JEE MainsJEE AdvanceBITSAT

JEE Mains | PYQ

\( 20.0 \, \mathrm{dm^3} \) of an ideal gas ‘X’ at \( 600 \, \mathrm{K} \) and \( 0.5 \, \mathrm{MPa} \) undergoes isothermal reversible expansion until pressure of the gas is \( 0.2 \, \mathrm{MPa} \). Which of the following option is correct? (Given: \( \log 2 = 0.3010 \) and \( \log 5 = 0.6989 \))

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 _____ \( \text{K} \).

A rigid nitrogen tank stored inside a laboratory has a pressure of \( 30 \, \mathrm{atm} \) at \( 06{:}00 \,\mathrm{am} \) when the temperature is \( 27^{\circ}\mathrm{C} \). At \( 03{:}00 \,\mathrm{pm} \), when the temperature is \( 45^{\circ}\mathrm{C} \), the pressure in the tank will be __________ \( \mathrm{atm} \). [nearest integer]

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.

When a \( 60 \, \text{W} \) electric heater is immersed in a gas for \( 100 \, \text{s} \) in a constant volume container with adiabatic walls, the temperature of the gas rises by \( 5^\circ \text{C} \). The heat capacity of the given gas is ________ \( \text{J K}^{-1} \). (Nearest integer)

The incorrect expression among the following is:

The total number of intensive properties from the following is ________ Volume, Molar heat capacity, Molarity \( E^{\ominus} \) cell, Gibbs free energy change. Molar mass. Mole

For water at \( 100^\circ \text{C} \) and \( 1 \) \( \text{bar} \), \( \Delta_{\text{vap}}H - \Delta_{\text{vap}}U = \) ______ \( \times 10^{2} \) \( \text{J mol}^{-1} \). (Round off to the Nearest Integer)
[Use : \( R = 8.31 \) \( \text{J mol}^{-1} \text{K}^{-1} \)]
[Assume volume of \( \mathrm{H_2O{(l)}} \) is much smaller than volume of \( \mathrm{H_2O{(g)}} \). Assume \( \mathrm{H_2O{(g)}} \) can be treated as an ideal gas]

The gas phase reaction \( 2A (g) \rightleftharpoons A_{2} (g) \) at \( 400 \, \mathrm{K} \) has \( \Delta G^{\circ} = +25.2 \, \mathrm{kJ \, mol^{-1}} \). The equilibrium constant \( K_c \) for this reaction is _____ \( \times 10^{-2} \).
[Use: \( R = 8.3 \, \mathrm{J \, mol^{-1} \, K^{-1}} \), \( \ln 10 = 2.3 \), \( \log_{10} 2 = 0.30 \), \( 1 \, \mathrm{atm} = 1 \, \mathrm{bar} \)]
[antilog \( (-0.3) = 0.501 \)]

One mole of an ideal monoatomic gas is subjected to changes as shown in the graph. The magnitude of the work done (by the system or on the system) is ___________ \( \mathrm{J} \). (nearest integer)

Given: \( \log 2 = 0.3 \)
\( \ln 10 = 2.3 \)

Which of the following relations are correct?
(A) \( \Delta U = q + p\Delta V \)
(B) \( \Delta G = \Delta H - T\Delta S \)
(C) \( \Delta S = \frac{q_{rev}}{T} \)
(D) \( \Delta H = \Delta U - \Delta nRT \)
Choose the most appropriate answer from the options given below:

A system does \( 200 \, \mathrm{J} \) of work and at the same time absorbs \( 150 \, \mathrm{J} \) of heat. The magnitude of the change in internal energy is _______ \( \mathrm{J} \). (Nearest integer)

At \( 25^{\circ}\mathrm{C} \) and \( 1 \, \text{atm} \) pressure, the enthalpy of combustion of benzene \( (l) \) and acetylene \( (g) \) are \( -3268 \, \mathrm{kJ \, mol^{-1}} \) and \( -1300 \, \mathrm{kJ \, mol^{-1}} \), respectively. The change in enthalpy for the reaction \( 3\mathrm{C_2H_2} \, (g) \rightarrow \mathrm{C_6H_6} \, (l) \).

