Chapter 6

The true statement amongst the following is :(a) Both \(\Delta \mathrm{S}\) and \(\mathrm{S}\) are functions of temperature. (b) Both \(\mathrm{S}\) and \(\Delta \mathrm{S}\) are not functions of temperature. (c) \(\mathrm{S}\) is not a function of temperature but \(\Delta \mathrm{S}\) is a function of temperature. (d) \(\mathrm{S}\) is a function of temperature but \(\Delta \mathrm{S}\) is not a function of temperature.

Lattice enthalpy and enthalpy of solution of \(\mathrm{NaCl}\) are \(788 \mathrm{~kJ} \mathrm{~mol}^{-1}\) and \(4 \mathrm{~kJ} \mathrm{~mol}^{-1}\), respectively. The hydration enthalpy of \(\mathrm{NaCl}\) is : [Main Sep. 05, 2020 (II)] (a) \(-780 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (b) \(780 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) \(-784 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (d) \(784 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

The true statement amongst the following is : [Main Jan. 09, 2020 (II)] (a) Both \(\Delta \mathrm{S}\) and \(\mathrm{S}\) are functions of temperature. (b) Both \(\mathrm{S}\) and \(\Delta \mathrm{S}\) are not functions of temperature. (c) \(\mathrm{S}\) is not a function of temperature but \(\Delta \mathrm{S}\) is a function of temperature. (d) \(\mathrm{S}\) is a function of temperature but \(\Delta \mathrm{S}\) is not a function of temperature.

Five moles of an ideal gas at 1 bar and \(298 \mathrm{~K}\) is expanded into vacuum to double the volume. The work done is :(a) \(C_{V}\left(T_{2}-T_{1}\right)\) (b) \(-\mathrm{RT}\left(\mathrm{V}_{2}-\mathrm{V}_{1}\right)\) (c) \(-\mathrm{RT} \ln \mathrm{V}_{1} / \mathrm{V}_{1}\) (d) zero

For one mole of an ideal gas, which of these statements must be true? [Main Sep. 04, 2020 (I)] (1) \(\mathrm{U}\) and \(\mathrm{H}\) each depends only on temperature (2) Compressibility factor \(z\) is not equal to 1 (3) \(\mathrm{C}_{\mathrm{P}, \mathrm{m}}-\mathrm{C}_{\mathrm{V}, \mathrm{m}}=\mathrm{R}\) (4) \(\mathrm{dU}=\mathrm{C}_{\mathrm{V}} \mathrm{dT}\) for any process (a) (1) and (3) (b) (2), (3) and (4)

Among the following, the set of parameters that represents path functions. is:(A) \(q+w\) (B) \(q\) (C) \(w\)

Among the following, the set of parameters that represents path functions, is:(A) \(q+w\) (B) \(q\) (C) \(w\)

If enthalpy of atomisation for \(\mathrm{Br}_{2}(\square)\) is \(x \mathrm{~kJ} / \mathrm{mol}\) and bond enthalpy for \(\mathrm{Br}_{2}\) is \(y \mathrm{~kJ} / \mathrm{mol}\), the relation between them: [Main Jan. 09, 2020 (I)] (a) is \(x=y\) (b) does not exist (c) is \(x>y\) (d) is \(x

5 moles of an ideal gas at \(100 \mathrm{~K}\) are allowed to undergo reversible compression till its temperature becomes \(200 \mathrm{~K}\). If \(\mathrm{C}_{V}=28 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-}\) ' calculate \(\Delta \mathrm{U}\) and \(\Delta \mathrm{pV}\) for this process. \(\left(\mathrm{R}=8.0 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)\)(a) \(\Delta \mathrm{U}=14 \mathrm{~kJ} ; \Delta(\mathrm{pV})=18 \mathrm{~kJ}\) (b) \(\Delta \mathrm{U}=14 \mathrm{~kJ} ; \Delta(\mathrm{pV})=0.8 \mathrm{~kJ}\) (c) \(\Delta \mathrm{U}=14 \mathrm{~kJ} ; \Delta(\mathrm{pV})=4 \mathrm{~kJ}\) (d) \(\Delta \mathrm{U}=14 \mathrm{~kJ} ; \Delta(\mathrm{pV})=8.0 \mathrm{~kJ}\)

