest integer)
[Given : M is a p-block metal and $\dfrac{2.303RT}F=0.059$ V]

One half cell in a voltaic cell is constructed by dipping silver rod in $\ce{AgNO3}$ solution of unknown concentration, other half cell is Zn rod dipped in 1 molar solution of $\ce{ZnSO4}$.

A voltage of 1.60 V is measured at 298 K for this cell. What is the concentration of $\ce{Ag+}$ ions used in terms of $\log x$ ($x=[\ce{Ag+}]$) ?

$E^\circ_{\ce{Zn^{2+}}/\ce{Zn}}=-0.76$ V, $E^\circ_{\ce{Ag+}/\ce{Ag}}=+0.80$ V, $\dfrac{2.303RT}F=0.059$ V

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 ?

The cell potential for the following cell
$$\mathrm{Pt\,|H_2(g)|H^+(aq)\,||\,Cu^{2+}(0.01\ M)|Cu(s)}$$
is 0.576 V at 298 K. The pH of the solution is ______. (Nearest integer)

(Given : $E^\circ_{\mathrm{Cu^{2+}/Cu}}=0.34$ V and $\dfrac{2.303RT}F=0.06$ V)

$$\mathrm{Cu(s)+Sn^{2+}(0.001M)\rightarrow Cu^{2+}(0.01M)+Sn(s)}$$
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$^{-1}$]

The cell potential for the given cell at 298 K

$\mathrm{Pt\,|\,H_2(g,1\,bar)\,|\,H^+(aq)\,||\,Cu^{2+}(aq)\,|\,Cu(s)}$

is 0.31V. The pH of the acidic solution is found to be 3, whereas the concentration of $\mathrm{Cu^{2+}}$ is $10^{-x}$ M. The value of $x$ is ______.

(Given: $E^\ominus_{\mathrm{Cu^{2+}/Cu}}=0.34$ V and $\dfrac{2.303RT}F=0.06$ V)

In which of the following half cells, electrochemical reaction is pH dependent ?

The cell potential for $\mathrm{Zn|Zn^{2+}(aq)||Sn^{x+}|Sn}$ is 0.801 V at 298 K. The reaction quotient for the above reaction is $10^{-2}$. The number of electrons involved in the given electrochemical cell reaction is ______.

(Given : $E^\circ_{\mathrm{Zn^{2+}|Zn}}=-0.763$ V, $E^\circ_{\mathrm{Sn^{x+}|Sn}}=+0.008$ V and $\dfrac{2.303RT}F=0.06$ V)

For a cell, Cu(s) | Cu$^{2+}$(0.001 M) || Ag$^+$ (0.01 M) | Ag (s) the cell potential is found to be 0.43 V at 298 K. The magnitude of standard electrode potential for Cu$^{2+}$/Cu is _______ $\times10^{-2}$ V.

[Given : $E^\ominus_{\mathrm{Ag^+/Ag}}$ = 0.80 V and $\dfrac{2.303RT}F$ = 0.06 V]

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 _______.

Some standard electrode potentials at 298 K are given below:

Couple	$E^\circ$
$\ce{Pb^{2+}/Pb}$	−0.13 V
$\ce{Ni^{2+}/Ni}$	−0.24 V
$\ce{Cd^{2+}/Cd}$	−0.40 V
$\ce{Fe^{2+}/Fe}$	−0.44 V

To a solution containing 0.001 M of $\mathbf X^{2+}$ and 0.1 M of $\mathbf Y^{2+}$, the metal rods $\mathbf X$ and $\mathbf Y$ are inserted (at 298 K) and connected by a conducting wire. This resulted in dissolution of $\mathbf X$. The correct combination(s) of $\mathbf X$ and $\mathbf Y$, respectively, is(are)

(Given: Gas constant, R = 8.314 J K$^{-1}$ mol$^{-1}$, Faraday constant, F = 96500 C mol$^{-1}$)

For the electrochemical cell,

$$\ce{Mg(s) | Mg^{2+}(aq, 1 M) || Cu^{2+}(aq, 1 M) | Cu(s)}$$

the standard emf of the cell is 2.70 V at 300 K. When the concentration of $\ce{Mg^{2+}}$ is changed to $x$ M, the cell potential changes to 2.67 V at 300 K. The value of $x$ is ______.

(given, $\dfrac FR = 11500\ \mathrm{K\,V^{-1}}$, where $F$ is the Faraday constant and $R$ is the gas constant, $\ln(10) = 2.30$)

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]

To find the standard potential of $\ce{M^3+/M}$ electrode, the following cell is constituted : $\ce{Pt/M/M^3+}$(0.001 mol L$^{-1}$)/$\ce{Ag+}$(0.01 mol L$^{-1}$)/Ag

The emf of the cell is found to be 0.421 volt at 298 K. The standard potential of half reaction $\ce{M^3+ + 3e- -> M}$ at 298 K will be :

(Given $E^\circ_{\ce{Ag+/Ag}}$ at 298 K = 0.80 Volt)

For the following electrochemical cell at 298 K,
$$\mathrm{Pt}(s)\mid\ce{H2}(g,1\text{ bar})\mid\ce{H+}(aq,1\text{ M})\parallel\ce{M^{4+}}(aq),\ce{M^{2+}}(aq)\mid\mathrm{Pt}(s)$$
$E_{cell}=0.092$ V when $\dfrac{[\ce{M^{2+}}(aq)]}{[\ce{M^{4+}}(aq)]}=10^x$.

Given: $E^0_{\ce{M^{4+}}/\ce{M^{2+}}}=0.151$ V; $2.303\dfrac{RT}{F}=0.059$ V

The value of $x$ is

At 298 K, the standard reduction potentials are 1.51 V for $\ce{MnO4- | Mn^2+}$, 1.36 V for $\ce{Cl2 | Cl-}$, 1.07 V for $\ce{Br2 | Br-}$, and 0.54 V for $\ce{I2 | I-}$. At pH = 3, permanganate is expected to oxidize : $\left(\dfrac{RT}F=0.059\text{ V}\right)$

The solubility product ($K_{sp}$; mol³ dm⁻⁹) of $\ce{MX2}$ at 298 K based on the information available for the given concentration cell is (take $2.303\times R\times298/F=0.059$ V)

Consider the following cell reaction:
$$\ce{2Fe(s) + O2(g) + 4H+(aq) -> 2Fe^{2+}(aq) + 2H2O(l)}\qquad E^\circ=1.67\ \mathrm V$$
At $[\ce{Fe^{2+}}]=10^{-3}$ M, $P(\ce{O2})=0.1$ atm and pH = 3, the cell potential at 25 °C is

For the above cell