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JEE Mains | PYQ

If the conductivity of mercury at \( 0^\circ \text{C} \) is \( 1.07 \times 10^{6} \, \text{S m}^{-1} \) and the resistance of a cell containing mercury is \( 0.243 \, \Omega \), then the cell constant of the cell is \( x \times 10^{4} \, \text{m}^{-1} \). The value of \( x \) is:

The standard reduction potentials at \( 298 \, \text{K} \) for the following half cells are given below:
\( \text{Cr}_2\text{O}_7^{2-} + 14\text{H}^{+} + 6e^{-} \rightarrow 2\text{Cr}^{3+} + 7\text{H}_2\text{O}, \, E^{\circ} = 1.33 \, \text{V} \)
\( \text{Fe}^{3+} (\text{aq}) + 3e^{-} \rightarrow \text{Fe}, \, E^{\circ} = -0.04 \, \text{V} \)
\( \text{Ni}^{2+} (\text{aq}) + 2e^{-} \rightarrow \text{Ni}, \, E^{\circ} = -0.25 \, \text{V} \)
\( \text{Ag}^{+} (\text{aq}) + e^{-} \rightarrow \text{Ag}, \, E^{\circ} = 0.80 \, \text{V} \)
\( \text{Au}^{3+} (\text{aq}) + 3e^{-} \rightarrow \text{Au}, \, E^{\circ} = 1.40 \, \text{V} \)
Consider the given electrochemical reactions,
The number of metal(s) which will be oxidized by \( \text{Cr}_2\text{O}_7^{2-} \), in aqueous solution is _______.

The standard reduction potential values of some of the p-block ions are given below. Predict the one with the strongest oxidising capacity.

Consider the following two half-cell reactions along with the standard reduction potential given:
\( \text{CO}_{2} + 6\text{H}^{+} + 6e^{-} \rightarrow \text{CH}_{3}\text{OH} + \text{H}_{2}\text{O} \quad E^{0}_{\text{red}} = 0.02 \, \text{V} \)
\( \dfrac{1}{2}\text{O}_{2} + 2\text{H}^{+} + 2e^{-} \rightarrow \text{H}_{2}\text{O} \quad E^{0}_{\text{red}} = 1.23 \, \text{V} \)
A fuel cell was set up using the above two reactions such that the cell operates under the standard condition of \( 1 \, \text{bar} \) pressure and \( 298 \, \text{K} \) temperature. The fuel cell works with \( 80\% \) efficiency. If the work derived from the cell using \( 1 \, \text{mol} \) of \( \text{CH}_{3}\text{OH} \) is used to compress an ideal gas isothermally against a constant pressure of \( 1 \, \text{kPa} \), then the change in the volume of the gas, \( \Delta V = \) _________ \( \text{m}^{3} \). (nearest integer)
Given : \( F = 96500 \, \text{C mol}^{-1} \)

Standard electrode potentials for a few half cells are mentioned below:
\( E^\circ_{\mathrm{Cu^{2+}/Cu}} = 0.34 \, \mathrm{V}, \; E^\circ_{\mathrm{Zn^{2+}/Zn}} = -0.76 \, \mathrm{V} \)
\( E^\circ_{\mathrm{Ag^{+}/Ag}} = 0.80 \, \mathrm{V}, \; E^\circ_{\mathrm{Mg^{2+}/Mg}} = -2.37 \, \mathrm{V} \)
Which one of the following cells gives the most negative value of \( \Delta G^\circ \)?

For lead storage battery pick the correct statements.
A. During charging of battery, \( \mathrm{PbSO_4} \) on anode is converted into \( \mathrm{PbO_2} \)
B. During charging of battery, \( \mathrm{PbSO_4} \) on cathode is converted into \( \mathrm{PbO_2} \)
C. Lead storage battery consists of grid of lead pack with \( \mathrm{PbO_2} \) as anode
D. Lead storage battery has \( \sim 38\% \) solution of sulphuric acid as an electrolyte
Choose the correct answer from the options given below:

The major product of the following reaction is: \( \mathrm{CH_3CH_2CH{=}O} \xrightarrow[\text{reflux}]{\text{excess } \mathrm{HCHO}\ \text{alkali}} \ ? \)

Match List –I with List –II

Choose the correct answer form the options given below:

$
\text{The electrode potential of the following half cell at } 298 \text{ K}
$
$
\text{X} \mid \text{X}^{2+}(0.001\text{M}) \parallel \text{Y}^{2+}(0.01\text{M}) \mid \text{Y is }\underline{\qquad\qquad} \times 10^{-2}\text{ V (Nearest integer).}
$
$
\text{Given : } E^\circ_{\text{X}^{2+} \mid \text{X}} = -2.36\text{ V}
$
$
E^\circ_{\text{Y}^{2+} \mid \text{Y}} = +0.36\text{ V}
$
$
\frac{2.303\text{RT}}{\text{F}} = 0.06\text{ V}
$

One of the commonly used electrode is calomel electrode. Under which of the following categories, calomel electrode comes?

The cell potential for \( \mathrm{Zn|Zn^{2+}(aq)||Sn^{x+}|Sn} \) is \( 0.801 \, \text{V} \) at \( 298 \, \text{K} \). The reaction quotient for the above reaction is \( 10^{-2} \). The number of electrons involved in the given electrochemical cell reaction is _______.
(Given : \( E^{0}_{\mathrm{Zn^{2+}|Zn}} = -0.763 \, \text{V} \), \( E^{0}_{\mathrm{Sn^{x+}|Sn}} = +0.008 \, \text{V} \) and \( \dfrac{2.303RT}{F} = 0.06 \, \text{V} \))

\( 0.2\% \, (\text{w/v}) \) solution of \( \text{NaOH} \) is measured to have resistivity \( 870.0 \, \text{m}\,\Omega\,\text{m} \). The molar conductivity of the solution will be __________ \( \times 10^{2} \, \text{mS dm}^{2} \, \text{mol}^{-1} \). (Nearest integer)

On charging the lead storage battery, the oxidation state of lead changes from \( x_{1} \) to \( y_{1} \) at the anode and from \( x_{2} \) to \( y_{2} \) at the cathode. The values of \( x_{1}, y_{1}, x_{2}, y_{2} \) are respectively:

The mass of silver (Molar mass of \( \mathrm{Ag} : 108 \, \text{g mol}^{-1} \)) displaced by a quantity of electricity which displaces \( 5600 \, \text{mL} \) of \( \mathrm{O_2} \) at S.T.P. will be ________ \( \text{g} \).