The difference between \(\Delta \mathrm{H}\) and \(\Delta \mathrm{U}(\Delta \mathrm{H}-\Delta \mathrm{U})\), when the combustion of one mole of heptane (I) is carried out at a temperature \(\mathrm{T}\), is equal to [Main April \(10, \mathbf{2 0 1 9}\) (II)] (a) \(-4 \mathrm{RT}\) (b) \(-3 \mathrm{RT}\) (c) \(4 \mathrm{RT}\) (d) \(3 \mathrm{RT}\)

The combustion of benzene (1) gives \(\mathrm{CO}_{2}(\mathrm{~g})\) and \(\mathrm{H}_{2} \mathrm{O}(l) .\) Given that heat of combustion of benzene at constant volume is \(-3263.9 \mathrm{~kJ} \mathrm{~mol}^{-}\) I at \(25^{\circ} \mathrm{C}\); heat of combustion (in \(\mathrm{kJ} \mathrm{mol}^{-1}\) ) of benzene at constant pressure will be : \(\left(\mathrm{R}=8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right)\) [Main 2018] (a) \(4152.6\) (b) \(-452.46\) (c) 3260 (d) \(-3267.6\)

The process with negative entropy change is: (a) Dissociation of \(\mathrm{CaSO}_{4}(\mathrm{~s})\) to \(\mathrm{CaO}(\mathrm{s})\) and \(\mathrm{SO}_{3}(\mathrm{~g})\) (b) Sublimation of dry ice (c) Dissolution of iodine in water (d) Synthesis of ammonia from \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\)

For which of the following reactions, \(\Delta \mathrm{H}\) is equal to \(\Delta \mathrm{U}\) ? [Main Online April 15, 2018 (I)] (a) \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{NH}_{3}(\mathrm{~g})\) (b) \(2 \mathrm{HI}(\mathrm{g}) \rightarrow \mathrm{H}_{2}(\mathrm{~g})+\mathrm{I}_{2}(\mathrm{~g})\) (c) \(2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{SO}_{3}(\mathrm{~g})\) (d) \(2 \mathrm{NO}_{2}(\mathrm{~g}) \rightarrow \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g})\)

The process with negative entropy change is: [Main Jan. 10, 2019 (II)] (a) Dissociation of \(\mathrm{CaSO}_{4}(\mathrm{~s})\) to \(\mathrm{CaO}(\mathrm{s})\) and \(\mathrm{SO}_{3}(\mathrm{~g})\) (b) Sublimation of dry ice (c) Dissolution of iodine in water (d) Synthesis of ammonia from \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\)

Given \(\mathrm{C}_{\text {(graphite) }}+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g}) ; \Delta_{r} \mathrm{H}^{\circ}=-393.5 \mathrm{~kJ} \mathrm{~mol}^{-1}\) \(\mathrm{H}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(1) ; \Delta_{r} \mathrm{H}^{\circ}=-285.8 \mathrm{~kJ} \mathrm{~mol}^{-1}\) \(\mathrm{CO}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(1) \rightarrow \mathrm{CH}_{4}(\mathrm{~g})+2 \mathrm{O}_{2}(\mathrm{~g})\) \(\Delta_{r} \mathrm{H}^{\circ}=+890.3 \mathrm{~kJ} \mathrm{~mol}^{-1}\) Based on the above thermochemical equations, the value of \(\Delta_{r} \mathrm{H}^{\circ}\) at \(298 \mathrm{~K}\) for the reaction \(\mathrm{C}_{\text {(graphite) }}+2 \mathrm{H}_{2}(\mathrm{~g}) \rightarrow \mathrm{CH}_{4}(\mathrm{~g})\) will be : [Main 2017] (a) \(+74.8 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (b) \(+144.0 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) \(-74.8 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (d) \(-144.0 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

For which of the following processes, \(\Delta \mathrm{S}\) is negative?(a) \(\mathrm{C}\) (diamond \() \rightarrow \mathrm{C}\) (graphite) (b) \(\mathrm{N}_{2}(\mathrm{~g}\), latm \() \rightarrow \mathrm{N}_{2}(\mathrm{~g}, 5 \mathrm{~atm})\) (c) \(\mathrm{N}_{2}(\mathrm{~g}, 273 \mathrm{~K}) \rightarrow \mathrm{N}_{2}(\mathrm{~g}, 300 \mathrm{~K})\) (d) \(\mathrm{H}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{H}(\mathrm{g})\)

