Consider the reaction 3 CH₄(g) → C₃H₈(g) + 2 H₂(g). (a) Using data from Appendix C, calculate ΔG° at 298 K.

Consider the reaction 3 CH₄(g) → C₃H₈(g) + 2 H₂(g). (b) Calculate ΔG at 298 K if the reaction mixture consists of 40.0 atm of CH₄, 0.0100 atm of C₃H₈(g), and 0.0180 atm of H₂.

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: (a) NaHCO₃(s) ⇌ NaOH(s) + CO₂(g)

Consider the decomposition of barium carbonate: BaCO₃(s) ⇌ BaO(s) + CO₂(g) Using data from Appendix C, calculate the equilibrium pressure of CO₂ at (a) 298 K.

Consider the decomposition of barium carbonate: BaCO₃(s) ⇌ BaO(s) + CO₂(g) Using data from Appendix C, calculate the equilibrium pressure of CO₂ at (b) 1100 K.

Consider the reaction PbCO₃(s) ⇌ PbO(s) + CO₂(g) Using data in Appendix C, calculate the equilibrium pressure of CO2 in the system at (a) 400 °C (b) 180 °C.

The value of K_a for nitrous acid (HNO₂) at 25 °C is given in Appendix D. (a) Write the chemical equation for the equilibrium that corresponds to K_a.

The value of K_a for nitrous acid (HNO₂) at 25 °C is given in Appendix D. (b) By using the value of Ka, calculate ΔG° for the dissociation of nitrous acid in aqueous solution.

The value of K_a for nitrous acid (HNO₂) at 25 °C is given in Appendix D. (c) What is the value of ΔG at equilibrium?

The value of K_a for nitrous acid (HNO₂) at 25 °C is given in Appendix D. (d) What is the value of ΔG when [H⁺] = 5.0⨉10^-2 M, [NO₂^-] = 6.0⨉10^-4 M, and [HNO₂] = 0.20 M?

The K_b for methylamine (CH₃NH₂) at 25 °C is given in Appendix D. (a) Write the chemical equation for the equilibrium that corresponds to K_b.

The K_b for methylamine (CH₃NH₂) at 25 °C is given in Appendix D. (d) What is the value of ΔG when [H⁺] = 6.7 × 10^-9 M, [CH₃NH₃⁺] = 2.4 × 10^-3 M, and [CH₃NH₂] = 0.098 M?

(a) Which of the thermodynamic quantities T, E, q, w, and S are state functions? (b) Which depend on the path taken from one state to another?

(d) For a reversible isothermal process, write an expression for ΔE in terms of q and w and an expression for ΔS in terms of q and T.

The crystalline hydrate Cd(NO₃)₂⋅4 H₂O(s) loses water when placed in a large, closed, dry vessel at room temperature: Cd(NO₃)₂⋅4 H₂O(s) → Cd(NO₃)₂(s) + 4 H₂O(g) This process is spontaneous and ΔH° is positive at room temperature.

(a) What is the sign of ΔS° at room temperature?

The crystalline hydrate Cd(NO₃)₂⋅4 H₂O(s) loses water when placed in a large, closed, dry vessel at room temperature: Cd(NO₃)₂⋅4 H₂O(s) → Cd(NO₃)₂(s) + 4 H₂O(g) This process is spontaneous and ΔH° is positive at room temperature.

(b) If the hydrated compound is placed in a large, closed vessel that already contains a large amount of water vapor, does ΔS° change for this reaction at room temperature?

For each of the following processes, indicate whether the signs of ΔS and ΔH are expected to be positive, negative, or about zero. (a) A solid sublimes. (b) The temperature of a sample of Co(s) is lowered from 60 °C to 25 °C. (c) Ethyl alcohol evaporates from a beaker. (d) A diatomic molecule dissociates into atoms. (e) A piece of charcoal is combusted to form CO₂(g) and H₂O(g).

The reaction 2 Mg(s) + O₂(g) ⟶ 2 MgO(s) is highly spontaneous. A classmate calculates the entropy change for this reaction and obtains a large negative value for ΔS°. Did your classmate make a mistake in the calculation? Explain.

Consider a system that consists of two standard playing dice, with the state of the system defined by the sum of the values shown on the top faces. (f) Calculate the absolute entropy of the two-dice system.

