Chapter 19

As shown here, one type of computer keyboard cleaner contains liquefied \(1,1\) -difluoroethane \(\left(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{F}_{2}\right),\) which is a gas at atmospheric pressure. When the nozzle is squeezed, the \(1,1\) -difluoroethane vaporizes out of the nozzle at high pressure, blowing dust out of objects. (a) Based on your experience, is the vaporization a spontaneous process at room temperature? (b) Defining the \(1,1\) -difluoroethane as the system, do you expect \(q_{s y s}\) for the process to be positive or negative? (c) Predict whether \DeltaS is positive or negative for this process. (d) Given your answers to (a), (b), and (c), do you think the operation of this product depends more on enthalpy or entropy? [Sections 19.1 and 19.2\(]\)

Which of the following processes are spontaneous and which are nonspontaneous: (a) the ripening of a banana, (b) dissolution of sugar in a cup of hot coffee, (c) the reaction of nitrogen atoms to form \(\mathrm{N}_{2}\) molecules at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{atm},(\mathbf{d})\) lightning, (e) formation of \(\mathrm{CH}_{4}\) and \(\mathrm{O}_{2}\) molecules from \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) at room temperature and 1 atm of pressure?

Which of the following processes are spontaneous: (a) the melting of ice cubes at \(-10^{\circ} \mathrm{C}\) and 1 atm pressure; (b) separating a mixture of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) into two separate samples, one that is pure \(\mathrm{N}_{2}\) and one that is pure \(\mathrm{O}_{2}\);(c) alignment of iron filings in a magnetic field; (d) the reaction of hydrogen gas with oxygen gas to form water vapor at room temperature; (e) the dissolution of HCl(g) in water to form concentrated hydrochloric acid?

Indicate whether each statement is true or false. (a) A reaction that is spontaneous in one direction will be nonspontaneous in the reverse direction under the same reaction conditions. (b) All spontaneous processes are fast. (c) Most spontaneous processes are reversible. (d) An isothermal process is one in which the system loses no heat. (e) The maximum amount of work can be accomplished by an irreversible process rather than a reversible one.

(a) Can endothermic chemical reactions be spontaneous? (b) Can a process be spontaneous at one temperature and nonspontaneous at a different temperature? (c) Water can be decomposed to form hydrogen and oxygen, and the hydrogen and oxygen can be recombined to form water. Does this mean that the processes are thermodynamically reversible? (d) Does the amount of work that a system can do on its surroundings depend on the path of the process?

Consider the vaporization of liquid water to steam at a pressure of 1 atm. (a) Is this process endothermic or exothermic? (b) In what temperature range is it a spontaneous process? (c) In what temperature range is it a nonspontaneous process? (d) At what temperature are the two phases in equilibrium?

The normal freezing point of \(n\) -octane \(\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)\) is \(-57^{\circ} \mathrm{C}\) . (a) Is the freezing of \(n\) -octane an endothermic or exothermic process? (b) In what temperature range is the freezing of \(n\) -octane a spontaneous process? (c) In what temperature range is it a nonspontaneous process? (d) Is there any temperature at which liquid \(n\) -octane and solid \(n\) -octane are in equilibrium? Explain.

Consider a process in which an ideal gas changes from state 1 to state 2 in such a way that its temperature changes from 300 K to 200 K. (a) Does the temperature change depend on whether the process is reversible or irreversible? (b) Is this process isothermal? (c) Does the change in the internal energy, \(\Delta E,\) depend on the particular pathway taken to carry out this change of state?

A system goes from state 1 to state 2 and back to state \(1 .\) (a) Is \(\Delta E\) the same in magnitude for both the forward and reverse processes? (b) Without further information, can you conclude that the amount of heat transferred to the system as it goes from state 1 to state 2 is the same or different as compared to that upon going from state 2 back to state 1\(?(\mathbf{c})\) Suppose the changes in state are reversible processes. Is the work done by the system upon going from state 1 to state 2 the same or different as compared to that upon going from state 2 back to state 1\(?\)

Consider a system consisting of an ice cube. (a) Under what conditions can the ice cube melt reversibly? If the ice cube melts reversibly, is \(\Delta H\) zero for the process?