For a reaction, \(\mathrm{A}(\mathrm{g}) \rightarrow \mathrm{A}(\mathrm{l}) ; \Delta \mathrm{H}=-3 \mathrm{RT}\). The correct statement for the reaction is: (a) \(\Delta \mathrm{H}=\Delta \mathrm{U} \neq \mathrm{O}\) (b) \(\Delta \mathrm{H}=\Delta \mathrm{U}=\mathrm{O}\) (c) \(|\Delta \mathrm{H}|<|\Delta \mathrm{U}|\) (d) \(|\Delta \mathrm{H}|>|\Delta \mathrm{U}|\)

The standard state Gibbs free energies of formation of C(graphite) and \(\mathrm{C}\) (diamond) at \(T=298 \mathrm{~K}\) are \(\Delta_{f} G^{0}[\mathrm{C}\) (graphite) \(]=0 \mathrm{~kJ} \mathrm{~mol}^{-1}\) \(\Delta_{f} G^{0}[\mathrm{C}\) (diamond) \(]=2.9 \mathrm{~kJ} \mathrm{~mol}^{-1}\) The standard state means that the pressure should be 1 bar, and substance should be pure at a given temperature. The conversion of graphite \([\mathrm{C}\) (graphite) \(]\) to diamond \(\left[C\right.\) (diamond)] reduces its volume by \(2 \times 10^{-}\) \({ }^{6} \mathrm{~m}^{3} \mathrm{~mol}^{-1} .\) If \(C\) (graphite) is converted to \(\mathrm{C}\) (diamond) isothermally at \(T\) \(=298 \mathrm{~K}\), the pressure at which \(\mathrm{C}\) (graphite) is in equilibrium with \(\mathrm{C}\) (diamond), is [Useful information : \(\left.1 \mathrm{~J}=1 \mathrm{~kg} \mathrm{~m}^{2} \mathrm{~s}^{-2} ; 1 \mathrm{~Pa}=1 \mathrm{~kg} \mathrm{~m}^{-1} \mathrm{~s}^{-2} ; 1 \mathrm{bar}=10^{5} \mathrm{~Pa}\right]\) [Adv. 2017] (a) 14501 bar (b) 58001 bar (c) \(1450 \mathrm{bar}\) (d) 29001 bar

A gas undergoes change from state \(\mathrm{A}\) to state \(\mathrm{B}\). In this process, the heat absorbed and work done by the gas is \(5 \mathrm{~J}\) and \(8 \mathrm{~J}\), respectively. Now gas is brought back to \(\mathrm{A}\) by another process during which \(3 \mathrm{~J}\) of heat is evolved. In this reverse process of \(\mathrm{B}\) to \(\mathrm{A}\) :(a) \(10 \mathrm{~J}\) of the work will be done by the gas. (b) \(6 \mathrm{~J}\) of the work will be done by the gas. (c) \(10 \mathrm{~J}\) of the work will be done by the surrounding on gas. (d) \(6 \mathrm{~J}\) of the work will be done by the surrounding on gas.

The heats of combustion of carbon and carbon monoxide are \(-393.5\) and \(-283.5 \mathrm{~kJ} \mathrm{~mol}^{-1}\), respectively. The heat of formation (in \(\mathrm{kJ}\) ) of carbon monoxide per mole is : [Main 2016] (a) \(-676.5\) (b) \(-110.5\) (c) \(110.5\) (d) \(676.5\)

If 100 mole of \(\mathrm{H}_{2} \mathrm{O}_{2}\) decomposes at 1 bar and \(300 \mathrm{~K}\), the work done (kJ) by one mole of \(\mathrm{O}_{2}(\mathrm{~g})\) as it expands against 1 bar pressure is :\(\left(\mathrm{R}=83 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right)\) (a) \(124.50\) (b) \(249.00\) (c) \(498.00\) (d) \(62.25\)

A reaction at 1 bar is non-spontaneous at low temperature but becomes spontaneous at high temperature. Identify the correct statement about the reaction among the following :(a) \(\Delta \mathrm{H}\) is negative while \(\Delta \mathrm{S}\) is positive (b) Both \(\Delta \mathrm{H}\) and \(\Delta \mathrm{S}\) are negative (c) \(\Delta \mathrm{H}\) is positive while \(\Delta \mathrm{S}\) is negative (d) Both \(\Delta \mathrm{H}\) and \(\Delta \mathrm{S}\) are positive.