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

An average person needs about \( 10000 \, \text{kJ} \) energy per day. The amount of glucose (molar mass \( = 180.0 \, \text{g mol}^{-1} \)) needed to meet this energy requirement is __________ \( \text{g} \). (Nearest integer)
(Use : \( \Delta_c H (\text{glucose}) = -2700 \, \text{kJ mol}^{-1} \).)

For combustion of one mole of magnesium in an open container at $300\text{ K}$ and $1\text{ bar}$ pressure, $\Delta_{\text{C}}\text{H}^{\ominus} = -601.70\text{ kJ mol}^{-1}$, the magnitude of change in internal energy for the reaction is __________ $\text{kJ}$.

(Nearest integer)

(Given : $\text{R} = 8.3\text{ J K}^{-1}\text{ mol}^{-1}$)

Given below are two statements:
Statement I: When a system containing ice in equilibrium with water (liquid) is heated, heat is absorbed by the system and there is no change in the temperature of the system until whole ice gets melted.
Statement II: At melting point of ice, there is absorption of heat in order to overcome intermolecular forces of attraction within the molecules of water in ice and kinetic energy of molecules is not increased at melting point.
In the light of the above statements, choose the correct answer from the options given below:

\( 17.0 \, \text{g} \) of \( \text{NH}_3 \) completely vapourises at \( -33.42^\circ \text{C} \) and \( 1 \, \text{bar} \) pressure and the enthalpy change in the process is \( 23.4 \, \text{kJ mol}^{-1} \). The enthalpy change for the vapourisation of \( 85 \, \text{g} \) of \( \text{NH}_3 \) under the same conditions is ________ \( \text{kJ} \).

The standard enthalpy and standard entropy of decomposition of \( \mathrm{N_2O_4} \) to \( \mathrm{NO_2} \) are \( 55.0 \, \text{kJ mol}^{-1} \) and \( 175.0 \, \text{J /K}^{}/\text{ mol}^{} \) respectively. The standard free energy change for this reaction at \( 25^\circ \text{C} \) in \( \text{J mol}^{-1} \) is _________ (Nearest integer).

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 \( -286 \, \text{kJ mol}^{-1} \).

At \( 25^\circ \text{C} \), \( 50 \, \text{g} \) of iron reacts with HCl to form \( \mathrm{FeCl}_2 \). The evolved hydrogen gas expands against a constant pressure of \( 1 \, \text{bar} \). The work done by the gas during this expansion is __________ \( \text{J} \).
(Round off to the Nearest Integer). [Given : \( R = 8.314 \, \text{J mol}^{-1} \text{K}^{-1} \). Assume hydrogen is an ideal gas] [Atomic mass of Fe is \( 55.85 \, \text{u} \)]

\( 500 \, \text{J} \) of energy is transferred as heat to \( 0.5 \, \text{mol} \) of Argon gas at \( 298 \, \text{K} \) and \( 1.00 \, \text{atm} \). The final temperature and the change in internal energy respectively are: Given: \( R = 8.3 \, \text{J K}^{-1} \, \text{mol}^{-1} \)

One mole of an ideal gas at \( 350 \, \text{K} \) is in a \( 2.0 \, \text{L} \) vessel of thermally conducting walls, which are in contact with the surroundings. It undergoes isothermal reversible expansion from \( 2.0 \, \text{L} \) to \( 3.0 \, \text{L} \) against a constant pressure of \( 4 \, \text{atm} \). The change in entropy of the surrounding (\( \Delta S \)) is ______ \( \text{J K}^{-1} \) (Nearest integer) Given \( R = 8.314 \, \text{J K}^{-1} \, \text{mol}^{-1} \)

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 \( R = 8.314 \, \text{J K}^{-1} \text{mol}^{-1} \))

\( 30.4 \ \text{kJ} \) of heat is required to melt one mole of sodium chloride and the entropy change at the melting point is \( 28.4 \ \text{J K}^{-1} \text{ mol}^{-1} \) at \( 1 \ \text{atm} \). The melting point of sodium chloride is ________ \( \text{K} \) (Nearest Integer)

At the sea level, the dry air mass percentage composition is given as nitrogen gas: \( 70.0 \), oxygen gas: \( 27.0 \) and argon gas: \( 3.0 \). If total pressure is \( 1.15 \) atm, then calculate the ratio of following respectively:
(i) partial pressure of nitrogen gas to partial pressure of oxygen gas
(ii) partial pressure of oxygen gas to partial pressure of argon gas
(Given: Molar mass of N, O and Ar are \( 14 \), \( 16 \) and \( 40 \, \mathrm{g \, mol^{-1}} \) respectively.)