Consider what happens when a sample of the explosive TNT is detonated under atmospheric pressure. (a) Is the detonation a reversible process? (b) What is the sign of \(q\) for this process? (c) Is \(w\) positive, negative, or zero for the process?

Indicate whether each statement is true or false. (a) \(\Delta S\) is a state function. ( b) If a system undergoes a reversible change, the entropy of the universe increases.(c) If a system undergoes a reversible process, the change in entropy of the system is exactly matched by an equal and opposite change in the entropy of the surroundings. (d) If a system undergoes a reversible process, the entropy change of the system must be zero.

Indicate whether each statement is true or false. (a) The entropy of the universe increases for any spontaneous process. (b) The entropy change of the system is equal and opposite that of the surroundings for any irreversible process. (c) The entropy of the system must increase in any spontaneous process. (a) The entropy change for an isothermal process depends on both the absolute temperature and the amount of heat reversibly transferred.

The normal boiling point of \(\mathrm{Br}_{2}(l)\) is \(58.8^{\circ} \mathrm{C},\) and its molar enthalpy of vaporization is \(\Delta H_{\mathrm{vap}}=29.6 \mathrm{kJ} / \mathrm{mol}\) (a) When \(\mathrm{Br}_{2}(l)\) boils at its normal boiling point, does its entropy increase or decrease? (b) Calculate the value of \(\Delta S\) when 1.00 mol of \(\mathrm{Br}_{2}(l)\) is vaporized at \(58.8^{\circ} \mathrm{C}\) .

The element gallium (Ga) freezes at \(29.8^{\circ} \mathrm{C},\) and its molar enthalpy of fusion is \(\Delta H_{\text { fus }}=5.59 \mathrm{k} \mathrm{k} / \mathrm{mol}\) . (a) When molten gallium solidifies to Ga(s) at its normal melting point, is \(\Delta S\) positive or negative? (b) Calculate the value of \(\Delta S\) when 60.0 g of Ga(l) solidifies at \(29.8^{\circ} \mathrm{C}\) .

Indicate whether each statement is true or false. (a) The second law of thermodynamics says that entropy is conserved. (b) If the entropy of the system increases during a reversible process, the entropy change of the surroundings must decrease by the same amount. (c) In a certain spontaneous process the system undergoes an entropy change of \(4.2 \mathrm{J} / \mathrm{K} ;\) therefore, the entropy change of the surroundings must be \(-4.2 \mathrm{J} / \mathrm{K}\)

(a) Does the entropy of the surroundings increase for spontaneous processes? (b) In a particular spontaneous process the entropy of the system decreases. What can you conclude about the sign and magnitude of \(\Delta S_{\text { surr. }} ?(\mathbf{c})\) During a certain reversible process, the surroundings undergo an entropy change, \(\Delta S_{\text { surr }}=-78 \mathrm{J} / \mathrm{K}\) . What is the entropy change of the system for this process?

(a) What sign for \(\Delta S\) do you expect when the volume of 0.200 mol of an ideal gas at \(27^{\circ} \mathrm{Cis}\) increased isothermally from an initial volume of 10.0 \(\mathrm{L} ?(\mathbf{b})\) If the final volume is 18.5 \(\mathrm{L}\) , calculate the entropy change for the process. (c) Do you need to specify the temperature to calculate the entropy change?

(a) What sign for \(\Delta S\) do you expect when the pressure on 0.600 mol of an ideal gas at 350 \(\mathrm{K}\) is increased isothermally from an initial pressure of 0.750 atm? (b) If the final pressure on the gas is 1.20 atm, calculate the entropy change for the process. (c) Do you need to specify the temperature to calculate the entropy change?

For the isothermal expansion of a gas into a vacuum, \(\Delta E=0, q=0,\) and \(w=0 .\) (a) Is this a spontaneous process? (b) Explain why no work is done by the system during this process. (c) What is the "driving force" for the expansion of the gas: enthalpy or entropy?

(a) What is the difference between a state and a microstate of a system? (b) As a system goes from state A to state \(B,\) its entropy decreases. What can you say about the number of microstates corresponding to each state? (c) In a particular spontaneous process, the number of microstates available to the system decreases. What can you conclude about the sign of \(\Delta S_{\text { surr }}\) ?