For complete combustion of ethanol, $$ \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+3 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})+3 \mathrm{H}_{2} \mathrm{O}(l) $$ the amount of heat produced as measured in bomb calorimeter, is \(1364.47\) \(\mathrm{kJ} \mathrm{mol}^{-1}\) at \(25^{\circ} \mathrm{C}\). Assuming ideality the enthalpy of combustion, \(\Delta_{\mathrm{c}} \mathrm{H}\), for the reaction will be: \(\left(\mathrm{R}=8.314 \mathrm{~kJ} \mathrm{~mol}^{-1}\right)\) [Main 2014] (a) \(-1366.95 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (b) \(-1361.95 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) \(-1460.95 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (d) \(-1350.50 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

One mole of an ideal gas at \(300 \mathrm{~K}\) in thermal contact with surroundings expands isothermally from \(1.0 \mathrm{~L}\) to \(2.0 \mathrm{~L}\) against a constant pressure of \(3.0 \mathrm{~atm}\). In this process, the change in entropy of surroundings \(\left(\Delta S_{\text {surr }}\right)\) in \(\mathrm{JK}^{-1}\) is\((1 \mathrm{~L} \mathrm{~atm}=101.3 \mathrm{~J})\) (a) \(5.763\) (b) \(1.013\) (c) \(-1.013\) (d) \(-5.763\)

A piston filled with \(0.04\) mol of an ideal gas expands reversibly from \(50.0 \mathrm{~mL}\) to \(375 \mathrm{~mL}\) at a constant temperature of \(37.0^{\circ} \mathrm{C}\). As it does so, it absorbs \(208 \mathrm{~J}\) of heat. The values of \(\mathrm{q}\) and \(\mathrm{w}\) for the process will be:\((\mathrm{R}=8.314 \mathrm{~J} / \mathrm{mol} \mathrm{K})(\ln 7.5=2.01)\) (a) \(\mathrm{q}=+208 \mathrm{~J}, \mathrm{w}=-208 \mathrm{~J}\) (b) \(\mathrm{q}=-208 \mathrm{~J}, \mathrm{w}=-208 \mathrm{~J}\) (c) \(\mathrm{q}=-208 \mathrm{~J}, \mathrm{w}=+208 \mathrm{~J}\) (d) \(\mathrm{q}=+208 \mathrm{~J}, \mathrm{w}=+208 \mathrm{~J}\)

For the process \(\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) at \(T=100^{\circ} \mathrm{C}\) and 1 atmosphere pressure, the correct choice is (a) \(\Delta S_{\text {system }}>0\) and \(\Delta S_{\text {surroundings }}>0\) (b) \(\Delta S_{\text {system }}>0\) and \(\Delta S_{\text {surroundings }}<0\) (c) \(\Delta S_{\text {system }}<0\) and \(\Delta S_{\text {surroundings }}>0\) (d) \(\Delta S_{\text {system }}<0\) and \(\Delta S_{\text {surroundings }}<0\)

Which of the following statements/relationships is not correct in thermodynamic changes?(a) \(\Delta \mathrm{U}=0\) (isothermal reversible expansion of a gas) (b) \(\mathrm{w}=-\mathrm{nRT} \ln \frac{\mathrm{V}_{2}}{\mathrm{~V}_{1}}\) (isothermal reversible expansion of an ideal gas) (c) \(\mathrm{w}=\mathrm{nRT} \ln \frac{\mathrm{V}_{2}}{\mathrm{~V}_{1}}\) (isothermal reversible expansion of an ideal gas) (d) For a system of constant volume heat involved directly changes to internal energy.