For the cell \( \mathrm{Cu(s)}\,|\,\mathrm{Cu^{2+}(aq)}\,(0.1\,\mathrm{M})\,||\,\mathrm{Ag^{+}(aq)}\,(0.01\,\mathrm{M})\,|\,\mathrm{Ag(s)} \) the cell potential \( E_1 = 0.3095 \, \text{V} \).
For the cell \( \mathrm{Cu(s)}\,|\,\mathrm{Cu^{2+}(aq)}\,(0.1\,\mathrm{M})\,||\,\mathrm{Ag^{+}(aq)}\,(0.001\,\mathrm{M})\,|\,\mathrm{Ag(s)} \) the cell potential = ____________ \( \times 10^{-2} \) \( \text{V} \). (Round off to the Nearest Integer).
[Use : \( \dfrac{2.303\,RT}{F} = 0.059 \)]

For the given reactions
\( \mathrm{Sn^{2+}} + 2e^- \rightarrow \mathrm{Sn} \)
\( \mathrm{Sn^{4+}} + 4e^- \rightarrow \mathrm{Sn} \)
the electrode potentials are; \( E^{0}_{\mathrm{Sn^{2+}/Sn}} = -0.140 \, \text{V} \) and \( E^{0}_{\mathrm{Sn^{4+}/Sn}} = 0.010 \, \text{V} \). The magnitude of standard electrode potential for \( \mathrm{Sn^{4+}/Sn^{2+}} \) i.e. \( E^{0}_{\mathrm{Sn^{4+}/Sn^{2+}}} \) is __________ \( \times 10^{-2} \, \text{V} \).
(Nearest integer)

The molar conductivity of a conductivity cell filled with \( 10 \) moles of \( 20 \, \mathrm{mL} \) \( \mathrm{NaCl} \) solution is \( \Lambda_{m_1} \) and that of \( 20 \) moles another identical cell having \( 80 \, \mathrm{mL} \) \( \mathrm{NaCl} \) solution is \( \Lambda_{m_2} \). The conductivities exhibited by these two cells are same. The relationship between \( \Lambda_{m_2} \) and \( \Lambda_{m_1} \) is:

For the reaction
$2\text{Fe}^{3+}(\text{aq}) + 2\text{I}^-(\text{aq}) \rightarrow 2\text{Fe}^{2+}(\text{aq}) + \text{I}_2(\text{s})$
the magnitude of the standard molar free energy change,
$\Delta_{\text{r}}\text{G}_{\text{m}}^\circ = -\text{________ kJ}$ (Round off to the Nearest Integer).

The \( \left( \frac{\partial E}{\partial T} \right)_P \) of different types of half cells are as follows:

(Where \( E \) is the electromotive force)
Which of the above half cells would be preferred to be used as reference electrode?

The amount of electricity in Coulomb required for the oxidation of \( 1 \, \text{mol} \) of \( \text{H}_2\text{O} \) to \( \text{O}_2 \) is ______ \( \times 10^{5} \, \text{C} \).

The logarithm of equilibrium constant for the reaction $\text{Pd}^{2+} + 4\text{Cl}^- \rightleftharpoons \text{PdCl}_4^{2-}$ is $\underline{\hspace{1cm}}$ (Nearest integer).

Given: $\frac{2.303\text{RT}}{\text{F}} = 0.06\text{V}$

$\text{Pd}^{2+}_{(\text{aq})} + 2\text{e}^- \rightleftharpoons \text{Pd(s)} \, \text{E}^\theta = 0.83\text{V}$

$\text{PdCl}_4^{2-}(\text{aq}) + 2\text{e}^- \rightleftharpoons \text{Pd(s)} + 4\text{Cl}^-(\text{aq}) \, \text{E}^\theta = 0.65\text{V}$

These are physical properties of an element:
(A) Sublimation enthalpy
(B) Ionisation enthalpy
(C) Hydration enthalpy
(D) Electron gain enthalpy
The total number of above properties that affect the reduction potential is _______. (Integer answer)

The number of incorrect statements from the following is__________
A The electrical work that a reaction can perform at constant pressure and temperature is equal to the reaction Gibbs energy
B \( E_\text{cell}^{\circ} \) is dependent on the pressure
C \( \displaystyle \dfrac{\text{d}E^\ominus_{\text{cell}}}{\text{dT}} = \dfrac{\Delta_r S^\ominus}{nF} \)
D A cell is operating reversibly if the cell potential is exactly balanced by an opposing source of potential difference.

Correct order of limiting molar conductivity for cations in water at \( 298 \, \text{K} \) is:

Based on the data given below:
\( E^\circ_{Cr_2O_7^{2-}/Cr^{3+}} = 1.33 \, \text{V} \)       \( E^\circ_{Cl_2/Cl^-} = 1.36 \, \text{V} \)
\( E^\circ_{MnO_4^-/Mn^{2+}} = 1.51 \, \text{V} \)      \( E^\circ_{Cr^{3+}/Cr} = -0.74 \, \text{V} \)
The strongest reducing agent is:

Match List - I with List - II:

Choose the most appropriate answer from the options given below:

The hydrogen electrode is dipped in a solution of \( \mathrm{pH} = 3 \) at \( 25^\circ \mathrm{C} \). The potential of the electrode will be — __________ × \( 10^{-2} \) V.
\(\displaystyle
 \left(\frac{2.303\,RT}{F} = 0.059\,\mathrm{V}\right) \)

\( \text{Cu(s)} + \text{Sn}^{2+}(0.001 \, \text{M}) \longrightarrow \text{Cu}^{2+}(0.01 \, \text{M}) + \text{Sn(s)} \)
The Gibbs free energy change for the above reaction at \( 298 \, \text{K} \) is \( x \times 10^{-1} \, \text{kJ mol}^{-1} \).
The value of \( x \) is ________. [Nearest integer]
[Given: \( E^\ominus_{\text{Cu}^{2+}/\text{Cu}} = 0.34 \, \text{V} \); \( E^\ominus_{\text{Sn}^{2+}/\text{Sn}} = -0.14 \, \text{V} \); \( F = 96500 \, \text{C mol}^{-1} \)]

The molar conductivities at infinite dilution of barium chloride, sulphuric acid and hydrochloric acid are \( 280 \), \( 860 \) and \( 426 \; \mathrm{S \, cm^{2} \, mol^{-1}} \) respectively. The molar conductivity at infinite dilution of barium sulphate is ______ \( \mathrm{S \, cm^{2} \, mol^{-1}} \).

The number of correct statements from the following is ________.
A. \( E_{cell} \) is an intensive parameter
B. A negative \( E^{\ominus} \) means that the redox couple is a stronger reducing agent than the \( \mathrm{H^{+}/H_2} \) couple
C. The amount of electricity required for oxidation or reduction depends on the stoichiometry of the electrode reaction
D. The amount of chemical reaction which occurs at any electrode during electrolysis by a current is proportional to the quantity of electricity passed through the electrolyte

The amount of charge in \( \mathrm{F} \) (Faraday) required to obtain one mole of iron from \( \mathrm{Fe_3O_4} \) is __________. (Nearest Integer)

Given below are two statements:
\( 1 \,\text{M} \) aqueous solutions of each of \( \mathrm{Cu(NO_3)_2,\,AgNO_3,\,Hg_2(NO_3)_2,\,Mg(NO_3)_2} \) are electrolysed using inert electrodes.
\( \text{Given } E_{\text{Ag}^+/\text{Ag}}^\theta = 0.80\text{ V}, \, E_{\text{Hg}_2^{2+}/\text{Hg}}^\theta = 0.79\text{ V}, \, E_{\text{Cu}^{2+}/\text{Cu}}^\theta = 0.34\text{ V and } E_{\text{Mg}^{2+}/\text{Mg}}^\theta = -2.37\text{ V}\)
Statement (I): With increasing voltage, the sequence of deposition of metals on the cathode will be Ag, Hg and Cu.
Statement (II): Magnesium will not be deposited at cathode instead oxygen gas will be evolved at the cathode.
In the light of the above statements, choose the most appropriate answer from the options given below:

Identify the factor from the following that does not affect electrolytic conductance of a solution.

