Chapter 18

What is the origin of the name thermodynamics?

State the first law of thermodynamics in your own words. What equation defines the change in the internal energy in terms of heat and work? Define the meaning of the symbols, including the significance of their algebraic signs.

How is a change in the internal energy defined in terms of the initial and final internal energies?

What is the algebraic sign of \(\Delta E\) for an endothermic change? Why?

Which thermodynamic quantity corresponds to the heat at constant volume? Which corresponds to the heat at constant pressure?

What are the units of \(P \Delta V\) if pressure is expressed in pascals and volume is expressed in cubic meters?

What is a spontaneous change? What role does kinetics play in determining the apparent spontaneity of a chemical reaction?

List five changes that you have encountered recently that occurred spontaneously. List five changes that are nonspontaneous that you have caused to occur.

At constant pressure, what role does the enthalpy change play in determining the spontaneity of an event?

An instant cold pack purchased in a pharmacy contains a packet of solid ammonium nitrate surrounded by a pouch of water. When the packet of \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) is broken, the solid dissolves in water and a cooling of the mixture occurs because the solution process for \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) in water is endothermic. Explain, in terms of what happens to the molecules and ions, why this mixing occurs spontaneously.

How is the entropy of a substance affected by (a) an increase in temperature, (b) a decrease in volume, (c) changing from a liquid to a solid, and (d) dissociating into individual atoms?

Will the entropy change for each of the following be positive or negative? (a) Moisture condenses on the outside of a cold glass. (b) Raindrops form in a cloud. (c) Gasoline vaporizes in the carburetor of an automobile engine. (d) Air is pumped into a tire. (e) Frost forms on the windshield of your car. (f) Sugar dissolves in coffee.

On the basis of our definition of entropy, suggest why entropy is a state function.

State the second law of thermodynamics.

How can a process have a negative entropy change for the system, and yet still be spontaneous?

Explain the terms \(\Delta S_{\text {universe }}, \Delta S_{\text {system }},\) and \(\Delta S_{\text {surroundings, }}\) and how they relate to each other.

Explain how the entropy of the surroundings of a reaction is related to the enthalpy of the reaction.

Define Gibbs free energy in your own words.

In terms of the algebraic signs of \(\Delta H\) and \(\Delta S,\) under which of the following circumstances will a change be spontaneous: (a) At all temperatures? (b) At low temperatures but not at high temperatures? (c) At high temperatures but not at low temperatures?

State the third law of thermodynamics in your own words.

Explain why the units for entropy have a dependence on temperature- for example, why are the units \(\mathrm{J} \mathrm{mol}^{-1} \mathrm{~K}^{-1}\) ?

Explain why the values of \(\Delta H\) for elements in their standard state are \(0 \mathrm{~kJ} \mathrm{~mol}^{-1}\), but the values for the standard entropy, \(S,\) for elements are \(\operatorname{not} 0 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\).

Would you expect the entropy of an alloy (a solution of two metals) to be zero at \(0 \mathrm{~K}\) ? Explain your answer.

What is the equation expressing the change in the Gibbs free energy for a reaction occurring at constant temperature and pressure?

Why can \(\Delta G^{\circ}\) be calculated at different temperatures using \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) at \(298.15 \mathrm{~K}\) ?

How is free energy related to useful work?

What is a thermodynamically reversible process? How is the amount of work obtained from a change related to thermodynamic reversibility?

In what way is free energy related to equilibrium?

Considering the fact that the formation of a bond between two atoms is exothermic and is accompanied by an entropy decrease, explain why all chemical compounds decompose into individual atoms if heated to a high enough temperature.

Sketch the shape of the free energy curve for a chemical reaction that has a positive \(\Delta G^{\circ}\). Indicate the composition of the reaction mixture corresponding to equilibrium.

Write the equation that relates the free energy change to the value of the reaction quotient for a reaction.

How is the equilibrium constant related to the standard free energy change for a reaction? (Write the equation.)

What is the value of \(\Delta G^{\circ}\) for a reaction for which \(K=1\) ?

Define the term atomization energy.

Why are the heats of formation of gaseous atoms from their elements endothermic quantities?

A certain system absorbs \(0.300 \mathrm{~kJ}\) of heat and has \(0.700 \mathrm{~kJ}\) of work performed on it. What is the value of \(\Delta E\) for the change? Is the overall change exothermic or endothermic?

The value of \(\Delta E\) for a certain change is \(-1455 \mathrm{~J}\). During the change, the system absorbs \(812 \mathrm{~J}\) of heat. Did the system do work, or was work done on the system? How much work, expressed in joules, was involved?