Given : (I) \(\mathrm{H}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(l)\); \(\Delta \mathrm{H}_{298 \mathrm{~K}}^{\circ}=-285.9 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (II) \(\mathrm{H}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\); $$ \Delta \mathrm{H}_{298 \mathrm{~K}}^{\circ}=-241.8 \mathrm{~kJ} \mathrm{~mol}^{-1} $$ The molar enthalpy of vapourisation of water will be : [Main Online April 9, 2013] (a) \(241.8 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (b) \(22.0 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) \(44.1 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (d) \(527.7 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

The standard enthalpies of formation of \(\mathrm{CO}_{2}(\mathrm{~g}), \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) and glucose(s) at \(25^{\circ} \mathrm{C}\) are \(-400 \mathrm{~kJ} / \mathrm{mol},-300 \mathrm{~kJ} / \mathrm{mol}\) and \(-1300 \mathrm{~kJ} / \mathrm{mol}\), respectively. The standard enthalpy of combustion per gram of glucose at \(25^{\circ} \mathrm{C}\) is[Adv. 2013-I] (a) \(+2900 \mathrm{~kJ}\) (b) \(-2900 \mathrm{~kJ}\) (c) \(-16.11 \mathrm{~kJ}\) (d) \(+16.11 \mathrm{~kJ}\)

When one mole of monoatomic ideal gas at \(T \mathrm{~K}\) undergoes adiabatic change under a constant external pressure ofl atm, volume changes from 1 litre to 2 litre. The final temperature in Kelvin would be [2005S] (a) \(\frac{T}{2^{(2 / 3)}}\) (b) \(T+\frac{2}{3} \times 0.0821\) (c) \(T\) (d) \(T-\frac{2}{3} \times 0.0821\)

The species which by definition has ZERO standard molar enthalpy of formation at \(298 \mathrm{~K}\) is [2010] (a) \(\mathrm{Br}_{2}(\mathrm{~g})\) (b) \(\mathrm{Cl}_{2}(\mathrm{~g})\) (c) \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (d) \(\mathrm{CH}_{4}\) (g)

A mono-atomic ideal gas undergoes a process in which the ratio of \(P\) to \(V\) at any instant is constant and equals to 1 . What is the molar heat capacity of the gas \([\mathbf{2 0 0 6}-\mathbf{3 M} ;-1]\) (a) \(\frac{3 R}{2}\) (b) \(2 R\) (c) 0 (d) \(\frac{5 R}{2}\)

For the process \(\mathrm{H}_{2} \mathrm{O}(1)(1 \mathrm{bar}, 373 \mathrm{~K}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{g})(1 \mathrm{bar}, 373 \mathrm{~K})\), the correct set of thermodynamic parameters is [2007] (a) \(\Delta G=0, \Delta S=+\mathrm{ve}\) (b) \(\Delta G=0, \Delta S=-\mathrm{ve}\) (c) \(\Delta G=+\) ve, \(\Delta S=0\) (d) \(\Delta G=-\mathrm{ve}, \Delta S=+\mathrm{ve}\)

Two moles of an ideal gas is expanded isothermally and reversibly from 1 litre to 10 litres at \(300 \mathrm{~K}\). The enthalpy change (in \(\mathrm{kJ}\) ) for the process is [2004S] (a) \(11.4 \mathrm{~kJ}\) (b) \(-11.4 \mathrm{~kJ}\) (c) \(0 \mathrm{~kJ}\) (d) \(4.8 \mathrm{~kJ}\)

The value of \(\log _{10} K\) for a reaction \(A \rightleftharpoons B\) is \(\left(\right.\) Given : \(\Delta_{r} H_{298 \mathrm{~K}}^{\circ}=-54.07 \mathrm{~kJ} \mathrm{~mol}^{-1}, \Delta_{r} S_{298 \mathrm{~K}}^{\circ}\) \(=10 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\) and \(R=8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\); \(2.303 \times 8.314 \times 298=5705)\) (a) 5 (b) 10 (c) 95 (d) 100

One mole of a non-ideal gas undergoes a change of state ( \(2.0\) atm, 3.0L, 95K) \(\rightarrow(4.0\) atm \(, 5.0 \mathrm{~L}, 245 \mathrm{~K})\) with a change in internal energy, \(\Delta U=30.0 \mathrm{~L} \mathrm{~atm} .\) The change in enthalpy \((\Delta H)\) of the process in \(\mathrm{L}\) atm is [2002S] (a) \(40.0\) (b) \(42.3\) (c) \(44.0\) (d) not defined, because pressure is not constant