The effect of temperature on spontaneity of reactions are represented as:

The incorrect combinations are:

\( 40\% \) of \( \text{HI} \) undergoes decomposition to \( \text{H}_2 \) and \( \text{I}_2 \) at \( 300 \, \text{K} \). \( \Delta G^\ominus \) for this decomposition reaction at one atmosphere pressure is ________ \( \text{J mol}^{-1} \). [Nearest integer] (Use \( R = 8.31 \, \text{J K}^{-1} \text{mol}^{-1} \); \( \log 2 = 0.3010 \), \( \ln 10 = 2.3 \), \( \log 3 = 0.477 \))

A fish swimming in water body when taken out from the water body is covered with a film of water of weight \( 36 \, \mathrm{g} \). When it is subjected to cooking at \( 100^\circ \mathrm{C} \), then the internal energy for vaporization in \( \mathrm{kJ \, mol^{-1}} \) is _______. [Nearest integer]
[Assume steam to be an ideal gas. Given $\Delta_{\text{vap}}H^\ominus$ for water at \( 373 \, \mathrm{K} \) and \( 1 \, \mathrm{bar} \) is \( 41.1 \, \mathrm{kJ \, mol^{-1}} \); \( R = 8.31 \, \mathrm{J \, K^{-1} \, mol^{-1}} \)]

\( 4.0 \, \text{L} \) of an ideal gas is allowed to expand isothermally into vacuum until the total volume is \( 20 \, \text{L} \). The amount of heat absorbed in this expansion is ______ \( \text{L atm} \).

The correct order of molar heat capacities measured at \( 298 \, \text{K} \) and \( 1 \, \text{bar} \) is:

One mole of an ideal gas expands isothermally and reversibly from \( 10 \, \text{dm}^3 \) to \( 20 \, \text{dm}^3 \) at \( 300 \, \text{K} \). \( \Delta U \), \( q \) and work done in the process respectively are
Given: \( R = 8.3 \, \text{J K}^{-1} \text{mol}^{-1} \)
\( \ln 10 = 2.3 \)
\( \log 2 = 0.30 \)
\( \log 3 = 0.48 \)

If the enthalpy of sublimation of Li is \( 155 \, \mathrm{kJ \, mol^{-1}} \), enthalpy of dissociation of \( \mathrm{F_2} \) is \( 150 \, \mathrm{kJ \, mol^{-1}} \), ionization enthalpy of Li is \( 520 \, \mathrm{kJ \, mol^{-1}} \), electron gain enthalpy of F is \( -313 \, \mathrm{kJ \, mol^{-1}} \), standard enthalpy of formation of LiF is \( -594 \, \mathrm{kJ \, mol^{-1}} \). The magnitude of lattice enthalpy of LiF is ________ \( \mathrm{kJ \, mol^{-1}} .\) (Nearest Integer)

Two vessels \( A \) and \( B \) are connected via stopcock. The vessel \( A \) is filled with a gas at a certain pressure. The entire assembly is immersed in water and is allowed to come to thermal equilibrium with water. After opening the stopcock the gas from vessel \( A \) expands into vessel \( B \) and no change in temperature is observed in the thermometer. Which of the following statement is true?

For the reaction \( 2\text{NO}_2 (g) \rightleftharpoons \text{N}_2\text{O}_4 (g) \), when \( \Delta S = -176.0 \, \text{J K}^{-1} \) and \( \Delta H = -57.8 \, \text{kJ mol}^{-1} \), the magnitude of \( \Delta G \) at \( 298 \, \text{K} \) for the reaction is ____ \( \text{kJ mol}^{-1} \).