Would each of the following changes increase, decrease, or have no effect on the number of microstates available to a system: (a) increase in temperature, (b) decrease in volume, (c) change of state from liquid to gas?

(a) What do you expect for the sign of \(\Delta S\) in a chemical reaction in which 2 mol of gaseous reactants are converted to 3 mol of gaseous products? (b) For which of the processes in Exercise 19.11 does the entropy of the system increase?

(a) In a chemical reaction, two gases combine to form a solid. What do you expect for the sign of \(\Delta S ?\) (b) How does the entropy of the system change in the processes described in Exercise 19.12\(?\)

Does the entropy of the system increase, decrease, or stay the same when (a) a solid melts, (b) a gas liquefies, (c) a solid sublimes?

Does the entropy of the system increase, decrease, or stay the same when (a) the temperature of the system increases, (b) the volume of a gas increases, (c) equal volumes of ethanol and water are mixed to form a solution?

Indicate whether each statement is true or false. (a) The third law of thermodynamics says the entropy of a perfect, pure crystal at absolute zero increases with the mass of the crystal. (b) "Translational motion" of molecules refers to their change in spatial location as a func-tion of time. ( c ) "Rotational" and "vibrational" motions contribute to the entropy in atomic gases like He and Xe.(d) The larger the number of atoms in a molecule, the more degrees of freedom of rotational and vibrational motion it likely has.

Indicate whether each statement is true or false. (a) Unlike enthalpy, where we can only ever know changes in \(H,\) we can know absolute values of \(S\) . (b) If you heat a gas such as \(\mathrm{CO}_{2},\) you will increase its degrees of translational, rotational and vibrational motions. (c) \(\mathrm{CO}_{2}(g)\) and \(\mathrm{Ar}(g)\) have nearly the same molar mass. At a given temperature, they will have the same number of microstates.

For each of the following pairs, predict which substance has the higher entropy per mole at a given temperature: (a) \(\operatorname{Ar}(l)\) or \(\operatorname{Ar}(g),(\mathbf{b}) \operatorname{He}(g)\) at 3 atm pressure or \(\operatorname{He}(g)\) at 1.5 atm pressure, (c) 1 mol of \(\mathrm{Ne}(g)\) in 15.0 \(\mathrm{L}\) or 1 \(\mathrm{mol}\) of \(\mathrm{Ne}(g)\) in \(1.50 \mathrm{L},(\mathbf{d}) \mathrm{CO}_{2}(g)\) or \(\mathrm{CO}_{2}(s) .\)

For each of the following pairs, predict which substance possesses the larger entropy per mole: (a) 1 1 mol of \(\mathrm{O}_{2}(g)\) at \(300^{\circ} \mathrm{C}, 0.01\) atm, or 1 \(\mathrm{mol}\) of \(\mathrm{O}_{3}(g)\) at \(300^{\circ} \mathrm{C}, 0.01\) atm; (b) 1 \(\mathrm{mol}\) of \(\mathrm{H}_{2} \mathrm{O}(g)\) at \(100^{\circ} \mathrm{C}, 1 \mathrm{atm},\) or 1 \(\mathrm{mol}\) of \(\mathrm{H}_{2} \mathrm{O}(l)\) at \(100^{\circ} \mathrm{C}, 1\) atm; \((\mathbf{c}) 0.5 \mathrm{mol}\) of \(\mathrm{N}_{2}(g)\) at \(298 \mathrm{K}, 20 \mathrm{-L}\) volume, or 0.5 \(\mathrm{mol} \mathrm{CH}_{4}(g)\) at \(298 \mathrm{K}, 20-\mathrm{volume} ;(\mathbf{d}) 100 \mathrm{g} \mathrm{Na}_{2} \mathrm{SO}_{4}(s)\) at \(30^{\circ} \mathrm{C}\) or 100 \(\mathrm{g} \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)\) at \(30^{\circ} \mathrm{C} .\)

