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- The accompanying diagram shows how the free energy, G, changes during a hypothetical reaction A(g) + B(g) → C(g). On the left are pure reactants A and B, each at 1 atm, and on the right is the pure product, C, also at 1 atm. Indicate whether each of the following statements is true or false. (a) The minimum of the graph corresponds to the equilibrium mixture of reactants and products for this reaction. (b) At equilibrium, all of A and B have reacted to give pure C. (c) The entropy change for this reaction is positive. (d) The ‘x’ on the graph corresponds to ΔG for the reaction. (e) ΔG for the reaction corresponds to the difference between the top left of the curve and the bottom of the curve.
Problem 1
Problem 1d
Two different gases occupy the two bulbs shown here. Consider the process that occurs when the stopcock is opened, assuming the gases behave ideally. (d) How does the process affect the entropy of the surroundings?
- As shown here, one type of computer keyboard cleaner contains liquefied 1,1-difluoroethane (C2H4F2), 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. (d) Given your answers to (a), (b), and (c), do you think the operation of this product depends more on enthalpy or entropy? (a) Based on your experience, is the vaporization a spontaneous process at room temperature?
Problem 2
Problem 3b
b. If energy can flow in and out of the system to maintain a constant temperature during the process, what can you say about the entropy change of the surroundings as a result of this process?
Problem 4
Predict the signs of ΔH and ΔS for this reaction. Explain your choice.
Problem 5c
The accompanying diagram shows how entropy varies with temperature for a substance that is a gas at the highest temperature shown. (c) If this substance is a perfect crystal at T = 0 K, what is the value of S at this temperature?
- Methanol (CH3OH) can be made by the controlled oxidation of methane: CH4(g) + 1/2 O2(g) → CH3OH(g) (c) Calculate ΔG° at 298 K. Under standard conditions, is the reaction spontaneous at this temperature? (d) Is there a temperature at which the reaction would be at equilibrium under standard conditions and that is low enough so that the compounds involved are likely to be stable?
Problem 7
Problem 7b
The accompanying diagram shows how ΔH (red line) and TΔS (blue line) change with temperature for a hypothetical reaction.
(b) In what temperature range is this reaction spontaneous?
- Using data from Appendix C, write the equilibrium-constant expression and calculate the value of the equilibrium constant and the free-energy change for these reactions at 298 K: (b) 2 HBr(g) + Cl2(g) ⇌ 2 HCl(g) + Br2(g) (c) 2 SO2(g) + O2(g) ⇌ 2 SO3(g)
Problem 8
Problem 9a
Consider a reaction A2(𝑔) + B2(𝑔) ⇌ 2 AB(𝑔), atoms of A shown in red in the diagram and atoms of B shown in blue. (a) If 𝐾𝑐 = 1, which box represents the system at equilibrium?
Problem 11d
Which of the following processes are spontaneous and which are nonspontaneous: (d) lightning
Problem 11e
Which of the following processes are spontaneous and which are nonspontaneous: (e) formation of CH4 and O2 molecules from CO2 and H2O at room temperature and 1 atm of pressure?
Problem 12
Which of the following processes are spontaneous?
a. the melting of ice cubes at −10 °C and 1 atm pressure
b. separating a mixture of N2 and O2 into two separate samples, one that is pure N2 and one that is pure O2
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
Problem 13
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?
Problem 14
Problem 14d
(d) Does the amount of work that a system can do on its surroundings depend on the path of the process?
Problem 15a
Consider the vaporization of liquid water to steam at a pressure of 1 atm. (a) Is this process endothermic or exothermic?
Problem 15b
Consider the vaporization of liquid water to steam at a pressure of 1 atm. (b) In what temperature range is it a spontaneous process?
Problem 15c
Consider the vaporization of liquid water to steam at a pressure of 1 atm. (c) In what temperature range is it a nonspontaneous process?
Problem 15d
Consider the vaporization of liquid water to steam at a pressure of 1 atm. (d) At what temperature are the two phases in equilibrium?
Problem 16b
The normal freezing point of n-octane (C8H18) is -57 °C. (b) In what temperature range is the freezing of n-octane a spontaneous process?
Problem 17a
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?
Problem 17b
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. (b) Is this process isothermal?
Problem 18c
A system goes from state 1 to state 2 and back to state 1. (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?
Problem 19
Problem 21d
Indicate whether each statement is true or false. (a) ΔS 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.
Problem 23a
The normal boiling point of Br2(l) is 58.8 °C, and its molar enthalpy of vaporization is ΔHvap = 29.6 kJ/mol. (a) When Br2(l) boils at its normal boiling point, does its entropy increase or decrease?
Problem 23b
The normal boiling point of Br2(𝑙) is 58.8 °C, and its molar enthalpy of vaporization is Δ𝐻vap=29.6 kJ/mol. (b) Calculate the value of Δ𝑆 when 1.00 mol of Br2(𝑙) is vaporized at 58.8 °C.
Problem 24a
The element gallium (Ga) freezes at 29.8 °C, and its molar enthalpy of fusion is ΔHfus = 5.59 kJ/mol. (a) When molten gallium solidifies to Ga(s) at its normal melting point, is ΔS positive or negative?
Problem 24b
The element gallium (Ga) freezes at 29.8 °C, and its molar enthalpy of fusion is ΔHfus = 5.59 kJ/mol. (b) Calculate the value of ΔS when 60.0 g of Ga(l) solidifies at 29.8 °C.