Chapter 4

A quantity of \(1.6 \mathrm{~g}\) helium gas is expanded adiabatically \(3.0\) times and then compressed isobarically to the initial volume. Assume ideal behaviour of gas and both the processes reversible. The entropy change of the gas in this process is \((\ln 3=1.1)\) (a) \(-1.1 \mathrm{cal} / \mathrm{K}\) (b) \(+1.1 \mathrm{cal} / \mathrm{K}\) (c) \(-2.2 \mathrm{cal} / \mathrm{K}\) (d) \(+2.2 \mathrm{cal} / \mathrm{K}\)

The entropy change of \(2.0\) moles of an ideal gas whose adiabatic exponent \(\gamma=1.50\), if as a result of a certain process, the gas volume increased \(2.0\) times while the pressure dropped \(4.0\) times, is \((\ln 2=0.7)\) (a) \(-11.64 \mathrm{~J} / \mathrm{K}\) (b) \(+11.64 \mathrm{~J} / \mathrm{K}\) (c) \(-34.92 \mathrm{~J} / \mathrm{K}\) (d) \(+34.92 \mathrm{~J} / \mathrm{K}\)

Each of the vessels 1 and 2 contain \(1.2\) moles of gaseous helium. The ratio of the vessels volumes is \(V_{2} / V_{1}=2.0\), and the ratio of the absolute temperature of helium in them is \(T_{1} / T_{2}=2.0\). Assuming the gas to be ideal, find the different of gas entropies in these vessels, \(S_{2}-S_{1}\). \((\ln 2=0.7)\) (a) \(0.84 \mathrm{cal} / \mathrm{K}\) (b) \(4.2 \mathrm{cal} / \mathrm{K}\) (c) \(-0.84 \mathrm{cal} / \mathrm{K}\) (d) \(-4.2 \mathrm{cal} / \mathrm{K}\)

For which of the following process, \(\Delta S\) is negative? (a) \(\mathrm{H}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{H}(\mathrm{g})\) (b) \(\mathrm{N}_{2}(\mathrm{~g}, 1 \mathrm{~atm}) \rightarrow \mathrm{N}_{2}(\mathrm{~g}, 8 \mathrm{~atm})\) (c) \(2 \mathrm{SO}_{3}(\mathrm{~g}) \rightarrow 2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g})\) (d) \(\mathrm{C}\) (graphite) \(\rightarrow \mathrm{C}\) (diamond)

Entropy decrease during (a) crystallization of sucrose from solution (b) rusting of iron (c) melting of ice (d) vaporization of camphor

At very low temperature, the heat capacity of crystals is equal to \(C=a T^{3}\), where \(a\) is a constant. Find the entropy of a crystal as a function of temperature in this temperature interval. (a) \(S=\frac{a \cdot T^{3}}{3}\) (b) \(S=a T^{3}\) (c) \(\frac{a \cdot T^{2}}{2}\) (d) \(\frac{a \cdot T}{3}\)

An isolated system comprises the liquid in equilibrium with vapours. At this stage, the molar entropy of the vapour is (a) less than that of liquid (b) more than that of liquid (c) equal to zero (d) equal to that of liquid

Choose the substance which has higher possible entropy (per mole) at a given temperature. (a) solid carbon dioxide (b) nitrogen gas at 1 atm (c) nitrogen gas at \(0.01\) atm (d) nitrogen gas at \(0.00001\) atm

The change that does not increase entropy (a) evaporation of liquid (b) condensation (c) sublimation (d) melting of solid

Ammonium chloride when dissolved in water leads to cooling sensation. The dissolution of \(\mathrm{NH}_{4} \mathrm{Cl}\) at constant temperature is accompanied by (a) increase in entropy (b) decrease in entropy (c) no change in entropy (d) no change in enthalpy

Which of the following would be expected to have the largest entropy per mole? (a) \(\mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{~s})\) (b) \(\mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{I})\) (c) \(\mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{~g})\) (d) \(\mathrm{SO}_{2}(\mathrm{~g})\)

When one mole of an ideal gas is compressed to half of its initial volume and simultaneously heated to twice its temperature, the change in entropy is (a) \(C_{\mathrm{V}} \ln 2\) (b) \(C_{\mathrm{P}} \ln 2\) (c) \(R \ln 2\) (d) \(\left(C_{\mathrm{V}}-R\right) \ln 2\)