The enthalpy of vapourization of liquid is \(30 \mathrm{~kJ} \mathrm{~mol}^{-1}\) and entropy of vapourization is \(75 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}\). The boiling point of the liquid at \(1 \mathrm{~atm}\) is [2004S] (a) \(250 \mathrm{~K}\) (b) \(400 \mathrm{~K}\) (c) \(450 \mathrm{~K}\) (d) \(600 \mathrm{~K}\)

Which one of the following statements is false? [2001S] (a) Work is a state function. (b) Temperature is a state function. (c) Change in the state is completely defined when the initial and final states are specified. (d) Work appears at the boundary of the system.

In thermodynamics, a process is called reversible when (a) surroundings and system change into each other. (b) there is no boundary between system and surroundings. (c) the surroundings are always in equilibrium with the system. (d) the system changes into the surroundings spontaneously.

In a constant volume calorimeter, \(3.5 \mathrm{~g}\) of a gas with molecular weight 28 was burnt in excess oxygen at \(298.0 \mathrm{~K}\). The temperature of the calorimeter was found to increase from \(298.0 \mathrm{~K}\) to \(298.45 \mathrm{~K}\) due to the combustion process. Given that the heat capacity of the calorimeter is \(2.5 \mathrm{~kJ} \mathrm{~K}^{-1}\), the numerical value for the enthalpy of combustion of the gas in \(\mathrm{kJ} \mathrm{mol}^{-1}\) is

For a dimerization reaction, \(2 \mathrm{~A}(\mathrm{~g}) \rightarrow \mathrm{A}_{2}(\mathrm{~g})\) at \(298 \mathrm{~K}, \Delta \mathrm{U}^{\Theta}=-20 \mathrm{~kJ} \mathrm{~mol}^{-1}, \Delta \mathrm{S}^{\Theta}=-30 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\), then the \(\Delta \mathrm{G}^{\Theta}\) will be \(\quad\) J.

The internal energy change (in \(\mathrm{J}\) ) when \(90 \mathrm{~g}\) of water undergoes complete evaporation at \(100^{\circ} \mathrm{C}\) is \(.\) (Given : \(\Delta \mathrm{H}_{\text {vap }}\) for water at \(373 \mathrm{~K}=41 \mathrm{~kJ} / \mathrm{mol}, \mathrm{R}=8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\) )

At constant volume, \(4 \mathrm{~mol}\) of an ideal gas when heated from \(300 \mathrm{~K}\) to \(500 \mathrm{~K}\) changes its internal energy by \(5000 \mathrm{~J}\). The molar heat capacity at constant volume is [Main Jan. 08, 2020 (II)]

For the reaction ; \(\mathrm{A}(1) \rightarrow 2 \mathrm{~B}(\mathrm{~g})\) \(\Delta \mathrm{U}=2.1 \mathrm{kcal}, \Delta \mathrm{S}=20 \mathrm{cal} \mathrm{K}^{-1}\) at \(300 \mathrm{~K}\) Hence \(\Delta \mathrm{G}\) in kcal is.

Tin is obtained from cassiterite by reduction with coke. Use the data given below to determine the minimum temperature (in \(\mathrm{K}\) ) at which the reduction of cassiterite by coke would take place. [Adv. 2020] At \(298 \mathrm{~K}: \Delta_{f} H^{0}\left(\mathrm{SnO}_{2}(s)\right)=-581.0 \mathrm{~kJ} \mathrm{~mol}^{-1}\), \(\Delta_{f} H^{0}\left(\mathrm{CO}_{2}(g)\right)=-394.0 \mathrm{~kJ} \mathrm{~mol}^{-1}\) \(S^{0}\left(\mathrm{SnO}_{2}(s)\right)=56.0 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\), \(S^{0}(\operatorname{Sn}(s))=52.0 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\) \(S^{0}(\mathrm{C}(s))=6.0 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}, \quad S^{0}\left(\mathrm{CO}_{2}(g)\right)=210.0 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\). Assume that the enthalpies and the entropies are temperature independent.