The emf of cell is \( 0.83 \, \mathrm{V} \) at \( 298 \, \mathrm{K} \). It could be increased by:

In an electrochemical reaction of lead, at standard temperature, if \( E^\circ_{(\mathrm{Pb^{2+}/Pb)}} = m \) Volt and \( E^\circ_{(\mathrm{Pb^{4+}/Pb)}} = n \) Volt, then the value of \( E^\circ_{(\mathrm{Pb^{2+}/Pb^{4+}})} \) is given by \( m - xn \). The value of \( x \) is _______. (Nearest integer)

The cell potential for the given cell at \( 298 \, \mathrm{K} \)
\( \mathrm{Pt \, | \, H_2(g,\,1 \, bar) \, | \, H^+(aq) \, || \, Cu^{2+}(aq) \, | \, Cu(s)} \)
is \( 0.31 \, \mathrm{V} \). The pH of the acidic solution is found to be \( 3 \), whereas the concentration of \( \mathrm{Cu^{2+}} \) is \( 10^{-x} \, \mathrm{M} \). The value of \( x \) is ______.
(Given : \( E^\ominus_{\mathrm{Cu^{2+}/Cu}} = 0.34 \, \mathrm{V} \) and \( 2.303RT/F = 0.06 \, \mathrm{V} \) )

The magnitude of the change in oxidising power of the \\( \mathrm{MnO_4^{-}/Mn^{2+}} \\) couple is \\( x \times 10^{-4} \, \text{V} \\), if the \\( \mathrm{H^+} \\) concentration is decreased from \\( 1 \, \text{M} \\) to \\( 10^{-4} \, \text{M} \\) at \\( 25^\circ \text{C} \\) (Assume concentration of \\( \mathrm{MnO_4^{-}} \\) and \\( \mathrm{Mn^{2+}} \\) to be same on change in \\( \mathrm{H^+} \\) concentration). The value of \\( x \\) is _____ (Rounded off to the nearest integer)
[Given: \\( \frac{2.303RT}{F} = 0.059 \\)]

At \( 298 \, \text{K} \), the molar conductivity of \( x\% \) (w/w) \( \text{MX} \) solution (aqueous) is \( 123.5 \, \text{cm}^2 \, \text{mol}^{-1} \). The conductance of same solution is \( 1.9 \times 10^{-3} \, \text{S} \). The value of \( x \) is __________ \( \times 10^{-2} \).
(Given: cell constant \( = 1.3 \, \text{cm}^{-1} \); molar mass of \( \text{MX} \) is \( 75 \, \text{g mol}^{-1} \), density of aqueous solution of \( \text{MX} \) at \( 298 \, \text{K} \) is \( 1.0 \, \text{g mL}^{-1} \))

\( 1 \) Faraday electricity was passed through \( \mathrm{Cu}^{2+} \) \( (1.5 \, \mathrm{M}, \, 1 \, \mathrm{L}) \)/Cu and \( 0.1 \) Faraday was passed through \( \mathrm{Ag}^{+} \) \( (0.2 \, \mathrm{M}, \, 1 \, \mathrm{L}) \)/Ag electrolytic cells. After this the two cells were connected as shown below to make an electrochemical cell. The emf of the cell thus formed at \( 298 \, \mathrm{K} \) is ________ \( \mathrm{mV} \) (Nearest integer)

Given:
\( E^{\circ}_{\mathrm{Cu}^{2+}/\mathrm{Cu}} = 0.34 \, \mathrm{V} \)
\( E^{\circ}_{\mathrm{Ag}^{+}/\mathrm{Ag}} = 0.8 \, \mathrm{V} \)
\( \frac{2.303RT}{F} = 0.06 \, \mathrm{V} \)

Which of the following has least tendency to liberate \( \mathrm{H_2} \) from mineral acids?

The value of conductivity of some materials at \( 298.15 \, \text{K} \) in \( \text{S m}^{-1} \) are \( 2.1 \times 10^{3} \), \( 1.0 \times 10^{-16} \), \( 1.2 \times 10 \), \( 3.191 \), \( 1.5 \times 10^{-2} \), \( 1 \times 10^{-7} \), \( 1.0 \times 10^{3} \). The number of conductors among the materials is ________.

Consider the above electrochemical cell where a metal electrode (\( M \)) is undergoing redox reaction by forming \( \mathrm{M^+ (M \rightarrow M^+ + e^-)} \). The cation \( \mathrm{M^+} \) is present in two different concentrations \( c_1 \) and \( c_2 \) as shown above. Which of the following statement is correct for generating a positive cell potential? 

At what pH, given half cell \( \mathrm{MnO_4^-} \) \( (0.1\,\mathrm{M}) \) | \( \mathrm{Mn^{2+}} \) \( (0.001\,\mathrm{M}) \) will have electrode potential of \( 1.282\,\mathrm{V} \)? ______. (Nearest Integer)
Given \( E^\circ_{\mathrm{MnO_4/Mn^{2+}}} = 1.54\,\mathrm{V} \), \( \frac{2.303RT}{F} = 0.059\,\mathrm{V} \)

The metals that are employed in the battery industries are:
A. \( \mathrm{Fe} \)
B. \( \mathrm{Mn} \)
C. \( \mathrm{Ni} \)
D. \( \mathrm{Cr} \)
E. \( \mathrm{Cd} \)
Choose the correct answer from the options given below:

The product, which is not obtained during the electrolysis of brine solution is:

The reaction \( \dfrac{1}{2}\,\mathrm{H}_2(g) + \mathrm{AgCl}(s) \rightleftharpoons \mathrm{H}^+(aq) + \mathrm{Cl}^-(aq) + \mathrm{Ag}(s) \) occurs in which of the given galvanic cell.

\( 40 \, \text{mL} \) of a mixture of \( \mathrm{CH_3COOH} \) and \( \mathrm{HCl} \) (aqueous solution) is titrated against \( 0.1 \, \text{M} \) \( \mathrm{NaOH} \) solution conductometrically. Which of the following statement is correct?

