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JEE Mains | PYQ

\( \text{Cu(s)} + \text{Sn}^{2+}(0.001 \, \text{M}) \longrightarrow \text{Cu}^{2+}(0.01 \, \text{M}) + \text{Sn(s)} \)
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 amount of charge in \( \mathrm{F} \) (Faraday) required to obtain one mole of iron from \( \mathrm{Fe_3O_4} \) 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 \( 2.303RT/F = 0.06 \, \mathrm{V} \) )

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

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 \( 22.7 \, \text{L mol}^{-1} \) ]

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 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

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 _______ \( \times 10^{-3} \, \mathrm{cm^{-1}} \).

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 \( \dfrac{2.303RT}{F} = 0.06 \, \text{V} \)]

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:

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)

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 \( -\mathrm{C}_6\mathrm{H}_5 \)]

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 ______.

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 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 ______.