Chapter 6

A system is said to be \(\ldots \ldots \ldots \ldots \ldots .\) if it can neither exchange matter nor energy with the surroundings.

The standard molar enthalpies of formation of cyclohexane(1)and benzene(1) at \(25^{\circ} \mathrm{C}\) are \(-156\) and \(+49 \mathrm{~kJ} \mathrm{~mol}^{-1}\) respectively. The standard enthalpy of hydrogenation of cyclohexene(1) at \(25^{\circ} \mathrm{C}\) is \(-119\) \(\mathrm{kJ} \mathrm{mol}^{-1}\). Use these data to estimate the magnitude of the resonance energy of benzene.

First law of thermodynamics is not adequate in predicting the direction of a process.

The polymerisation of ethylene to linear polyethylene is represented by the reaction [1994 - 2 Marks] \(n \mathrm{CH}_{2}=\mathrm{CH}_{2} \longrightarrow \mathrm{E} \mathrm{CH}_{2}-\mathrm{CH}_{2} \frac{1}{\pi}\) where \(n\) has a large integral value. Given that the average enthalpies of bond dissociation for \(\mathrm{C}=\mathrm{C}\) and \(\mathrm{C}-\mathrm{C}\) at \(298 \mathrm{~K}\) are \(+590\) and \(+331 \mathrm{~kJ}\) \(\mathrm{mol}^{-1}\), respectively, calculate the enthalpy of polymerisation per mole of ethylene at \(298 \mathrm{~K}\).

In thermodynamics, the \(P-V\) work done is given by $$ w=-\int d V P_{e x t} $$ For a system undergoing a particular process, the work done is, $$ w=-\int d V\left(\frac{R T}{V-b}-\frac{a}{V^{2}}\right) $$ This equation is applicable to a [Adv. 2020] (a) system that satisfies the van der Waals equation of state. (b) process that is reversible and isothermal. (c) process that is reversible and adiabatic. (d) process that is irreversible and at constant pressure.

A gas mixture of \(3.67\) litres of ethylene and methane on complete combustion at \(25^{\circ} \mathrm{C}\) produces \(6.11\) litres of \(\mathrm{CO}_{2}\). Find out the amount of heat evolved on burning one litre of the gas mixture. The heats of combustion of ethylene and methane are \(-1423\) and \(-891 \mathrm{~kJ} \mathrm{~mol}^{-1}\) at \(25^{\circ} \mathrm{C}\).

An ideal gas is expanded from \(\left(P_{1}, V_{1}, T_{1}\right)\) to \(\left(P_{2}, V_{2}, T_{2}\right)\) under different conditions. The correct statement(s) among the following is (are) (a) The work done on the gas is maximum when it is compressed irreversibly from \(\left(P_{2}, V_{2}\right)\) to \(\left(P_{1}, V_{1}\right)\) against constant pressure \(P_{1}\) (b) If the expansion is carried out freely, it is simultaneously both isothermal as well as adiabatic (c) The work done by the gas is less when it is expanded reversibly from \(V_{1}\) to \(V_{2}\) under adiabatic conditions as compared to that when expanded reversibly from \(V_{1}\) to \(V_{2}\) under isothermal conditions (d) The change in internal energy of the gas is (i) zero, if it is expanded reversibly with \(T_{1}=T_{2}\), and (ii) positive, if it is expanded reversibly under adiabatic conditions with \(T_{1} \neq T_{2}\)

The standard enthalpy of combustion at \(25^{\circ} \mathrm{C}\) of hydrogen, cyclohexene \(\left(\mathrm{C}_{6} \mathrm{H}_{10}\right)\) and cyclohexane \(\left(\mathrm{C}_{6} \mathrm{H}_{12}\right)\) are \(-241,-3800\) and \(-\) \(3920 \mathrm{~kJ} /\) mole respectively. Calculate the heat of hydrogenation of cyclohexene.

Among the following, the intensive property is (properties are) (a) molar conductivity (b) electromotive force (c) resistance (d) heat capacity

Given the following standard heats of reactions: (i) heat of formation of water \(=-68.3 \mathrm{kcal}\); (ii) heat of combustion of acetylene \(=-310.6 \mathrm{kcal}\); (iii) heat of combustion of ethylene \(=-337.2 \mathrm{kcal}\); Calculate the heat of reaction for the hydrogenation of acetylene at constant volume \(\left(25^{\circ} \mathrm{C}\right)\).

Among the following the state function(s) is (are) (a) Internal energy (b) Irreversible expansion work (c) Reversible expansion work (d) Molar enthalpy

The molar heats of combustion of \(\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{~g}), \mathrm{C}\) (graphite) and \(\mathrm{H}_{2}(\mathrm{~g})\) are \(310.62\) kcal, \(94.05\) kcal and \(68.32\) kcal, respectively. Calculate the standard heat of formation of \(\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{~g})\)

Identify the intensive quantities from the following: (a) Enthalpy (b) Temperature (c) Volume (d) Refractive Index

The heat content of the products is more than that of the reactants in an ............... reaction.