\( \text{Pt(s)} \mid \text{H}_2 \text{(g)} (1\text{bar}) \mid\mid \text{H}^+ \text{(aq)} (1\text{M}) \mid\mid \text{M}^{3+} \text{(aq)}, \text{M}^+ \text{(aq)} \mid \text{Pt (s)} \).
The \( E_{\text{cell}} \) for the given cell is \( 0.1115 \, \text{V} \) at \( 298 \, \text{K} \) when \( \dfrac{[\text{M}^+ \, (\text{aq})]}{[\text{M}^{3+} \, (\text{aq})]} = 10^a \). The value of \( a \) is ______. Given:
$\text{Given: } E^\theta_{\text{M}^{3+}/\text{M}^+} = 0.2\text{V}$
$\frac{2.303\text{RT}}{\text{F}} = 0.059\text{V}$

Consider the cell at \( 25^{\circ}\text{C} \)
\( \mathrm{Zn \; | \; Zn^{2+}(aq),(1M) \; || \; Fe^{3+}(aq), Fe^{2+}(aq) \; | \; Pt(s)} \)
The fraction of total iron present as \( \mathrm{Fe^{3+}} \) ion at the cell potential of \( 1.500 \, \text{V} \) is \( x \times 10^{-2} \). The value of \( x \) is __________. (Nearest integer)
(Given: \( E^{\circ}_{\mathrm{Fe^{3+}/Fe^{2+}}} = 0.77 \, \text{V}, \, E^{\circ}_{\mathrm{Zn^{2+}/Zn}} = -0.76 \, \text{V} \) )

One Faraday of electricity liberates \( x \times 10^{-1} \) gram atom of copper from copper sulphate. \( x \) is ______.

For a closed circuit Daniell cell, which of the following plots is the accurate one at a given temperature?

The molar conductance of an infinitely dilute solution of ammonium chloride was found to be \( 185 \, \mathrm{S \, cm^2 \, mol^{-1}} \) and the ionic conductance of hydroxyl and chloride ions are \( 170 \) and \( 70 \, \mathrm{S \, cm^2 \, mol^{-1}} \), respectively. If molar conductance of \( 0.02 \, \mathrm{M} \) solution of ammonium hydroxide is \( 85.5 \, \mathrm{S \, cm^2 \, mol^{-1}} \), its degree of dissociation is given by \( x \times 10^{-1} \). The value of \( x \) is __________. (Nearest integer)

A dilute solution of sulphuric acid is electrolyzed using a current of \( 0.10 \, \text{A} \) for \( 2 \) hours to produce hydrogen and oxygen gas. The total volume of gases produced at STP is ________ \( \text{cm}^3 \). (Nearest integer)
[Given: Faraday constant \( F = 96500 \, \text{C mol}^{-1} \) at STP, molar volume of an ideal gas is \( 22.7 \, \text{L mol}^{-1} \) ]

Which of the following electrolyte can be used to obtain \( \mathrm{H_2S_2O_8} \) by the process of electrolysis?

The reaction at cathode in the cells commonly used in clocks involves.

For a strong electrolyte, a plot of molar conductivity against \( (\text{concentration})^{1/2} \) is a straight line, with a negative slope, the correct unit for the slope is:

The molar conductivity of a weak electrolyte when plotted against the square root of its concentration, which of the following is expected to be observed?

The standard cell potential \( \left(E^\circ_{\text{cell}}\right) \) of a fuel cell based on the oxidation of methanol in air that has been used to power television relay station is measured as \( 1.21 \, \text{V} \). The standard half cell reduction potential for \( \mathrm{O_2} \) \( \left(E^\circ_{\mathrm{O_2/H_2O}}\right) \) is \( 1.229 \, \text{V} \).
Choose the correct statement:

In the given electrochemical cell, \( \mathrm{Ag(s) \, | \, AgCl(s) \, | \, FeCl_2(aq), \, FeCl_3(aq) \, | \, Pt(s)} \) at \( 298 \, \text{K} \), the cell potential (\( E_\text{cell} \)) will increase when:
A. Concentration of \( \mathrm{Fe^{2+}} \) is increased.
B. Concentration of \( \mathrm{Fe^{3+}} \) is decreased.
C. Concentration of \( \mathrm{Fe^{2+}} \) is decreased.
D. Concentration of \( \mathrm{Fe^{3+}} \) is increased.
E. Concentration of \( \mathrm{Cl^-} \) is increased.

Choose the correct answer from the options given below:

The resistance of a conductivity cell with cell constant \( 1.14 \,\mathrm{cm^{-1}} \), containing \( 0.001 \,\mathrm{M} \) \( \mathrm{KCl} \) at \( 298 \,\mathrm{K} \) is \( 1500 \,\Omega \). The molar conductivity of \( 0.001 \,\mathrm{M} \) \( \mathrm{KCl} \) solution at \( 298 \,\mathrm{K} \) in \( \mathrm{S\,cm^2\, mol^{-1}} \) is _______. (Integer answer)

The limiting molar conductivities of \( \mathrm{NaI} \), \( \mathrm{NaNO_3} \) and \( \mathrm{AgNO_3} \) are \( 12.7 \), \( 12.0 \) and \( 13.3 \) \( \text{mS m}^2 \text{mol}^{-1} \), respectively (all at \( 25^\circ \text{C} \)). The limiting molar conductivity of \( \mathrm{AgI} \) at this temperature is ________ \( \text{mS m}^2 \text{mol}^{-1} \).

For the given cell \( \mathrm{Fe^{2+}_{(aq)} + Ag^{+}_{(aq)} \rightarrow Fe^{3+}_{(aq)} + Ag_{(s)}} \)
The standard cell potential of the above reaction is:Given:

For the electro chemical cell
\( \mathrm{M \;|\; M^{2+} \;||\; X \;|\; X^{2-}} \)
\( E^\circ_{(M^{2+}/M)} = 0.46 \, \text{V} \) and \( E^\circ_{(X/X^{2-})} = 0.34 \, \text{V} \)
Which of the following is correct?

For the reaction taking place in the cell: 
$\text{Pt(s)} | \text{H}_2\text{(g)} | \text{H}^+\text{(aq)} || \text{Ag}^+\text{(aq)} | \text{Ag(s)}$

$E^0_{\text{cell}} = +0.5332\text{ V}$.
The value of $\Delta_f G^0$ is _________ $\text{kJ mol}^{-1}$. (in nearest integer)

Resistance of a conductivity cell (cell constant \( 129\,\mathrm{m^{-1}} \)) filled with \( 74.5\,\mathrm{ppm} \) solution of \( \mathrm{KCl} \) is \( 100\,\Omega \) (labelled as solution \( 1 \)). When the same cell is filled with \( \mathrm{KCl} \) solution of \( 149\,\mathrm{ppm} \), the resistance is \( 50\,\Omega \) (labelled as solution \( 2 \)). The ratio of molar conductivity of solution \( 1 \) and solution \( 2 \) is i.e., \( \frac{\Lambda_1}{\Lambda_2} = x \times 10^{-3} \). The value of \( x \) is __________. (Nearest integer)
Given, molar mass of \( \mathrm{KCl} \) is \( 74.5\,\mathrm{g\,mol^{-1}} \)

