Electrochemistry

At 300 K, the molar conductivities of the aqueous solutions of three salts at two different concentrations are given below:

Salt	Concentration (M)	Molar conductivity (S cm$^2$ mol$^{-1}$)
$\ce{NaNO3}$	0.01	111
	0.04	101
$\ce{NaCl}$	0.01	117
	0.04	107
$\ce{AgNO3}$	0.01	125
	0.04	116

The conductivity of a saturated aqueous solution of AgCl is $1.40\times10^{-6}$ S cm$^{-1}$ at 300 K. If the solubility of AgCl in water at 300 K is X mol L$^{-1}$, then $\log_{10}(X^{-1})$ is

(Assume that AgCl dissolved in water ionizes completely and that the molar conductivity of saturated AgCl solution is equal to its limiting molar conductivity.)

An electrochemical cell is constructed using half cells in the direction of spontaneous change
$$\ce{Fe(OH)2(s) + 2e- -> Fe(s) + 2OH-(aq)}\qquad E^\theta=-0.88\ \mathrm V$$
and $$\ce{AgBr(s) + e- -> Ag(s) + Br-(aq)}\qquad E^\theta=+0.07\ \mathrm V$$
Which of the following option is correct ?

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$^{-1}$

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

At 298 K, the molar conductivity of $x$% (w/w) MX solution (aqueous) is 123.5 S cm² mol$^{-1}$. The conductance of same solution is $1.9\times10^{-3}$ S. The value of $x$ is ________ $\times10^{-2}$.

(Given : cell constant = 1.3 cm$^{-1}$; molar mass of MX is 75 g mol$^{-1}$, density of aqueous solution of MX at 298 K is 1.0 g mL$^{-1}$)

Consider the following data.

Electrolyte	$\Lambda^\circ_m$ (S cm² mol$^{-1}$)
$\ce{BaCl2}$	$x_1$
$\ce{H2SO4}$	$x_2$
HCl	$x_3$

$\ce{BaSO4}$ is sparingly soluble in water. If the conductivity of the saturated $\ce{BaSO4}$ solution is $x$ S cm$^{-1}$ then the solubility product of $\ce{BaSO4}$ can be given as

(Here $\Lambda_m=\Lambda^\circ_m$)

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 :

In an electrochemical cell, dichromate ions in aqueous acidic medium are reduced to $\ce{Cr^3+}$. The current (in amperes) that flows through the cell for 48.25 minutes to produce 1 mole of $\ce{Cr^3+}$ is _____.

Use: 1 Faraday $= 96500\ \mathrm{C\,mol^{-1}}$

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: $\Delta_fG^\circ_{\ce{CO2}} = -394\ \mathrm{kJ\,mol^{-1}}$; $\Delta_fG^\circ_{\text{water}} = -237\ \mathrm{kJ\,mol^{-1}}$; $\Delta_fG^\circ_{\text{butane}} = -18\ \mathrm{kJ\,mol^{-1}}$

In a conductometric titration, small volume of titrant of higher concentration is added stepwise to a larger volume of titrate of much lower concentration, and the conductance is measured after each addition.

The limiting ionic conductivity ($\Lambda_0$) values (in $\mathrm{mS\,m^2\,mol^{-1}}$) for different ions in aqueous solutions are given below:

Ions	$\ce{Ag+}$	$\ce{K+}$	$\ce{Na+}$	$\ce{H+}$	$\ce{NO3-}$	$\ce{Cl-}$	$\ce{SO4^2-}$	$\ce{OH-}$	$\ce{CH3COO-}$
$\Lambda_0$	6.2	7.4	5.0	35.0	7.2	7.6	16.0	19.9	4.1

For different combinations of titrates and titrants given in List-I, the graphs of 'conductance' versus 'volume of titrant' are given in List-II.

Match each entry in List-I with the appropriate entry in List-II and choose the correct option.

An aqueous solution of hydrazine ($\ce{N2H4}$) is electrochemically oxidized by $\ce{O2}$, thereby releasing chemical energy in the form of electrical energy. One of the products generated from the electrochemical reaction is $\ce{N2(g)}$.

Choose the correct statement(s) about the above process

Plotting $1/\Lambda_\mathrm{m}$ against $c\Lambda_\mathrm{m}$ for aqueous solutions of a monobasic weak acid (HX) resulted in a straight line with y-axis intercept of P and slope of S. The ratio $\mathrm{P}/\mathrm{S}$ is

[$\Lambda_\mathrm{m}$ = molar conductivity; $\Lambda^\circ_\mathrm{m}$ = limiting molar conductivity; c = molar concentration; $K_\mathrm{a}$ = dissociation constant of HX]

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]

Consider the strong electrolytes $\mathrm{Z_mX_n}$, $\mathrm{U_mY_p}$ and $\mathrm{V_mX_n}$. Limiting molar conductivity $(\Lambda^0)$ of $\mathrm{U_mY_p}$ and $\mathrm{V_mX_n}$ are 250 and 440 S cm$^2$ mol$^{-1}$, respectively. The value of $(m + n + p)$ is ________.

Given:

Ion	$\mathrm{Z^{n+}}$	$\mathrm{U^{p+}}$	$\mathrm{V^{n+}}$	$\mathrm{X^{m-}}$	$\mathrm{Y^{m-}}$
$\lambda^0$ (S cm$^2$ mol$^{-1}$)	50.0	25.0	100.0	80.0	100.0

$\lambda^0$ is the limiting molar conductivity of ions

The plot of molar conductivity $(\Lambda)$ of $\mathrm{Z_mX_n}$ vs $c^{1/2}$ is given below.

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

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

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)

The resistance of a conductivity cell containing 0.01 M KCl solution at 298 K is $1750\ \Omega$. If the conductivity of 0.01M KCl solution at 298 K is $0.152\times10^{-3}\ \mathrm{S\,cm^{-1}}$, then the cell constant of the conductivity cell is ______ $\times10^{-3}\ \mathrm{cm^{-1}}$.

Which one of the following alkaline earth metal ions has the highest ionic mobility in its aqueous solution ?