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JEE Mains | PYQ

When \( \Delta H_{\text{vap}} = 30 \, \text{kJ/m ol} \) and \( \Delta S_{\text{vap}} = 75 \, \text{J mol}^{-1} \, \text{K}^{-1} \), then the temperature of vapor, at one atmosphere is _____ \( \text{K} \).

Three moles of an ideal gas are compressed isothermally from \( 60 \, \text{L} \) to \( 20 \, \text{L} \) using constant pressure of \( 5 \, \text{atm} \). Heat exchange \( Q \) for the compression is — ____________________ Lit. atm.

Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following:

Combustion of \( 1 \) mole of benzene is expressed at
\( \mathrm{C_6H_6 (l)} + \dfrac{15}{2} \mathrm{O_2 (g)} \rightarrow 6 \mathrm{CO_2 (g)} + 3 \mathrm{H_2O (l)} \)
The standard enthalpy of combustion of \( 2 \) mol of benzene is \( -x' \) kJ. \( x = \_ \_ \_ \_ \_ \).
Given:
\( 1. \) Standard Enthalpy of formation of \( 1 \) mol of \( \mathrm{C_6H_6 (l)} \), for the reaction \( 6 \, \mathrm{C} \) (graphite) \( + \, 3 \mathrm{H_2 (g)} \rightarrow \mathrm{C_6H_6 (l)} \) is \( 48.5 \, \text{kJ mol}^{-1} \).
\( 2. \) Standard Enthalpy of formation of \( 1 \) mol of \( \mathrm{CO_2 (g)} \), for the reaction \( \mathrm{C} \) (graphite) \( + \, \mathrm{O_2 (g)} \rightarrow \mathrm{CO_2 (g)} \) is \( -393.5 \, \text{kJ mol}^{-1} \).
\( 3. \) Standard and Enthalpy of formation of \( 1 \) mol of \( \mathrm{H_2O (l)} \), for the reaction \( \mathrm{H_2 (g)} + \dfrac{1}{2} \mathrm{O_2 (g)} \rightarrow \mathrm{H_2O (l)} \) is \( -286 \, \text{kJ mol}^{-1} \).

An ideal gas \( \vec{C}_V = \dfrac{5}{2} R \), is expanded adiabatically against a constant pressure of \( 1 \ \mathrm{atm} \) until it doubles in volume. If the initial temperature and pressure is \( 298 \ \mathrm{K} \) and \( 5 \ \mathrm{atm} \), respectively then the final temperature is ________ \( \mathrm{K} \) (nearest integer). [\( \vec{C}_V \) is the molar heat capacity at constant volume]

Consider the following reaction at \( 298 \, \text{K} \), \( \frac{3}{2}\text{O}_2 (g) \rightleftharpoons \text{O}_3 (g) \), \( K_p = 2.47 \times 10^{-29} \).
\( \Delta_r G^\circ \) for the reaction is __________ \( \text{kJ} \). (Given \( R = 8.314 \, \text{J K}^{-1} \text{mol}^{-1} \))

Consider the figure provided.
\( 1 \) mol of an ideal gas is kept in a cylinder, fitted with a piston, at the position A, at \( 18^\circ \mathrm{C} \). If the piston is moved to position B, keeping the temperature unchanged, then ‘\( x \)’ L atm work is done in this reversible process. \( x = \) ______ L atm. (Nearest integer)
[Given: Absolute temperature \( = {}^\circ\mathrm{C} + 273.15 \), \( R = 0.08206 \) L atm \( \mathrm{mol^{-1} K^{-1}} \)]

If \( 5 \) moles of an ideal gas expands from \( 10 \, \text{L} \) to a volume of \( 100 \, \text{L} \) at \( 300 \, \text{K} \) under isothermal and reversible condition then work, \( w \), is \( -x \) J. The value of \( x \) is ________.
(Given \( R = 8.314 \; \text{J K}^{-1} \text{mol}^{-1} \))

For the reaction at \( 298 \, \mathrm{K} \), \( 2A + B \rightarrow C \), and \( \Delta H = 400 \, \mathrm{kJ\, mol^{-1}} \) and \( \Delta S = 0.2 \, \mathrm{kJ\, mol^{-1}\, K^{-1}} \). The reaction will become spontaneous above ______ \( \mathrm{K} \).

\( \Delta_{\text{vap}} H^{\ominus} \) for water is \( +40.79 \, \text{kJ mol}^{-1} \) at \( 1 \, \text{bar} \) and \( 100^{\circ} \text{C} \). Change in internal energy for this vapourisation under same condition is __________ \( \text{kJ mol}^{-1} \). (Integer answer)
 (Given \( R = 8.3 \, \text{J K}^{-1} \, \text{mol}^{-1} \))

The heat of combustion of solid benzoic acid at constant volume is \( -321.30 \, \text{kJ} \) at \( 27^\circ \mathrm{C} \). The heat of combustion at constant pressure is \( (-321.30 - xR) \, \text{kJ} \), the value of \( x \) is \( \_\_\_\_\_\_\_\_ \).

Which of the following is not correct?

For a certain thermochemical reaction \( \mathrm{M} \rightarrow \mathrm{N} \) at \( T = 400\,\mathrm{K} \), \( \Delta H^\ominus = 77.2\,\mathrm{kJ\,mol^{-1}} \), \( \Delta S = 122\,\mathrm{J\,K^{-1}} \), log equilibrium constant (\( \log K \)) is – __________ × \( 10^{-1} \).

If three moles of an ideal gas at \( 300 \, \text{K} \) expand isothermally from \( 30 \, \text{dm}^3 \) to \( 45 \, \text{dm}^3 \) against a constant opposing pressure of \( 80 \, \text{kPa} \), then the amount of heat transferred is __________ \( \text{J} \).

An ideal gas undergoes a cyclic transformation starting from the point A and coming back to the same point by tracing the path A → B → C → A as shown in the diagram above. The total work done in the process is ______ \( \text{J} \).