Consider the following data:
Heat of formation of \( \mathrm{CO_2(g)} = -393.5 \, \mathrm{kJ\,mol^{-1}} \)
Heat of formation of \( \mathrm{H_2O(l)} = -286.0 \, \mathrm{kJ\,mol^{-1}} \)
Heat of combustion of benzene \( = -3267.0 \, \mathrm{kJ\,mol^{-1}} \)
The heat of formation of benzene is __________ \( \mathrm{kJ\,mol^{-1}} \).
(Nearest integer)

The molar heat capacity for an ideal gas at constant pressure is \(20.785\,\mathrm{J\,K^{-1}\,mol^{-1}}\). The change in internal energy is \(5000\,\mathrm{J}\) upon heating it from \(300\,\mathrm{K}\) to \(500\,\mathrm{K}\). The number of moles of the gas at constant volume is \(\_\_\_\_\_\_\). [Nearest Integer] (Given \(R=8.314\,\mathrm{J\,K^{-1}\,mol^{-1}}\))

When \( 2 \, \text{litre} \) of ideal gas expands isothermally into vacuum to a total volume of \( 6 \, \text{litre} \), the change in internal energy is ________ \( \text{J} \). (Nearest integer)

For a given chemical reaction \( A \rightarrow B \) at \( 300 \, \text{K} \) the free energy change is \( -49.4 \, \text{kJ mol}^{-1} \) and the enthalpy of reaction is \( 51.4 \, \text{kJ mol}^{-1} \). The entropy change of the reaction is __________ \( \text{J K}^{-1} \text{ mol}^{-1} \).

For independent processes at \( 300 \, \text{K} \)

The number of non-spontaneous processes from the following is ____________.

\( 1 \) mole of ideal gas is allowed to expand reversibly and adiabatically from a temperature of \( 27^\circ \mathrm{C} \). The work done is \( 3 \, \mathrm{kJ\,mol^{-1}} \). The final temperature of the gas is ________ \( \mathrm{K} \) (Nearest integer). (Given \( C_V = 20 \, \mathrm{J\,mol^{-1}\,K^{-1}} \) )

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 \( \mathrm{mol^{-1} K^{-1}} \)]

Which of the following graphs correctly represents the variation of thermodynamic properties of Haber's process?

Match the LIST-I with LIST-II:

Choose the correct answer from the options given below:

Given below are two statements:
Statement I: For an ideal gas, heat capacity at constant volume is always greater than the heat capacity at constant pressure.
Statement II: In a constant volume process, no work is produced and all the heat withdrawn goes into the chaotic motion and is reflected by a temperature increase of the ideal gas.
In the light of the above statements, choose the correct answer from the options given below

A cup of water at \( 5^\circ \text{C} \) (system) is placed in a microwave oven and the oven is turned on for one minute during which the water begins to boil. Which of the following option is true?

For \( 1 \) mol of gas, the plot of \( pV \) vs. \( p \) is shown below. \( p \) is the pressure and \( V \) is the volume of the gas

What is the value of compressibility factor at point A?

A gas (Molar mass \( = 280 \, \mathrm{g \, mol^{-1}} \)) was burnt in excess \( \mathrm{O_2} \) in a constant volume calorimeter and during combustion the temperature of calorimeter increased from \( 298.0 \, \mathrm{K} \) to \( 298.45 \, \mathrm{K} \). If the heat capacity of calorimeter is \( 2.5 \, \mathrm{kJ \, K^{-1}} \) and enthalpy of combustion of gas is \( 9 \, \mathrm{kJ \, mol^{-1}} \) then amount of gas burnt is ______ \( \mathrm{g} \). (Nearest integer)

Which of the following properties will change when system containing solution \( 1 \) will become solution \( 2 \)?

Which of the following graphs between pressure ‘\( p \)’ versus volume ‘\( V \)’ represents the maximum work done?

Two flasks \( \text{I} \) and \( \text{II} \) shown below are connected by a valve of negligible volume.