Predict the sign of the entropy change of the system for each of the following reactions: $$\begin{array}{l}{\text { (a) } \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)} \\ {\text { (b) } \mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)} \\ {\text { (c) } 3 \mathrm{C}_{2} \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{6}(g)} \\ {\text { (d) } \mathrm{Al}_{2} \mathrm{O}_{3}(s)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{Al}(s)+3 \mathrm{H}_{2} \mathrm{O}(g)}\end{array}$$

Predict the sign of \(\Delta S_{\text { sys }}\) for each of the following processes: (a) Molten gold solidifies. (b) Gaseous \(C l_{2}\) dissociates in the stratosphere to form gaseous Cl atoms. (c) Gaseous CO reacts with gaseous \(\mathrm{H}_{2}\) to form liquid methanol, \(\mathrm{CH}_{3} \mathrm{OH} .(\mathbf{d})\) Calcium phosphate precipitates upon mixing \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}(a q)\) and \(\left(\mathrm{NH}_{4}\right)_{3} \mathrm{PO}_{4}(a q)\)

In each of the following pairs, which compound would you expect to have the higher standard molar entropy: (a) \(\mathrm{C}_{2} \mathrm{H}_{2}(g)\) or \(\mathrm{C}_{2} \mathrm{H}_{6}(g),(\mathbf{b}) \mathrm{CO}_{2}(g)\) or \(\mathrm{CO}(g) ?\)

Predict which member of each of the following pairs has the greater standard entropy at \(25^{\circ} \mathrm{C} :(\mathbf{a}) \operatorname{Sc}(s)\) or \(\operatorname{Sc}(g)\) (b) \(\mathrm{NH}_{3}(g)\) or \(\mathrm{NH}_{3}(a q),(\mathbf{c}) \mathrm{O}_{2}(g)\) or \(\mathrm{O}_{3}(g),(\mathbf{d}) \mathrm{C}(\mathrm{graphite})\) or \(\mathrm{C}(\) diamond). Use Appendix \(\mathrm{C}\) to find the standard entropy of each substance.

Predict which member of each of the following pairs has the greater standard entropy at \(25^{\circ} \mathrm{C} :(\mathbf{a}) \mathrm{C}_{6} \mathrm{H}_{6}(l)\) or \(\mathrm{C}_{6} \mathrm{H}_{6}(g)\) (b) \(\mathrm{CO}(g)\) or \(\mathrm{CO}_{2}(g),(\mathbf{c}) 1 \mathrm{mol} \mathrm{N}_{2} \mathrm{O}_{4}(g)\) or 2 \(\mathrm{mol} \mathrm{NO}_{2}(\mathrm{g})\) (d) \(\mathrm{HCl}(g)\) or \(\mathrm{HCl}(a q) .\) Use Appendix \(\mathrm{C}\) to find the standard entropy of each substance.

Using \(S^{\circ}\) values from Appendix \(\mathrm{C},\) calculate \(\Delta S^{\circ}\) values for the following reactions. In each case, account for the sign of \(\Delta S^{\circ} .\) $$ \begin{array}{l}{\text { (a) } \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)} \\ {\text { (b) } \mathrm{N}_{2} \mathrm{O}_{4}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)} \\ {\text { (c) } \mathrm{Be}(\mathrm{OH})_{2}(s) \longrightarrow \mathrm{BeO}(s)+\mathrm{H}_{2} \mathrm{O}(g)} \\ {\text { (d) } 2 \mathrm{CH}_{3} \mathrm{OH}(g)+3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)}\end{array} $$

Calculate \(\Delta S^{\circ}\) values for the following reactions by using tabulated \(S^{\circ}\) values from Appendix \(\mathrm{C} .\) In each case, explain the sign of \(\Delta S^{\circ} .\) $$ \begin{array}{l}{\text { (a) } \mathrm{HNO}_{3}(g)+\mathrm{NH}_{3}(g) \longrightarrow \mathrm{NH}_{4} \mathrm{NO}_{3}(s)} \\ {\text { (b) } 2 \mathrm{Fe}_{2} \mathrm{O}_{3}(s) \longrightarrow 4 \mathrm{Fe}(s)+3 \mathrm{O}_{2}(g)} \\ {\text { (c) } \mathrm{CaCO}_{3}(s, \text { calcite })+2 \mathrm{HCl}(g) \rightarrow} \\\ {\mathrm{CaCl}_{2}(s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)}\\\ {\text { (d) } 3 \mathrm{C}_{2} \mathrm{H}_{6}(g) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{6}(l)+6 \mathrm{H}_{2}(g)}\end{array} $$

(a) For a process that occurs at constant temperature, does the change in Gibbs free energy depend on changes in the enthalpy and entropy of the system? (b) For a certain process that occurs at constant \(T\) and \(P\) , the value of \(\Delta G\) is positive. Is the process spontaneous? (c) If \(\Delta G\) for a process is large, is the rate at which it occurs fast?