Choose the reaction(s) from the following options, for which the standard enthalpy of reaction is equal to the standard enthalpy of formation [Adv. 2019] (a) \(\frac{1}{8} \mathrm{~S}_{8}(\mathrm{~s})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{SO}_{2}(\mathrm{~g})\) (b) \(2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(1)\) (c) \(\frac{3}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{O}_{3}(\mathrm{~g})\) (d) \(2 \mathrm{C}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{~g})\)

Statement - 1 : There is a natural asymmetry between converting work to heat and converting heat to work. Statement - \(2:\) No process is possible in which the sole result is the absorption of heat form a reservoir and its complete conversion into work. [2008S] (a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (b) Statement- 1 is True, Statement-2 is True; Statement- 2 is NOT a correct explanation for Statement-1 (c) Statement- 1 is True, Statement- 2 is False (d) Statement- 1 is False, Statement- 2 is True

For a reaction taking place in a container in equilibrium with its surroundings, the effect of temperature on its equilibrium constant \(K\) in terms of change in entropy is described by [Adv. 2017] (a) With increase in temperature, the value of \(K\) for exothermic reaction decreases because the entropy change of the system is positive (b) With increase in temperature, the value of \(K\) for endothermic reaction increases because unfavourable change in entropy of the surroundings decreases (c) With increase in temperature, the value of \(K\) for endothermic reaction increases because the entropy change of the system is negative (d) With increase in temperature, the value of \(K\) for exothermic reaction decreases because favourable change in entropy of the surroundings decreases

Read the following statement and explanation and answer as per the options given below : Assertion : The heat absorbed during the isothermal expansion of an ideal gas against vacuum is zero. Reason : The volume occupied by the molecules of an ideal gas is zero. (a) If both assertion and reason are CORRECT, and reason is the CORRECT explanation of the assertion. (b) If both assertion and reason are CORRECT, but reason is NOT the CORRECT explanation of the assertion. (c) If assertion is CORRECT, but reason is INCORRECT. (d) If assertion is INCORRECT, but reason is CORRECT.

The following is (are) endothermic reaction(s): (a) Combustion of methane (b) Decomposition of water (c) Dehydrogenation of ethane to ethylene (d) Conversion of graphite to diamond

Match the transformations in column I with appropriate options in column II [2011] Column-I \(\quad\) Column-II (A) \(\mathrm{CO}_{2}(\mathrm{~s}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g})\) (p) phase transition (B) \(\mathrm{CaCO}_{3}(\mathrm{~s}) \rightarrow \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g})\) (q) allotropic change (C) \(2 \mathrm{H}^{\circ} \rightarrow \mathrm{H}_{2}(\mathrm{~g})\) (r) \(\Delta H\) is positive (D) \(\mathrm{P}_{\text {(white, solid) }} \rightarrow \mathrm{P}_{\text {(red, solid) }}\) (s) \(\Delta S\) is positive (t) \(\Delta S\) is negative

\(C_{v}\) value of \(\mathrm{He}\) is always \(3 R / 2\) but \(C_{v}\) value of \(\mathrm{H}_{2}\) is \(3 R / 2\) at low temperature and \(5 R / 2\) at moderate temperature and more than \(5 R / 2\) at higher temperature. Explain in two to three lines.

Two moles of a perfect gas undergo the following processes: (a) a reversible isobaric expansion from \((1.0 \mathrm{~atm}, 20.0 \mathrm{~L})\) to \((1.0 \mathrm{~atm}, 40.0\) L); (b) a reversible isochoric change of state from \((1.0 \mathrm{~atm}, 40.0 \mathrm{~L})\) to \((0.5\) atm, \(40.0 \mathrm{~L}\) ); (c) a reversible isothermal compression from \((0.5 \mathrm{~atm}, 40.0 \mathrm{~L})\) to \((1.0\) atm, \(20.0 \mathrm{~L}\) ). (i) Sketch with labels each of the processes on the same \(P-V\) diagram. (ii) Calculate the total work \((W)\) and the total heat change \((q)\) involved in the above processes. (iii) What will be the values of \(\Delta U, \Delta H\) and \(\Delta S\) for the overall process?

Show that the reaction \(\mathrm{CO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{~g})\) at \(300 \mathrm{~K}\), is spontaneous and exothermic, when the standard entropy change is \(-$$0.094 \mathrm{~kJ} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\). The standard Gibbs free energies of formation for \(\mathrm{CO}_{2}\) and \(\mathrm{CO}\) are \(-394.4\) and \(-137.2 \mathrm{~kJ} \mathrm{~mol}^{-1}\), respectively.

Anhydrous \(\mathrm{AlCl}_{3}\) is covalent. From the data given below, predict whether it would remain covalent or become ionic in aqueous solution. (Ionisation energy for \(\mathrm{Al}=5137 \mathrm{~kJ} \mathrm{~mol}^{-1} ; \Delta H_{\text {hydration for }}\) \(\mathrm{Al}^{3+}=-4665 \mathrm{~kJ} \mathrm{~mol}^{-1} ; \Delta H_{\text {hydration }}\) for \(\left.\mathrm{Cl}^{-}=-381 \mathrm{~kJ} \mathrm{~mol}^{-1} .\right)\)

In order to get maximum calorific output, a burner should have an optimum fuel to oxygen ratio which corresponds to 3 times as much oxygen as is required theoretically for complete combustion of the fuel. A burner which has been adjusted for methane as fuel (with \(x\) litre/hour of \(\mathrm{CH}_{4}\) and \(6 x\) litre/hour of \(\mathrm{O}_{2}\) ) is to be readjusted for butane, \(\mathrm{C}_{4} \mathrm{H}_{10}\). In order to get the same calorific output, what should be the rate of supply of butane and oxygen ? Assume that losses due to incomplete combustion, \(e t c\), are the same for both the fuels and the gases behave ideally. Heats of combustion : $$ \mathrm{CH}_{4}=809 \mathrm{~kJ} / \mathrm{mol} ; \mathrm{C}_{4} \mathrm{H}_{10}=2878 \mathrm{~kJ} / \mathrm{mol} $$