An amount of 5 mole \(\mathrm{H}_{2} \mathrm{O}(1)\) at \(100^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) is converted into \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) at \(100^{\circ} \mathrm{C}\) and 5 atm. \(\Delta G\) for the process is (a) zero (b) \(1865 \ln 5 \mathrm{cal}\) (c) \(3730 \ln 5 \mathrm{cal}\) (d) \(-3730 \ln 5 \mathrm{cal}\)

What is the entropy change when \(3.6 \mathrm{~g}\) of liquid water is completely converted into vapours at \(373 \mathrm{~K} ?\) The molar heat of vaporization is \(40.85 \mathrm{~kJ} / \mathrm{mol}\). (a) \(218.9 \mathrm{~J} / \mathrm{K}\) (b) \(2.189 \mathrm{~J} / \mathrm{K}\) (c) \(21.89 \mathrm{~J} / \mathrm{K}\) (d) \(0.2189 \mathrm{~J} / \mathrm{K}\)

Heat liberated by a given amount of an ideal gas undergoing reversible isothermal process is \(1200 \mathrm{cal}\) at \(300 \mathrm{~K}\). What is the Gibbs free energy change of the gas in this process? (a) zero (b) \(+1200\) cal (c) \(-1200\) cal (d) \(4 \mathrm{cal}\)

The entropy change in the fusion of one mole of a solid melting at \(300 \mathrm{~K}\) (latent heat of fusion, \(2930 \mathrm{~J} / \mathrm{mol}\) ) is (a) \(9.77 \mathrm{~J} / \mathrm{K}-\mathrm{mol}\) (b) \(10.73 \mathrm{~J} / \mathrm{K}-\mathrm{mol}\) (c) \(2930 \mathrm{~J} / \mathrm{K}-\mathrm{mol}\) (d) \(108.5 \mathrm{~J} / \mathrm{K}-\mathrm{mol}\)

Oxygen gas weighing \(64 \mathrm{~g}\) is expanded from 1 atm to \(0.25\) atm at \(30^{\circ} \mathrm{C}\). What is the entropy change, assuming the gas to be ideal? \((\ln 4=1.4, R=8.3 \mathrm{~J} / \mathrm{K}-\mathrm{mol})\) (a) \(23.24 \mathrm{~J} / \mathrm{K}\) (b) \(34.86 \mathrm{~J} / \mathrm{K}\) (c) \(46.48 \mathrm{~J} / \mathrm{K}\) (d) \(11.62 \mathrm{~J} / \mathrm{K}\)

The vapour pressures of water and ice at \(-10^{\circ} \mathrm{C}\) are \(0.28\) and \(0.26 \mathrm{~Pa}\), respectively. What is the free energy change for the process? \(\mathrm{H}_{2} \mathrm{O} \quad\left(1, \quad-10^{\circ} \mathrm{C}, \quad 0.28 \quad \mathrm{~Pa}, \quad 1 \quad\right.\) mole \()\) \(\rightarrow \mathrm{H}_{2} \mathrm{O}\left(\mathrm{s},-10^{\circ} \mathrm{C}, 0.26 \mathrm{~Pa}, 1 \mathrm{~mole}\right)\) (a) \(R \times 263 \times \ln \frac{14}{13}\) (b) \(R \times 263 \times \ln \frac{13}{14}\) (c) \(R \times 10 \times \ln \frac{13}{14}\) (d) \(R \times 10 \times \ln \frac{14}{13}\)

Two moles of an ideal monoatomic gas is heated from \(27^{\circ} \mathrm{C}\) to \(627^{\circ} \mathrm{C}\), reversibly and isochorically. The entropy of gas (a) increases by \(2 R \ln 3\) (b) increases by \(3 R \ln 3\) (c) decreases by \(2 R \ln 3\) (d) decreases by \(3 R \ln 3\)

A definite mass of a monoatomic ideal gas at 1 bar and \(27^{\circ} \mathrm{C}\) expands against \(\begin{array}{llll}\text { vacuum } & \text { from } & 1.2 \mathrm{dm}^{3} & \text { to } & 2.4 \mathrm{dm}^{3} \text { . }\end{array}\) The change in free energy of the gas, \(\Delta G\), is \((R=0.08\) bar- \(\mathrm{L} / \mathrm{K}-\mathrm{mol}, \ln 2=0.7)\) (a) 0 (b) \(-64\) bar- 1 (c) \(+84 \mathrm{~J}\) (d) \(-84 \mathrm{~J}\)