(a) Is the standard free-energy change, \(\Delta G^{\circ},\) always larger than \(\Delta G ?(\mathbf{b})\) For any process that occurs at constant temperature and pressure, what is the significance of \(\Delta G=0\) ? (c) For a certain process, \(\Delta G\) is large and negative. Does this mean that the process, necessarily has a low activation barrier?

For a certain chemical reaction, \(\Delta H^{\circ}=-35.4 \mathrm{kJ}\) and \(\Delta S^{\circ}=-85.5 \mathrm{J} / \mathrm{K}\) . (a) Is the reaction exothermic or endothermic? (b) Does the reaction lead to an increase or decrease in the randomness or disorder of the system?(c) Calculate \(\Delta G^{\circ}\) for the reaction at 298 \(\mathrm{K}\) . (d) Is the reaction spontaneous at 298 \(\mathrm{K}\) under standard conditions?

A certain reaction has \(\Delta H^{\circ}=+23.7 \mathrm{kJ}\) and \(\Delta S^{\circ}=\) \(+52.4 \mathrm{J} / \mathrm{K}\) . (a) Is the reaction exothermic or endothermic? (b) Does the reaction lead to an increase or decrease in the randomness or disorder of the system?(c) Calculate \(\Delta G^{\circ}\) for the reaction at 298 \(\mathrm{K}\) . (d) Is the reaction spontaneous at 298 \(\mathrm{K}\) under standard conditions?

Use data in Appendix C to calculate \(\Delta H^{\circ}, \Delta S^{\circ},\) and \(\Delta G^{\circ}\) at \(25^{\circ} \mathrm{C}\) for each of the following reactions. $$ \begin{array}{l}{\text { (a) } 4 \mathrm{Cr}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Cr}_{2} \mathrm{O}_{3}(s)} \\ {\text { (b) } \mathrm{BaCO}_{3}(s) \longrightarrow \mathrm{BaO}(s)+\mathrm{CO}_{2}(g)} \\\ {\text { (c) } 2 \mathrm{P}(s)+10 \mathrm{HF}(g) \longrightarrow 2 \mathrm{PF}_{5}(g)+5 \mathrm{H}_{2}(g)} \\ {\text { (d) } \mathrm{K}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{KO}_{2}(s)}\end{array} $$

Using data from Appendix \(\mathrm{C}\) , calculate \(\Delta G^{\circ}\) for the following reactions. Indicate whether each reaction is spontaneous at 298 \(\mathrm{K}\) under standard conditions. (a) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) (b) \(\mathrm{NO}_{2}(g)+\mathrm{N}_{2} \mathrm{O}(g) \longrightarrow 3 \mathrm{NO}(g)\) (c) \(6 \mathrm{Cl}_{2}(g)+2 \mathrm{Fe}_{2} \mathrm{O}_{3}(s) \rightarrow 4 \mathrm{FeCl}_{3}(s)+3 \mathrm{O}_{2}(g)\) (d) \(\mathrm{SO}_{2}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{S}(s)+2 \mathrm{H}_{2} \mathrm{O}(g)\)

Using data from Appendix \(\mathrm{C}\) , calculate \(\Delta G^{\circ}\) for the following reactions. Indicate whether each reaction is spontaneous at 298 \(\mathrm{K}\) under standard conditions. $$ \begin{array}{l}{\text { (a) } 2 \mathrm{Ag}(s)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{AgCl}(s)} \\ {\text { (b) } \mathrm{P}_{4} \mathrm{O}_{10}(s)+16 \mathrm{H}_{2}(g) \longrightarrow 4 \mathrm{PH}_{3}(g)+10 \mathrm{H}_{2} \mathrm{O}(g)} \\ {\text { (c) } \mathrm{CH}_{4}(g)+4 \mathrm{F}_{2}(g) \longrightarrow \mathrm{CF}_{4}(g)+4 \mathrm{HF}(g)} \\ {\text { (d) } 2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)}\end{array} $$