For the reaction, \(2 \mathrm{CO}+\mathrm{O}_{2} \longrightarrow 2 \mathrm{CO}_{2} ; \Delta H=-560 \mathrm{~kJ}\). Two moles of \(\mathrm{CO}\) and one mole of \(\mathrm{O}_{2}\) are taken in a container of volume \(1 \mathrm{~L}\). They completely form two moles of \(\mathrm{CO}_{2}\), the gases deviate appreciably from ideal behaviour. If the pressure in the vessel changes from 70 to \(40 \mathrm{~atm}\), find the magnitude (absolute value) of \(\Delta U\) at \(500 \mathrm{~K}\).(1 \(\mathrm{L}\) atm \(=0.1 \mathrm{~kJ})\)

The surface of copper gets tarnished by the formation of copper oxide. \(\mathrm{N}_{2}\) gas was passed to prevent the oxide formation during heating of copper at \(1250 \mathrm{~K}\). However, the \(\mathrm{N}_{2}\) gas contains 1 mole \(\%\) of water vapour as impurity. The water vapour oxidises copper as per the reaction given below: \(2 \mathrm{Cu}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{Cu}_{2} \mathrm{O}(\mathrm{s})+\mathrm{H}_{2}(\mathrm{~g})\) \(p_{\mathrm{H} 2}\) is the minimum partial pressure of \(\mathrm{H}_{2}\) (in bar) needed to prevent the oxidation at \(1250 \mathrm{~K}\). The value of \(\ln \left(p_{\mathrm{H} 2}\right)\) is (Given: total pressure \(=1\) bar, \(R\) (universal gas constant \()=8 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}, \ln\) \((10)=2.3 . \mathrm{Cu}(\mathrm{s})\) and \(\mathrm{Cu}_{2} \mathrm{O}(\mathrm{s})\) are mutually immiscible. At \(1250 \mathrm{~K}: 2 \mathrm{Cu}(\mathrm{s})+1 / 2 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{Cu}_{2} \mathrm{O}(\mathrm{s}) ;\) $$ \Delta G^{\circ}=-78,000 \mathrm{~J} \mathrm{~mol}^{-1} $$ $$ \begin{aligned} &\mathrm{H}_{2}(\mathrm{~g})+1 / 2 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) ; \Delta G^{\circ}=-1,78,000 \mathrm{~J} \mathrm{~mol}^{-1}\\\ &\text { ( } G \text { is the Gibbs energy) } \end{aligned} $$

Diborane is a potential rocket fuel which undergoes combustion according to the reaction. [2000 - 2 Marks] \(\mathrm{B}_{2} \mathrm{H}_{6}(\mathrm{~g})+3 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{B}_{2} \mathrm{O}_{3}(\mathrm{~s})+3 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) From the following data, calculate the enthalpy change for the combustion of diborane. \(2 \mathrm{~B}(\mathrm{~s})+\frac{3}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{B}_{2} \mathrm{O}_{3}(\mathrm{~s}) \quad \Delta H=-1273 \mathrm{~kJ} \mathrm{~mol}^{-1}\) \(\mathrm{H}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{H}_{2} \mathrm{O}(\ell) \quad \Delta H=-286 \mathrm{~kJ} \mathrm{~mol}^{-1}\) \(\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \longrightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \quad \Delta H=44 \mathrm{~kJ} \mathrm{~mol}^{-1}\) \(2 \mathrm{~B}(\mathrm{~s})+3 \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{B}_{2} \mathrm{H}_{6}(\mathrm{~g}) \quad \Delta H=36 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

An athlete is given \(100 \mathrm{~g}\) of glcuose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) of energy equivalent to \(1560 \mathrm{~kJ}\). He utilizes 50 percent of this gained energy in the event. In order to avoids storage of energy in the body, calculate the weight of water he would need to perspire. The enthalpy of evaporation of water is \(44 \mathrm{~kJ} /\) mole.

Estimate the average S-F bond energy in \(\mathrm{SF}_{6}\). The values of standard enthalpy of formation of \(\mathrm{SF}_{6}(\mathrm{~g}), \mathrm{S}(\mathrm{g})\) and \(\mathrm{F}(\mathrm{g})\) are \(:-1100,275\) and \(80 \mathrm{~kJ} \mathrm{~mol}^{-1}\) respectively.