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Ch.19 - Chemical Thermodynamics
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook
All textbooksBrown 14th EditionCh.19 - Chemical ThermodynamicsProblem 110a
Chapter 19, Problem 110a

Consider the following equilibrium: N2O4(g) ⇌ 2 NO2(g) Thermodynamic data on these gases are given in Appendix C. You may assume that ΔH° and ΔS° do not vary with temperature. (a) At what temperature will an equilibrium mixture contain equal amounts of the two gases?

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1
Identify the expression for the equilibrium constant, K, for the reaction: N2O4(g) ⇌ 2 NO2(g). The equilibrium constant can be expressed as K = [NO2]2 / [N2O4].
Set up the equation for the Gibbs free energy change (ΔG°) in terms of the standard enthalpy change (ΔH°) and the standard entropy change (ΔS°) at temperature T: ΔG° = ΔH° - TΔS°.
Relate ΔG° to the equilibrium constant K using the relationship ΔG° = -RT ln(K), where R is the gas constant and T is the temperature in Kelvin.
Combine the equations from steps 2 and 3 to solve for T when K = 1 (since at K = 1, the concentrations of N2O4 and NO2 are equal). This gives the equation: ΔH° - TΔS° = -RT ln(1). Since ln(1) = 0, simplify to ΔH° = TΔS°.
Solve for T by rearranging the equation from step 4: T = ΔH° / ΔS°. Use the values of ΔH° and ΔS° from the thermodynamic data provided in Appendix C to find the temperature at which the equilibrium mixture contains equal amounts of N2O4 and NO2.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. In this case, the equilibrium expression can be used to relate the concentrations of N2O4 and NO2 at a given temperature, allowing for the determination of conditions under which equal amounts of both gases are present.
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Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that helps predict the direction of chemical reactions and the position of equilibrium. The change in Gibbs Free Energy (ΔG) is related to the enthalpy (ΔH) and entropy (ΔS) of the system, and at equilibrium, ΔG equals zero. This relationship is crucial for determining the temperature at which equal concentrations of N2O4 and NO2 exist.
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Van 't Hoff Equation

The Van 't Hoff equation relates the change in the equilibrium constant (K) of a reaction to the change in temperature. It is expressed as ln(K2/K1) = -ΔH°/R(1/T2 - 1/T1), where R is the gas constant. This equation is essential for calculating the temperature at which the equilibrium concentrations of N2O4 and NO2 are equal, as it allows for the determination of K at different temperatures.
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Related Practice
Textbook Question
Carbon disulfide 1CS22 is a toxic, highly flammable substance. The following thermodynamic data are available for CS21l2 and CS21g2 at 298 K: (e) Use the data in the table to calculate ΔS° at 298 K for the vaporization of CS21l2. Is the sign of ΔS° as you would expect for a vaporization?
Textbook Question

An ice cube with a mass of 20 g at -20 °C (typical freezer temperature) is dropped into a cup that holds 500 mL of hot water, initially at 83 °C. What is the final temperature in the cup? The density of liquid water is 1.00 g>mL; the specific heat capacity of ice is 2.03 J>g@C; the specific heat capacity of liquid water is 4.184 J>g@C; the enthalpy of fusion of water is 6.01 kJ>mol.

Textbook Question
The following data compare the standard enthalpies and free energies of formation of some crystalline ionic substances and aqueous solutions of the substances:
(a) Write the formation reaction for AgNO31s2. Based on this reaction, do you expect the entropy of the system to increase or decrease upon the formation of AgNO31s2? (b) Use ΔH°f and ΔG°f of AgNO31s2 to determine the entropy change upon formation of the substance. Is your answer consistent with your reasoning in part (a)?
Textbook Question

The reaction SO2(g) + 2 H2S(g) ⇌ 3 S(s) + 2 H2O(g) is the basis of a suggested method for removal of SO2 from power-plant stack gases. The standard free energy of each substance is given in Appendix C. (a) What is the equilibrium constant for the reaction at 298 K? (c) If PSO2 = PH2S and the vapor pressure of water is 25 torr, calculate the equilibrium SO2 pressure in the system at 298 K.

Textbook Question

The reaction SO2(g) + 2 H2S(g) ⇌ 3 S(s) + 2 H2O(g) is the basis of a suggested method for removal of SO2 from power-plant stack gases. The standard free energy of each substance is given in Appendix C. (b) In principle, is this reaction a feasible method of removing SO2?

Textbook Question

The reaction SO2(g) + 2 H2S(g) ⇌ 3 S(s) + 2 H2O(g) is the basis of a suggested method for removal of SO2 from power-plant stack gases. The standard free energy of each substance is given in Appendix C. (d) Would you expect the process to be more or less effective at higher temperatures?