Octane \(\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)\) is a liquid hydrocarbon at room temperature that is a constituent of gasoline. (a) Write a balanced equation for the combustion of \(\mathrm{C}_{8} \mathrm{H}_{18}(l)\) to form \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l) .\) (b) Without using thermochemical data, predict whether \(\Delta G^{\circ}\) for this reaction is more negative or less negative than \(\Delta H^{\circ} .\)

Sulfur dioxide reacts with strontium oxide as follows: $$ \mathrm{SO}_{2}(g)+\mathrm{SrO}(g) \longrightarrow \mathrm{SrSO}_{3}(s) $$ (a) Without using thermochemical data, predict whether \(\Delta G^{\circ}\) for this reaction is more negative or less negative than \(\Delta H^{\circ} .\) (b) If you had only standard enthalpy data for this reaction, how would you estimate the value of \(\Delta G^{\circ}\) at \(298 \mathrm{K},\) using data from Appendix Con other substances.

Classify each of the following reactions as one of the four possible types summarized in Table \(19.3 :\) (i) spontanous at all temperatures; (ii) not spontaneous at any temperature; (iii) spontaneous at low \(T\) but not spontaneous at high \(T ;\) (iv) spontaneous at high T but not spontaneous at low \(T .\) $$ \begin{array}{c}{\text { (a) } \mathrm{N}_{2}(g)+3 \mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{NF}_{3}(g)} \\ {\Delta H^{\circ}=-249 \mathrm{kJ} ; \Delta S^{\circ}=-278 \mathrm{J} / \mathrm{K}}\\\\{\text { (b) } \mathrm{N}_{2}(g)+3 \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NCl}_{3}(g)} \\\ {\Delta H^{\circ}=460 \mathrm{kJ} ; \Delta S^{\circ}=-275 \mathrm{J} / \mathrm{K}} \\ {\text { (c) } \mathrm{N}_{2} \mathrm{F}_{4}(g) \longrightarrow 2 \mathrm{NF}_{2}(g)} \\ {\Delta H^{\circ}=85 \mathrm{kJ} ; \Delta S^{\circ}=198 \mathrm{J} / \mathrm{K}}\end{array} $$

From the values given for \(\Delta H^{\circ}\) and \(\Delta S^{\circ},\) calculate \(\Delta G^{\circ}\) for each of the following reactions at 298 \(\mathrm{K}\) . If the reaction is not spontaneous under standard conditions at 298 \(\mathrm{K}\) , at what temperature (if any) would the reaction become spontaneous? $$ \begin{array}{l}{\text { (a) } 2 \mathrm{PbS}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{PbO}(s)+2 \mathrm{SO}_{2}(g)} \\ {\Delta H^{\circ}=-844 \mathrm{kk} ; \Delta S^{\circ}=-165 \mathrm{J} / \mathrm{K}} \\\ {\text { (b) } 2 \mathrm{POCl}_{3}(g) \longrightarrow 2 \mathrm{PCl}_{3}(g)+\mathrm{O}_{2}(g)} \\ {\Delta H^{\circ}=572 \mathrm{kJ} ; \Delta S^{\circ}=179 \mathrm{J} / \mathrm{K}}\end{array} $$

A certain constant-pressure reaction is barely nonspontaneous at \(45^{\circ} \mathrm{C}\) . The entropy change for the reaction is 72 \(\mathrm{J} / \mathrm{K} .\) Estimate \(\Delta H .\)

For a particular reaction, \(\Delta H=-32 \mathrm{kJ}\) and \(\Delta S=-98 \mathrm{J} / \mathrm{K}\) . Assume that \(\Delta H\) and \(\Delta S\) do not vary with temperature. (a) At what temperature will the reaction have \(\Delta G=0\) ? (b) If \(T\) is increased from that in part (a), will the reaction be spontaneous or nonspontaneous?