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At \( 298 \, \text{K} \), the limiting molar conductivity of a weak monobasic acid is \( 4 \times 10^2 \, \text{S cm}^2 \, \text{mol}^{-1} \). At \( 298 \, \text{K} \), for an aqueous solution of the acid the degree of dissociation is \( \alpha \) and the molar conductivity is \( y \times 10^2 \, \text{S cm}^2 \, \text{mol}^{-1} \). At \( 298 \, \text{K} \), upon \( 20 \) times dilution with water, the molar conductivity of the solution becomes \( 3y \times 10^2 \, \text{S cm}^2 \, \text{mol}^{-1} \).
The value of \( \alpha \) is ____________.

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 \( \text{(in } \text{mS m}^2 \text{ mol}^{-1}\text{)} \) for different ions in aqueous solutions are given below:

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.

At \( 298 \, \text{K} \), the limiting molar conductivity of a weak monobasic acid is \( 4 \times 10^2 \, \text{S cm}^2 \, \text{mol}^{-1} \). At \( 298 \, \text{K} \), for an aqueous solution of the acid the degree of dissociation is \( \alpha \) and the molar conductivity is \( y \times 10^2 \, \text{S cm}^2 \, \text{mol}^{-1} \). At \( 298 \, \text{K} \), upon \( 20 \) times dilution with water, the molar conductivity of the solution becomes \( 3y \times 10^2 \, \text{S cm}^2 \, \text{mol}^{-1} \).
The value of \( y \) is ____________.

Plotting \( \frac{1}{\Lambda_m} \) against \( c \Lambda_m \) 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 \( P/S \) is:
[\( \Lambda_m = \) molar conductivity, \( \Lambda_m^\circ = \) limiting molar conductivity, \( c = \) molar concentration, \( K_a = \) dissociation constant of HX]

Consider the strong electrolytes \( \mathrm{Z_m X_n} \), \( \mathrm{U_m Y_p} \) and \( \mathrm{V_m X_n} \). Limiting molar conductivity \( \left(\Lambda^0\right) \) of \( \mathrm{U_m Y_p} \) and \( \mathrm{V_m X_n} \) are \( 250 \) and \( 440 \) \( \text{S cm}^2 \text{mol}^{-1} \) respectively. The value of \( (M+n+P) \) is _______.
Given:

\( \lambda^0 \) is the limiting molar conductivity of ions
The plot of molar conductivity \( (\Lambda) \) of \( \mathrm{Z_m X_n} \) vsc\( ^{1/2} \) is given below.

An aqueous solution of hydrazine \( \mathrm{(N_2H_4)} \) is electrochemically oxidized by \( \mathrm{O_2} \), thereby releasing chemical energy in the form of electrical energy. One of the products generated from electrochemical reaction is \( \mathrm{N_2(g)} \).
Choose the correct statement(s) about the above process:

At \( 300 \, \text{K} \), the molar conductivities of the aqueous solutions of three salts at two different concentrations are given below:

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

Some standard electrode potentials at \( 298 \,\text{K} \) are given below:
\( \text{Pb}^{2+}/\text{Pb} - 0.13 \,\text{V} \)
\( \text{Ni}^{2+}/\text{Ni} - 0.24 \,\text{V} \)
\( \text{Cd}^{2+}/\text{Cd} - 0.40 \,\text{V} \)
\( \text{Fe}^{2+}/\text{Fe} - 0.44 \,\text{V} \)
To a solution containing \( 0.001 \,\text{M} \) of \( X^{2+} \) and \( 0.1 \,\text{M} \) of \( Y^{2+} \), the metal rods \( X \) and \( Y \) are inserted \( (\text{at } 298 \,\text{K}) \) and connected by a conducting wire. This resulted in dissolution of \( X \). The correct combination(s) of \( X \) and \( Y \), respectively, is(are):
\( (\text{Given: Gas constant, } R = 8.314 \,\text{J K}^{-1}\text{mol}^{-1}, \text{ Faraday constant, } F = 96500 \,\text{C mol}^{-1}) \)

An electrochemical cell is fueled by the combustion of butane at \( 1 \, \text{bar} \) and \( 298 \, \text{K} \). Its cell potential is \( \dfrac{X}{F} \times 10^{3} \) volts, where \( F \) is the Faraday constant. The value of \( X \) is __________.
Use: Standard Gibbs energies of formation at \( 298 \, \text{K} \) are: \( \Delta_f G^\circ_{\text{CO}_2} = -394 \, \text{kJ} \, \text{mol}^{-1}; \; \Delta_f G^\circ_{\text{water}} = -237 \, \text{kJ} \, \text{mol}^{-1}; \; \Delta_f G^\circ_{\text{butane}} = -18 \, \text{kJ} \, \text{mol}^{-1} \).