In \( 3d \) series, the metal having the highest \( M^{2+} / M \) standard electrode potential is

Molar conductivity of a weak acid \( \mathrm{HQ} \) of concentration \( 0.18 \, \mathrm{M} \) was found to be \( \dfrac{1}{30} \) of the molar conductivity of another weak acid \( \mathrm{HZ} \) with concentration of \( 0.02 \, \mathrm{M} \). If \( \lambda^{\circ}_{Q^-} \) happened to be equal with \( \lambda^{\circ}_{Z^-} \), then the difference of the \( \mathrm{p}K_a \) values of the two weak acids \( (\mathrm{p}K_a{(\mathrm{HQ})} - \mathrm{p}K_a{(\mathrm{HZ})}) \) is ______. (Nearest integer)
[Given: degree of dissociation (\( \alpha \)) \( \ll 1 \) for both weak acids, \( \lambda^{\circ} \) : limiting molar conductivity of ions]

The resistance of a conductivity cell containing \( 0.01 \, \mathrm{M} \) \( \mathrm{KCl} \) solution at \( 298 \, \mathrm{K} \) is \( 1750 \, \Omega \). If the conductivity of \( 0.01 \, \mathrm{M} \) \( \mathrm{KCl} \) solution at \( 298 \, \mathrm{K} \) is \( 0.152 \times 10^{-3} \, \mathrm{S \, cm^{-1}} \), then the cell constant of the conductivity cell is _______ \( \times 10^{-3} \, \mathrm{cm^{-1}} \).

A metal surface of \( 100 \, \text{cm}^2 \) area has to be coated with nickel layer of thickness \( 0.001 \, \text{mm} \). A current of \( 2 \, \text{A} \) was passed through a solution of \( \text{Ni(NO}_3)_2 \) for ‘\( x \)’ seconds to coat the desired layer. The value of \( x \) is ________. (nearest integer) \( (\rho_{\text{Ni}} \text{ (density of Nickel) is } 10 \, \text{g mL}^{-1} , \text{ Molar mass of Nickel is } 60 \, \text{g mol}^{-1} , \; F = 96500 \, \text{C mol}^{-1}) \)

Given below are two statements:
Statement I: Mohr’s salt is composed of only three types of ions–ferrous, ammonium and sulfate.
Statement II: If the molar conductance at infinite dilution for ferrous, ammonium and sulfate ions are \( x_{1}, x_{2} \) and \( x_{3} \, \text{S cm}^{2} \text{ mol}^{-1} \), respectively then the molar conductance for Mohr’s salt solution at infinite dilution would be given by \( x_{1}+x_{2}+2 x_{3} \)
In the light of the given statements, choose the correct answer from the options given below:

For a $\text{Mg} | \text{Mg}^{2+}(\text{aq}) || \text{Ag}^{+}(\text{aq}) | \text{Ag}$ the correct Nernst Equation is:

MX is a sparingly soluble salt that follows the given solubility equilibrium at \( 298 \, \text{K} \).
\( \mathrm{MX (s)} \rightleftharpoons \mathrm{M^+ (aq)} + \mathrm{X^- (aq)} ; \quad K_{sp} = 10^{-10} \)
If the standard reduction potential for \( \text{M}^+(\text{aq}) \xrightarrow{+e^-} \text{M}(\text{s}) \) is \( \left( \text{E}^{\ominus}_{\text{M}^+/\text{M}} \right) = 0.79 \text{ V} \), then the value of the standard reduction potential for the metal/metal insoluble salt electrode \(\text{E}^{\ominus}_{\text{X}^-/\text{MX}(\text{s})/\text{M}} \). (nearest integer) 
[Given: \( \frac{2.303 RT}{F} = 0.059 \, \text{V} \)]

A conductivity cell with two electrodes (dark side) are half filled with infinitely dilute aqueous solution of a weak electrolyte. If volume is doubled by adding more water at constant temperature, the molar conductivity of the cell will:

For a cell \( \text{Cu(s)} \, | \, \mathrm{Cu^{2+}} \, (0.001\text{M}) \, \| \, \text{Ag+} \, (0.01\text{M}) \, | \, \text{Ag(s)} \) the cell potential is found to be \( 0.43 \, \text{V} \) at \( 298 \, \text{K} \). The magnitude of standard electrode potential for \( \mathrm{Cu^{2+}} / \text{Cu} \) is ______ \( \times 10^{-2} \, \text{V} \).
[Given: \( E^{\ominus}_{\text{Ag+}/\text{Ag}} = 0.80 \, \text{V} \) and \( \dfrac{2.303RT}{F} = 0.06 \, \text{V} \)]

The conductivity of a weak acid HA of concentration \( 0.001 \, \text{mol L}^{-1} \) is \( 2.0 \times 10^{-5} \, \text{S cm}^{-1} \). If \( \Lambda_m^{\circ} (\text{HA}) = 190 \, \text{S cm}^2 \text{ mol}^{-1} \), the ionization constant \( (K_a) \) of HA is equal to _______ \( \times 10^{-6} \). (Round off to the Nearest Integer)

\( \mathrm{FeO_4^{2-}} \xrightarrow{+2.2\,\mathrm{V}} \mathrm{Fe^{3+}} \xrightarrow{+0.70\,\mathrm{V}} \mathrm{Fe^{2+}} \xrightarrow{-0.45\,\mathrm{V}} \mathrm{Fe^{0}} \)
\( E^{0}_{\mathrm{FeO_4^{2-}/Fe^{2+}}} \) is \( x \times 10^{-3}\,\mathrm{V} \). The value of \( x \) is _________

Given below are two statements:
Statement I: For KI, molar conductivity increases steeply with dilution.
Statement II: For carbonic acid, molar conductivity increases slowly with dilution.
In the light of the above statements, choose the correct answer from the options given below:

Consider the following electrochemical cell at \( 298 \,\mathrm{K} \)
\( \mathrm{Pt} \,|\, \mathrm{HSnO_{2}^{-}} (\mathrm{aq}) \,|\, \mathrm{Sn(OH)_{6}^{2-}} (\mathrm{aq}) \,|\, \mathrm{OH^{-}} (\mathrm{aq}) \,|\, \mathrm{Bi_{2}O_{3}} (\mathrm{s}) \,|\, \mathrm{Bi} (\mathrm{s}) \). If the reaction quotient at a given time is \( 10^{6} \), then the cell EMF \( (E_{\text{cell}}) \) is _______ \( \times 10^{-1} \,\mathrm{V} \) (Nearest integer).
Given the standard half-cell reduction potential as \( E^{\circ}_{\mathrm{Bi_{2}O_{3}/Bi,OH^{-}}} = -0.44 \,\mathrm{V} \) and \( E^{\circ}_{\mathrm{Sn(OH)_{6}^{2-}/HSnO_{2}^{-},OH^{-}}} = -0.90 \,\mathrm{V} \)

Number of crystal from the following where body centred unit cell can be found, is __________ .
Cubic, tetragonal, orthorhombic, hexagonal, rhombohedral, monoclinic, triclinic.