When the valve is opened, the final pressure of the system in bar is \( x \times 10^{-2} \). The value of \( x \) is _______. (Nearest integer)
[Assume : Ideal gas; \( 1 \, \text{bar} = 10^{5} \, \text{Pa} \); Molar mass of \( \mathrm{N}_2 = 28.0 \, \text{g mol}^{-1} \); \( R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1} \)]

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 \( R = 8.314 \; \text{J K}^{-1} \text{mol}^{-1} \))

What happens when methane undergoes combustion in systems A and B respectively?

During which of the following processes, does entropy decrease ?
(A) Freezing of water to ice at \( 0^\circ\mathrm{C} \)
(B) Freezing of water to ice at \( -10^\circ\mathrm{C} \)
(C) \( \mathrm{N_2(g)} + 3\mathrm{H_2(g)} \rightarrow 2\mathrm{NH_3(g)} \)
(D) Adsorption of \( \mathrm{CO(g)} \) on lead surface
(E) Dissolution of \( \mathrm{NaCl} \) in water
Choose the correct answer from the options given below :

A liquid when kept inside a thermally insulated closed vessel at \( 25^\circ \mathrm{C} \) was mechanically stirred from outside. What will be the correct option for the following thermodynamic parameters?

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 ______ \( \mathrm{K} \).

2.2g of nitrous oxide ($\text{N}_2\text{O}$) gas is cooled at a constant pressure of 1atm from 310K to 270K causing the compression of the gas from 217.1mL to 167.75mL. The change in internal energy of the process, $\Delta\text{U}$ is '$-x$'J. The value of '$x$' is ________. [Nearest integer]

(Given: atomic mass of $\text{N} = 14\text{ g mol}^{-1}$ and $\text{O} = 16\text{ g mol}^{-1}$. Molar heat capacity of $\text{N}_2\text{O}$ is $100\text{ J K}^{-1}\text{ mol}^{-1}$)

Consider the reaction \( \text{X} \rightleftharpoons \text{Y} \) at \( 300 \, \text{K} \). If \( \Delta H^\theta \) and \( K \) are \( 28.40 \, \text{kJ} \, \text{mol}^{-1} \) and \( 1.8 \times 10^{-7} \) at the same temperature, then the magnitude of \( \Delta S^\theta\) for the reaction in \( \text{J K}^{-1} \text{ mol}^{-1} \) is ________ (Nearest integer)
(Given : \( R = 8.3 \, \text{J K}^{-1} \, \text{mol}^{-1} \), \( \ln 10 = 2.3 \), \( \log 3 = 0.48 \), \( \log 2 = 0.30 \))

Use the following data:

One mole each of A\(_2\)(g) and B\(_2\)(g) are taken in a \( 1 \) L closed flask and allowed to establish the equilibrium at \( 500 \) K.

\( \mathrm{A_2(g) + B_2(g) \rightleftharpoons 2\,AB(g)} \)

The value of \( x \) (in \( \mathrm{kJ\,mol^{-1}} \)) is __________. (Nearest Integer)

(Given: \( \log K = 2.2 \) \( R = 8.3 \\ \mathrm{J\,K^{-1}\,mol^{-1}} \))

\( \Delta_{\text{vap}} H^{\ominus} \) 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?

\( 200 \, \text{mL} \) of \( 0.2 \, \text{M} \) \( \mathrm{HCl} \) is mixed with \( 300 \, \text{mL} \) of \( 0.1 \, \text{M} \) \( \mathrm{NaOH} \). The molar heat of neutralization of this reaction is \( -57.1 \, \text{kJ} \). The increase in temperature in \( ^\circ \text{C} \) of the system on mixing is \( x \times 10^{-2} \). The value of \( x \) is ____________ (Nearest integer)
[Given: Specific heat of water \( = 4.18 \, \text{J} \, \text{g}^{-1} \text{K}^{-1} \), Density of water \( = 1.00 \, \text{g} \, \text{cm}^{-3} \)]
(Assume no volume change on mixing)

For water \( \Delta_{\text{vap}}H = 41 \, \text{kJ mol}^{-1} \) at \( 373 \, \text{K} \) and \( 1 \, \text{bar} \) pressure. Assuming that water vapour is an ideal gas that occupies a much larger volume than liquid water, the internal energy change during evaporation of water is ________ \( \text{kJ mol}^{-1} \).
[Use : \( R = 8.3 \, \text{J mol}^{-1} \, \text{K}^{-1} \).]