A standard air conditioner involves a refrigerant that is typically now a fluorinated hydrocarbon, such as CH₂F₂. An air-conditioner refrigerant has the property that it readily vaporizes at atmospheric pressure and is easily compressed to its liquid phase under increased pressure. The operation of an air conditioner can be thought of as a closed system made up of the refrigerant going through the two stages shown here (the air circulation is not shown in this diagram).

During expansion, the liquid refrigerant is released into an expansion chamber at low pressure, where it vaporizes. The vapor then undergoes compression at high pressure back to its liquid phase in a compression chamber. (c) In a central air-conditioning system, one chamber is inside the home and the other is outside. Which chamber is where, and why?

A standard air conditioner involves a refrigerant that is typically now a fluorinated hydrocarbon, such as CH₂F₂. An air-conditioner refrigerant has the property that it readily vaporizes at atmospheric pressure and is easily compressed to its liquid phase under increased pressure. The operation of an air conditioner can be thought of as a closed system made up of the refrigerant going through the two stages shown here (the air circulation is not shown in this diagram).

During expansion, the liquid refrigerant is released into an expansion chamber at low pressure, where it vaporizes. The vapor then undergoes compression at high pressure back to its liquid phase in a compression chamber. (e) Suppose that a house and its exterior are both initially at 31 °C. Some time after the air conditioner is turned on, the house is cooled to 24 °C. Is this process spontaneous or nonspontaneous?

Trouton’s rule states that for many liquids at their normal boiling points, the standard molar entropy of vaporization is about 88 J/mol‐K. b. Look up the normal boiling point of Br₂ in a chemistry handbook or at the WebElements website (www.webelements.com) and compare it to your calculation. What are the possible sources of error, or incorrect assumptions, in the calculation?

(c) In general, under which condition is ΔG°_f more positive (less negative) than ΔH°_f ? (i) When the temperature is high, (ii) when the reaction is reversible, (iii) when ΔS°_f is negative.

Consider the following three reactions: (i) Ti(s) + 2 Cl₂(g) → TiCl₄(1g) (a) For each of the reactions, use data in Appendix C to calculate ΔH°, ΔG°, K, and ΔS ° at 25 °C.

Consider the following three reactions: (i) Ti(s) + 2 Cl₂(g) → TiCl₄(1g) (ii) C₂H₆(g) + 7 Cl₂(g) → 2 CCl₄(g) + 6 HCl(g) (iii) BaO(s) + CO₂(g) → BaCO₃(s) (b) Which of these reactions are spontaneous under standard conditions at 25 °C?

Consider the following three reactions: (i) Ti(s) + 2 Cl₂(g) → TiCl₄(1g) (ii) C₂H₆(g) + 7 Cl₂(g) → 2 CCl₄(g) + 6 HCl(g) (iii) BaO(s) + CO₂(g) → BaCO₃(s) (c) For each of the reactions, predict the manner in which the change in free energy varies with an increase in temperature.

Using the data in Appendix C and given the pressures listed, calculate K_p and ΔG for each of the following reactions:

(a) N₂(g) + 3 H₂(g) → 2 NH₃(g) P_N2 = 2.6 atm, P_H2 = 5.9 atm, P_NH3 = 1.2 atm

(b) 2 N₂H₄(g) + 2 NO₂(g) → 3 N₂(g) + 4 H₂O(g) P_N2H4 = P_NO2 = 5.0 × 10^-2 atm, P_N2 = 0.5 atm, P_H2O = 0.3 atm

(c) N₂H₄(g) → N₂(g) + 2 H₂(g) P_N2H4 = 0.5 atm, P_N2 = 1.5 atm, P_H2 = 2.5 atm

(a) For each of the following reactions, predict the sign of ΔH° and ΔS° without doing any calculations. (i) 2 Mg(s) + O₂ (g) ⇌ 2 MgO(s) (ii) 2 KI(s) ⇌ 2 K(g) + I₂(g) (iii) Na₂(g) ⇌ 2 Na(g) (iv) 2 V₂O₅(s) ⇌ 4 V(s) + 5 O₂(g)

(b) Based on your general chemical knowledge, predict which of these reactions will have K>1. (i) 2 Mg(s) + O₂ (g) ⇌ 2 MgO(s) (ii) 2 KI(s) ⇌ 2 K(g) + I₂(g) (iii) Na₂(g) ⇌ 2 Na(g) (iv) 2 V₂O₅(s) ⇌ 4 V(s) + 5 O₂(g)