Molar ionic conductivities of divalent cation and anion are \( 57 \, \text{S cm}^2 \, \text{mol}^{-1} \) and \( 73 \, \text{S cm}^2 \, \text{mol}^{-1} \) respectively. The molar conductivity of solution of an electrolyte with the above cation and anion will be:

The molar conductivity for electrolytes A and B are plotted against \( c^{1/2} \) as shown below. Electrolytes A and B respectively are:

Given below are two statements:
Statement I : The limiting molar conductivity of \( \mathrm{KCl} \) (strong electrolyte) is higher compared to that of \( \mathrm{CH_3COOH} \) (weak electrolyte).
Statement II : Molar conductivity decreases with decrease in concentration of electrolyte.
In the light of the above statements, choose the most appropriate answer from the options given below:

The correct order of reduction potentials of the following pairs is
A. \( {Cl_2 / Cl^-} \)
B. \( {I_2 / I^-} \)
C. \( {Ag^+ / Ag} \)
D. \( {Na^+ / Na} \)
E. \( {Li^+ / Li} \)
Choose the correct answer from the options given below.

In a cell, the following reactions take place
\( \mathrm{Fe^{2+}} \rightarrow \mathrm{Fe^{3+}} + e^{-} \qquad E^\circ_{\mathrm{Fe^{3+}/Fe^{2+}}} = 0.77 \, \text{V} \)
\( 2\mathrm{I^-} \rightarrow \mathrm{I_2} + 2e^{-} \qquad E^\circ_{\mathrm{I_2/I^-}} = 0.54 \, \text{V} \)
The standard electrode potential for the spontaneous reaction in the cell is \( x \times 10^{-2} \, \text{V} \) \( 298 \, \text{K} \). The value of \( x \) is __________. (Nearest Integer)

At \(298 \, \text{K}\), the standard reduction potential for \(\mathrm{Cu^{2+}/Cu}\) electrode is \(0.34 \, \text{V}\).
Given: \(K_{sp}\,\mathrm{Cu(OH)_2} = 1 \times 10^{-20}\)
Take \( \dfrac{2.303\,RT}{F} = 0.059 \, \text{V} \)
The reduction potential at \(\mathrm{pH} = 14\) for the above couple is  \((-) x \times 10^{-2} \, \text{V}\). The value of \( x \) is __________.

Match List-I with List-II

Choose the correct answer from the options given below:

Consider the following electrochemical cell:
Pt|\( \mathrm{O}_2 (\mathrm{g}) \)|bar|HCl(aq)||\( \mathrm{M}^{2+} \)(aq, \( 1.0 \) \( \mathrm{M} \))|M(s)
The pH above which, oxygen gas would start to evolve at anode is __________ (nearest integer)

Stabdard reduction potential]
 and \( \frac{RT}{F}(2.303) = 0.059 \) \( \mathrm{V} \) at the given condition]

Consider the following electrochemical cell at standard condition.
\( \mathrm{Au(s)\,|\,QH_2,\,Q\,|\,NH_4X(0.01\,M)\,|\,Ag^+(1\,M)\,|\,Ag(s)} \) \( E_{\mathrm{cell}} = +0.4 \, \mathrm{V} \)
The couple \( \mathrm{QH_2/Q} \) represents quinhydrone electrode, the half cell reaction is given below:

\( \left[\text{Given : } E^{\circ}_{\mathrm{Ag^+/Ag}} = +0.8 \, \mathrm{V} \text{ and } \dfrac{2.303RT}{F} = 0.06 \, \mathrm{V} \right] \)
The \( \mathrm{p}K_b \) value of the ammonium halide salt \( (\mathrm{NH_4X}) \) used here is __________. (nearest integer)

How can an electrochemical cell be converted into an electrolytic cell?

Consider the following half cell reaction \( \mathrm{Cr_2O_7^{2-}(aq)} + 6e^- + 14\mathrm{H^+(aq)} \rightarrow 2\mathrm{Cr^{3+}(aq)} + 7\mathrm{H_2O(\ell)} \). The reaction was conducted with the ratio of \( \dfrac{[\mathrm{Cr^{3+}}]^2}{[\mathrm{Cr_2O_7^{2-}}]} = 10^{-6} \). The pH value at which the EMF of the half cell will become zero is ______. (Nearest integer value)
[Given: standard half cell reduction potential \( E^\circ_{\mathrm{Cr_2O_7^{2-},\,H^+/Cr^{3+}}} = 1.33 \, \text{V} \), \( \dfrac{2.303\,RT}{F} = 0.059 \, \text{V} \)]

Consider the following data.

BaSO\(_4\) is sparingly soluble in water. If the conductivity of the saturated BaSO\(_4\) solution is \( x \) \( \text{S cm}^{-1} \) then the solubility product of BaSO\(_4\) can be given as (Here \( \lambda_m = \Lambda^{\circ}_{m} \))

Given below are two statements:
Statement I: Aluminium is more electropositive than thallium as the standard electrode potential value of \( E^{\circ}_{\text{Al}^{3+}/\text{Al}} \) is negative and \( E^{\circ}_{\text{Tl}^{3+}/\text{Tl}} \) is positive.
Statement II: The sum of first three ionization enthalpies of boron is very high when compared to that of aluminium. Due to this reason boron forms covalent compounds only and aluminium forms \( \text{Al}^{3+} \) ion.
In the light of the above statements, choose the correct answer from the options given below

Electrolysis of \( 600 \, \mathrm{mL} \) aqueous solution of \( \mathrm{NaCl} \) for \( 5 \, \mathrm{min} \) changes the pH of the solution to \( 12 \). The current in Amperes used for the given electrolysis is ____________. (Nearest integer).

Consider the following redox reaction: \( \mathrm{MnO_4^-} + \mathrm{H^+} + \mathrm{H_2C_2O_4} \rightleftharpoons \mathrm{Mn^{2+}} + \mathrm{H_2O} + \mathrm{CO_2} \)
The standard reduction potentials are given as below \( (E^\circ_{\text{red}}) \):
\( E^\circ_{\mathrm{MnO_4^-/Mn^{2+}}} = +1.51 \, \text{V} \)
\( E^\circ_{\mathrm{CO_2/H_2C_2O_4}} = -0.49 \, \text{V} \)
In the equilibrium constant of the above reaction is given as \( K_{\mathrm{eq}} = 10^{x} \) , then the value of \( x = \) __________. (nearest Integer)

Given below are two statements :
Statement (I) : Corrosion is an electrochemical phenomenon in which pure metal acts as an anode and impure metal as a cathode.
Statement (II) : The rate of corrosion is more in alkaline medium than in acidic medium.
In the light of the above statements, choose the correct answer from the options given below :

The resistivity of a \( 0.8 \, \mathrm{M} \) solution of an electrolyte is \( 5 \times 10^{-3} \, \Omega \, \mathrm{cm} \). Its conductivity is ________ \( \times 10^{4} \, \Omega^{-1} \, \mathrm{cm^{2}} \, \mathrm{mol^{-1}} \). (Nearest integer)

The number of stereoisomers formed in a reaction of \( (\pm)\text{Ph}(\text{C}=\text{O})\text{C(OH)(CN)Ph} \) with \( \mathrm{HCN} \) is __________.
[Where Ph is \( -\mathrm{C}_6\mathrm{H}_5 \)]

Given below is the plot of the molar conductivity vs \( \sqrt{\text{concentration}} \) for \( \mathrm{KCl} \) in aqueous solution. 