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 – __________ × \( 10^{-1} \).

Match List - \( 1 \) with List - \( 11 \).

Choose the correct answer from the options given below:

Which of the following relation is not correct?

An athlete is given \(100 \ \mathrm{g}\) of glucose \( (\mathrm{C_6H_{12}O_6}) \) for energy. This is equivalent to \(1800 \ \mathrm{kJ}\) of energy. The \(50\%\) of this energy gained is utilized by the athlete for sports activities at the event. In order to avoid storage of energy, the weight of extra water he would need to perspire is ______ \( \mathrm{g} \) (Nearest integer)
Assume that there is not other way of consuming stored energy.
Given: The enthalpy of evaporation of water is \(45 \ \mathrm{kJ \ mol^{-1}}\)
Molar mass of \( \mathrm{C, H \ \& \ O} \) are \(12\), \(1\) and \(16 \ \mathrm{g \ mol^{-1}}\).

When \( 5 \) moles of He gas expand isothermally and reversibly at \( 300 \, \mathrm{K} \) from \( 10 \, \text{litre} \) to \( 20 \, \text{litre} \), the magnitude of the maximum work obtained is ________ \( \mathrm{J} \).
[nearest integer] (Given : \( R = 8.3 \, \mathrm{J\,K^{-1}\,mol^{-1}} \) and \( \log 2 = 0.3010 \) )

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 __________ \( \text{J} \).

For the reaction \( \mathrm{H_2F_2(g) \rightarrow H_2(g) + F_2(g)} \)
\( \Delta U = -59.6 \, \text{kJ mol}^{-1} \) at \( 27^\circ \text{C} \).
The enthalpy change for the above reaction is (−) ______ \( \text{kJ mol}^{-1} \) (nearest integer)
Given : \( R = 8.314 \, \text{J K}^{-1} \text{mol}^{-1} \)

Match List-I with List-II

Choose the correct answer from the options given below:

For the reaction, $\text{N}_2\text{O}_4 \rightleftharpoons 2\text{NO}_2$, graph is plotted as shown below. Identify correct statements.

A. Standard free energy change for the reaction is $-5.40\text{ kJ mol}^{-1}$.

B. As $\Delta G^{\ominus}$ in graph is positive, $\text{N}_2\text{O}_4$ will not dissociate into $\text{NO}_2$ at all.

C. Reverse reaction will go to completion.

D. When 1 mole of $\text{N}_2\text{O}_4$ changes into equi
librium mixture, value of $\Delta G^{\ominus} = -0.84\text{ kJ mol}^{-1}$.

E. When 2 mole of $\text{NO}_2$ changes into equilibrium mixture, $\Delta G^{\ominus}$ for equilibrium mixture is $-6.24\text{ kJ mol}^{-1}$.

Consider the graph of Gibbs free energy \( G \) vs Extent of reaction. The number of statements from the following which are true with respect to points \( (a) \), \( (b) \) and \( (c) \) is __________,

\((1)\)  Reaction is spontaneous at \( (a) \) and \( (b) \)
 \((2)\) Reaction is at equilibrium at point \( (b) \) and non-spontaneous at point \( (c) \)
\((3)\) Reaction is spontaneous at \( (a) \) and non-spontaneous at \( (c) \)
\((4)\) Reaction is non-spontaneous at \( (a) \) and \( (b) \)

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 ______ \( \text{J} \).

Heat treatment of muscular pain involves radiation of wavelength of about \( 900 \ \text{nm} \). Which spectral line of H atom is suitable for this?
Given: Rydberg constant \( R_H = 10^5 \ \text{cm}^{-1} \), \( h = 6.6 \times 10^{-34} \ \text{J s} \), \( c = 3 \times 10^8 \ \text{m/s} \)