Suppose that you were pumping an automobile tire with a hand pump that pushed 24.0 in. \(^{3}\) of air into the tire on each stroke, and that during one such stroke the opposing pressure in the tire was \(30.0 \mathrm{lb} / \mathrm{in} .^{2}\) above the normal atmospheric pressure of \(14.7 \mathrm{lb} / \mathrm{in} .^{2} .\) Calculate the number of joules of work accomplished during each stroke. \((1 \mathrm{~L} \mathrm{~atm}=101.325 \mathrm{~J})\)

Predict the sign of \(\Delta S\) for the following reactions. (a) The sublimation of \(\mathrm{I}_{2}(s)\) (b) \(\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(g)\) (c) \(2 \mathrm{Na}(s)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NaCl}(s)\)

A chemical system has three particles that can have energies of \(0,5,10,15,\) or \(20 \mathrm{~J}\). If the total energy of the system is \(30 \mathrm{~J}\), how many different ways can the particles be organized?

What factors must you consider to determine the sign of \(\Delta S\) for the reaction \(2 \mathrm{~N}_{2} \mathrm{O}(g) \longrightarrow 2 \mathrm{~N}_{2}(g)+\mathrm{O}_{2}(g)\) if it occurs at constant temperature?

Predict the algebraic sign of the entropy change for the following reactions. (a) \(\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{PCl}_{5}(g)\) (b) \(\mathrm{SO}_{2}(g)+\mathrm{CaO}(s) \longrightarrow \mathrm{CaSO}_{3}(s)\) (c) \(\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{CO}_{3}(a q)\) (d) \(\mathrm{Ni}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{NiCl}_{2}(a q)\)

Predict the algebraic sign of the entropy change for the following reactions. (a) \(\mathrm{I}_{2}(s) \longrightarrow \mathrm{I}_{2}(g)\) (b) \(\mathrm{Br}_{2}(g)+3 \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{BrCl}_{3}(g)\) (c) \(\mathrm{NH}_{3}(g)+\mathrm{HCl}(g) \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}(s)\) (d) \(\mathrm{CaO}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(s)\)

Under what conditions will the reaction be spontaneous? (a) \(\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\) $$ \begin{aligned} \Delta S<0 \text { and } \Delta H<0 \end{aligned} $$ (b) \(\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}(s) \longrightarrow \mathrm{Ba}^{2+}(a q)+2 \mathrm{NO}_{3}^{-}(a q)\) \(\Delta S>0\) and \(\Delta H>0\)

Under what conditions will the reaction be spontaneous? $$ \text { (a) } \begin{aligned} \mathrm{Al}_{2} \mathrm{O}_{3}(s)+2 \mathrm{Fe}(s) \longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+2 \mathrm{Al}(s) \\ \Delta S>0 \text { and } \Delta H>0 \end{aligned} $$ (b) \(\mathrm{CS}_{2}(g) \longrightarrow \mathrm{CS}_{2}(l)\) \(\Delta S<0\) and \(\Delta H<0\)

Given the following reactions and their \(\Delta G^{\circ}\) values, \(\mathrm{COCl}_{2}(g)+4 \mathrm{NH}_{3}(g) \longrightarrow\) $$ \begin{aligned} \mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}(s)+2 \mathrm{NH}_{4} \mathrm{Cl}(s) & \Delta G^{\circ}=-332.0 \mathrm{~kJ} \\ \mathrm{COCl}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{HCl}(g) \\ \Delta G^{\circ}=-141.8 \mathrm{~kJ} \end{aligned} $$ calculate the value of \(\Delta G^{\circ}\) for the reaction $$ \mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{NH}_{3}(g) $$

Chloroform, formerly used as an anesthetic and now believed to be a carcinogen, has a heat of vaporization \(\Delta H_{\text {vaporization }}=\) \(31.4 \mathrm{~kJ} \mathrm{~mol}^{-1}\). The change, \(\mathrm{CHCl}_{3}(l) \longrightarrow \mathrm{CHCl}_{3}(g)\) has \(\Delta S^{\circ}=94.2 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\). At what temperature do we expect \(\mathrm{CHCl}_{3}\) to boil (i.e., at what temperature will liquid and vapor be in equilibrium at 1 atm pressure)?

Isooctane, a minor constituent of gasoline, has a boiling point of \(99.3^{\circ} \mathrm{C}\) and a heat of vaporization of \(37.7 \mathrm{~kJ}\) \(\mathrm{mol}^{-1}\). What is \(\Delta S\) (in J \(\mathrm{mol}^{-1} \mathrm{~K}^{-1}\) ) for the vaporization of \(1 \mathrm{~mol}\) of isooctane?

Which of the following reactions (equations unbalanced) would be expected to be spontaneous at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) ? (a) \(\mathrm{PbO}(s)+\mathrm{NH}_{3}(g) \longrightarrow \mathrm{Pb}(s)+\mathrm{N}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) (b) \(\mathrm{NaOH}(s)+\mathrm{HCl}(g) \longrightarrow \mathrm{NaCl}(s)+\mathrm{H}_{2} \mathrm{O}(l)\) (c) \(\mathrm{Al}_{2} \mathrm{O}_{3}(s)+\mathrm{Fe}(s) \longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{Al}(s)\) (d) \(2 \mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2}(g)\)

What is the value of the equilibrium constant for a reaction for which \(\Delta G^{\circ}=0 ?\) What will happen to the composition of the system if we begin the reaction with the pure products?