If, for the higher concentration of \( \mathrm{KCl} \) solution, the resistance of the conductivity cell is \( 100 \, \Omega \), then the resistance of the same cell with the dilute solution is ‘\( x \)’ \( \Omega \). The value of \( x \) is ______. (Nearest integer)

$
\text{Consider the following redox reaction taking place in acidic medium}
$

$
\text{BH}_4^-(aq) + \text{ClO}_3^-(aq) \longrightarrow \text{H}_2\text{BO}_3^-(aq) + \text{Cl}^-(aq)
$

$
\text{If the Nernst equation for the above balanced reaction is}
$

$
E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{nF} \ln Q,
$

$
\text{then the value of } n \text{ is _____________. (Nearest integer)}
$

Potassium chlorate is prepared by electrolysis of \( \text{KCl} \) in basic solution as shown by following equation.
\( 6\text{OH}^- + \text{Cl}^- \rightarrow \text{ClO}_3^- + 3\text{H}_2\text{O} + 6e^- \)
A current of \( x \, \text{A} \) has to be passed for \( 10 \, \text{h} \) to produce \( 10.0 \, \text{g} \) of potassium chlorate. The value of \( x \) is ________ . (Nearest integer)
(Molar mass of \( \text{KClO}_3 = 122.6 \, \text{g mol}^{-1} \), \( F = 96500 \, \text{C} \) )

The potential for the given half cell at \( 298 \, \text{K} \) is (−) _______ \( \times 10^{-2} \, \text{V} \).
\( 2\mathrm{H}^+(\mathrm{aq}) + 2e^- \rightarrow \mathrm{H}_2(\mathrm{g}) \)
\( [\mathrm{H}^+] = 1 \, \text{M}, \; P_{\mathrm{H}_2} = 2 \, \text{atm} \)
[Given : \( 2.303 \, \frac{RT}{F} = 0.06 \, \text{V}, \; \log 2 = 0.3 \)]

The equilibrium constant for the reaction

$\text{Zn(s)} + \text{Sn}^{2+}(\text{aq}) \rightleftharpoons \text{Zn}^{2+}(\text{aq}) + \text{Sn(s)}$ is $1 \times 10^{20}$ at $298\text{ K}$. The magnitude of standard electrode potential of $\text{Sn/Sn}^{2+}$ if $\text{E}_{\text{Zn}^{2+}/\text{Zn}}^{\ominus} = -0.76\text{ V}$ is _________ $\times 10^{-2}\text{ V}$. (Nearest integer)

Given : $\frac{2.303\text{RT}}{\text{F}} = 0.059\text{ V}$

The quantity of electricity in Faraday needed to reduce \( 1 \, \text{mole} \) of \( \text{Cr}_2\text{O}_7^{2-} \) to \( \text{Cr}^{3+} \) is ______.

Electricity is passed through an acidic solution of \( Cu^{2+} \) till all the \( Cu^{2+} \) was exhausted, leading to the deposition of \( 300 \, \text{mg} \) of Cu metal. However, a current of \( 600 \, \text{mA} \) was continued to pass through the same solution for another \( 28 \) minutes by keeping the total volume of the solution fixed at \( 200 \, \text{mL} \). The total volume of oxygen evolved at STP during the entire process is _______ \( \text{mL} \). (Nearest integer)
[Given:
\( Cu^{2+}(aq) + 2e^- \rightarrow Cu(s) \quad E^\circ_{\text{red}} = +0.34 \, \text{V} \)
\( O_2(g) + 4H^+ + 4e^- \rightarrow 2H_2O \quad E^\circ_{\text{red}} = +1.23 \, \text{V} \)
Molar mass of Cu \( = 63.54 \, \text{g mol}^{-1} \)
Molar mass of \( O_2 = 32 \, \text{g mol}^{-1} \)
Faraday Constant \( = 96500 \, \text{C mol}^{-1} \)
Molar volume at STP \( = 22.4 \, \text{L} \)]

The mass of zinc produced by the electrolysis of zinc sulphate solution with a steady current of \( 0.015 \, \mathrm{A} \) for \( 15 \) minutes is __________ \( \times 10^{-4} \, \mathrm{g} \). (Atomic mass of zinc \( = 65.4 \, \mathrm{amu} \))

Assume a cell with the following reaction
\( \mathrm{Cu_{(s)}} + 2\,\mathrm{Ag^+}\,(1 \times 10^{-3}\,\mathrm{M}) \rightarrow \mathrm{Cu^{2+}}\,(0.250\,\mathrm{M}) + 2\,\mathrm{Ag_{(s)}} \) 
\( E^{\ominus}_{\text{cell}} = 2.97 \,\text{V} \)
\( E_{\text{cell}} \) for the above reaction is _______ V. (Nearest integer)
[Given: \( \log 2.5 = 0.3979, \ T = 298 \,\text{K} \)]

For a general redox reaction
Anode   \( \text{Red}_1 \rightarrow \text{Ox}_1^{n_1^+} + n_1e^- \)
Cathode   \( \text{Ox}_2 + n_2 e^- \rightarrow \text{Red}_2^{\,n_2-} \)
Which of the following statement is incorrect?

\( 1 \times 10^{-5} \, \mathrm{M} \, \mathrm{AgNO_3} \) is added to \( 1 \, \mathrm{L} \) of saturated solution of \( \mathrm{AgBr} \). The conductivity of this solution at \( 298 \, \mathrm{K} \) is \( \_\_\_\_\_ \times 10^{-8} \, \mathrm{S\,m^{-1}} \).
[Given: \( K_{sp}(\mathrm{AgBr}) = 4.9 \times 10^{-13} \) at \( 298 \, \mathrm{K} \), \( \Lambda^{0}_{\mathrm{Ag^+}} = 6 \times 10^{-3} \, \mathrm{S\,m^{2}\,mol^{-1}} \), \( \Lambda^{0}_{\mathrm{Br^-}} = 8 \times 10^{-3} \, \mathrm{S\,m^{2}\,mol^{-1}} \), \( \Lambda^{0}_{\mathrm{NO_3^-}} = 7 \times 10^{-3} \, \mathrm{S\,m^{2}\,mol^{-1}} \).]

An electrochemical cell is constructed using half cells in the direction of spontaneous change

Which of the following option is correct?