One mole of an ideal monoatomic gas undergoes adiabatic free expansion from 2 to \(20 \mathrm{dm}^{3}, 300 \mathrm{~K}\). The value of \(\Delta S\) for the gas is (a) 0 (b) \(+R \ln 10\) (c) \(-R \ln 10\) (d) \(+1.5 R \ln 10\)

For a reaction: \(\mathrm{A} \rightleftharpoons \mathrm{B}\), carried out at \(27^{\circ} \mathrm{C}\), the ratio of equilibrium concentrations of product to reactant changes by a factor of \(\mathrm{e}^{4}\) for every (a) \(1.2\) kcal rise in \(\Delta G^{\circ}\) (b) \(1.2 \mathrm{kcal}\) fall in \(\Delta G^{\circ}\) (c) \(2.4 \mathrm{kcal}\) rise in \(\Delta G^{\circ}\) (d) \(2.4\) kcal fall in \(\Delta G^{\circ}\)

Given the following entropy values (in \(\mathrm{J} / \mathrm{K}-\mathrm{mol}\) ) at \(298 \mathrm{~K}\) and 1 atm \(\mathrm{H}_{2}(\mathrm{~g})\) \(=130.6, \mathrm{Cl}_{2}(\mathrm{~g})=223.0\) and \(\mathrm{HCl}(\mathrm{g})=186.7\) The entropy change (in J/K-mol) for the reaction: \(\mathrm{H}_{2}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{HCl}(\mathrm{g})\), is (a) \(+540.3\) (b) \(+727.0\) (c) \(-166.9\) (d) \(+19.8\)

The \(\Delta G\) in the process of melting of ice at \(-15^{\circ} \mathrm{C}\) is (a) less than zero (b) greater than zero (c) equal to zero (d) none of these

For a system in equilibrium, \(\Delta G=0\) under conditions of constant (a) temperature and pressure (b) temperature and volume (c) pressure and volume (d) energy and volume

The solubility of \(\mathrm{NaCl}(\mathrm{s})\) in water at \(298 \mathrm{~K}\) is about 6 moles per litre. Suppose you add 1 mole of \(\mathrm{NaCl}(\mathrm{s})\) to a litre of water. For the reaction: \(\mathrm{NaCl}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}\) \(\rightarrow \mathrm{NaCl}(\mathrm{aq})\) (a) \(\Delta G>0, \Delta S>0\) (b) \(\Delta G<0, \Delta S>0\) (c) \(\Delta G>0, \Delta S<0\) (d) \(\Delta G<0, \Delta S<0\)

The values of \(\Delta G\) are very important in metallurgy. The \(\Delta G\) values for the following reactions at \(1000 \mathrm{~K}\) are given as: \(\mathrm{S}_{2}(\mathrm{~s})+2 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{SO}_{2}(\mathrm{~g}) ; \Delta G=-544 \mathrm{~kJ}\) \(2 \mathrm{Zn}(\mathrm{s})+\mathrm{S}_{2}(\mathrm{~s}) \rightarrow 2 \mathrm{ZnS}(\mathrm{s}) ; \Delta G=-293 \mathrm{~kJ}\) \(2 \mathrm{Zn}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{ZnO}(\mathrm{s}) ; \Delta G=-480 \mathrm{~kJ}\) The \(\Delta G\) for the reaction: \(2 \mathrm{ZnS}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{ZnO}(\mathrm{s})+2 \mathrm{SO}_{2}(\mathrm{~g})\) will be (a) \(-357 \mathrm{~kJ}\) (b) \(-731 \mathrm{~kJ}\) (c) \(-773 \mathrm{~kJ}\) (d) \(-229 \mathrm{~kJ}\)

What is the free energy change, \(\Delta G\), when \(1.0\) mole of water at \(100^{\circ} \mathrm{C}\) and 1 atm pressure is converted in to steam at \(100^{\circ} \mathrm{C}\) and 1 atm pressure? (a) \(540 \mathrm{cal}\) (b) \(-9800 \mathrm{cal}\) (c) \(9800 \mathrm{cal}\) (d) \(0 \mathrm{cal}\)

The enthalpy and entropy change for a chemical reaction are \(-2500 \mathrm{cal}\) and \(+7.4 \mathrm{cal} / \mathrm{K}\), respectively. The nature of reaction at \(298 \mathrm{~K}\) is (a) Spontaneous (b) Reversible (c) Irreversible (d) Non-spontaneous

For a reversible reaction, if \(\Delta G^{\circ}=0\), the equilibrium constant of the reaction should be equal to (a) Zero (b) 1 (c) 2 (d) 10