A solution of aluminium chloride is electrolysed for \( 30 \) minutes using a current of \( 2 \, \text{A} \). The amount of the aluminium deposited at the cathode is ________. [Given: molar mass of aluminium and chlorine are \( 27 \, \text{g mol}^{-1} \) and \( 35.5 \, \text{g mol}^{-1} \) respectively Faraday constant \( = 96500 \, \text{C mol}^{-1} \)]

The cell potential for the following cell \( \mathrm{Pt} \, | \, \mathrm{H_2(g)} \, | \, \mathrm{H^+(aq)} \, || \, \mathrm{Cu^{2+}(0.01 \, M)} \, | \, \mathrm{Cu(s)} \) is \( 0.576 \, \text{V} \) at \( 298 \, \text{K} \). The pH of the solution is __________. (Nearest integer)
(Given: \( E^0_{\mathrm{Cu^{2+}/Cu}} = 0.34 \, \text{V} \) and \( \frac{2.303 \, RT}{F} = 0.06 \, \text{V} \) )

Choose the correct representation of conductometric titration of benzoic acid vs sodium hydroxide.

A solution of \( \mathrm{Fe_2(SO_4)_3} \) is electrolyzed for \( x \) \( \text{min} \) with a current of \( 1.5 \, \text{A} \) to deposit \( 0.3482 \, \text{g} \) of \( \mathrm{Fe} \). The value of \( x \) is ___________ [nearest integer]
[Given : \( 1 \, \text{F} = 96500 \, \text{C} \, \text{mol}^{-1} \) ]
Atomic mass of \( \mathrm{Fe} = 56 \, \text{g} \, \text{mol}^{-1} \)

The quantity of silver deposited when one coulomb charge is passed through \( \mathrm{AgNO_3} \) solution:

Which out of the following is a correct equation to show change in molar conductivity with respect to concentration for a weak electrolyte, if the symbols carry their usual meaning:

Consider the cell $\text{Pt(s)} \mid \text{H}_2(\text{g, 1atm}) \mid \text{H}^+(\text{aq, 1M}) \parallel \text{Fe}^{3+}(\text{aq}), \text{Fe}^{2+}(\text{aq}) \mid \text{Pt(s)}$.

When the potential of the cell is $0.712\text{ V}$ at $298\text{ K}$, the ratio $[\text{Fe}^{2+}]/[\text{Fe}^{3+}]$ is _______.

(Nearest integer) $\left[\text{Given : } \text{Fe}^{3+} + \text{e}^- \rightleftharpoons \text{Fe}^{2+}, E^{\theta}{\text{Fe}^{3+}, \text{Fe}^{2+} \mid \text{Pt}} = 0.771; \frac{2.303RT}{F} = 0.06\text{ V}\right]$

At \( 298 \, \text{K} \), a \( 1 \) litre solution containing \( 10 \, \text{mmol} \) of \( \mathrm{Cr_2O_7^{2-}} \) and \( 100 \, \text{mmol} \) of \( \mathrm{Cr^{3+}} \) shows a pH of \( 3.0 \).
Given : \( \mathrm{CrO_7^{2-} \rightarrow Cr^{3+}} \) ; \( E^\circ = 1.330 \, \text{V} \) and \( \frac{2.303 \, RT}{F} = 0.059 \, \text{V} \)
The potential for the half cell reaction is \( x \times 10^{-3} \, \text{V} \). The value of \( x \) is ________.

The specific conductance of \( 0.0025 \, \text{M} \) acetic acid is \( 5 \times 10^{-5} \, \text{S cm}^{-1} \) at a certain temperature. The dissociation constant of acetic acid is ______ \( \times 10^{-7} \). (Nearest integer) Consider limiting molar conductivity of \( \mathrm{CH_3COOH} \) as \( 400 \, \text{S cm}^2 \, \text{mol}^{-1} \).

A constant current was passed through a solution of \( \mathrm{AuCl}_4^- \) ion between gold electrodes. After a period of \( 10.0 \) minutes, the increase in mass of cathode was \( 1.314 \, \text{g} \). The total charge passed through the solution is _______ \( \times 10^{-2} \, \text{F} \). (Given atomic mass of Au = \( 197 \))

The pH and conductance of a weak acid (HX) was found to be \( 5 \) and \( 4 \times 10^{-5} \, \text{S} \), respectively. The conductance was measured under standard condition using a cell where the electrode plates having a surface area of \( 1 \, \text{cm}^{2} \) were at a distance of \( 15 \, \text{cm} \) apart. The value of the limiting molar conductivity is ____________ \( \text{S m}^{2} \text{ mol}^{-1} \). (nearest integer)
(Given: degree of dissociation of the weak acid ( \( \alpha \) ) \( \ll 1 \))

Consider the cell

\( \mathrm{Pt(s)} \ | \ \mathrm{H_2(g)} \ (1 \ \mathrm{atm}) \ | \ \mathrm{H^+(aq}, [\mathrm{H^+}] = 1)\ \| \ \mathrm{Fe^{3+}(aq)}, \ \mathrm{Fe^{2+}(aq)} \ | \ \mathrm{Pt(s)} \) 

Given \( E^\circ_{\mathrm{Fe^{3+}/Fe^{2+}}} = 0.771 \ \mathrm{V} \) and \( E^\circ_{\mathrm{H^+/ \tfrac{1}{2} H_2}} = 0.0 \ \mathrm{V} \), \( T = 298 \ \mathrm{K} \)

If the potential of the cell is \(0.712 \ \mathrm{V}\), the ratio of concentration of \( \mathrm{Fe^{2+}} \) to \( \mathrm{Fe^{3+}} \) is ______. (Nearest integer)

The solubility product of a sparingly soluble salt \( A_2X_3 \) is \( 1.1 \times 10^{-23} \). If specific conductance of the solution is \( 3 \times 10^{-5} \, \text{S m}^{-1} \), the limiting molar conductivity of the solution is \( x \times 10^{-3} \, \text{S m}^2 \text{ mol}^{-1} \). The value of \( x \) is ______.

An electrochemical cell, consist of the following two redox couples, \( \mathrm{M^{x+} (aq) / M(s)[E_{\text{red}}^{\circ} = +0.15 \, V]} \) and \( \mathrm{Fe^{3+}(aq) / Fe(s)[E_{\text{red}}^{\circ} = -0.036 \, V]} \). 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 \( \dfrac{2.303RT}{F} = 0.059 \, V \) ]

The number of correct statements from the following is __________.
(A) Conductivity always decreases with decrease in concentration for both strong and weak electrolytes.
(B) The number of ions per unit volume that carry current in a solution increases on dilution.
(C) Molar conductivity increases with decrease in concentration.
(D) The variation in molar conductivity is different for strong and weak electrolytes.
(E) For weak electrolytes, the change in molar conductivity with dilution is due to decrease in degree of dissociation.

What pressure \( \text{(bar)} \) of \( \mathrm{H_2} \) would be required to make emf of hydrogen electrode zero in pure water at \( 25^\circ \mathrm{C} \)?