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Ch.18 - Free Energy and Thermodynamics
All textbooksTro 4th EditionCh.18 - Free Energy and ThermodynamicsProblem 89a
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Chapter 18, Problem 89a

Consider this reaction occurring at 298 K: N2O(g) + NO2(g) ⇌ 3 NO(g) a. Show that the reaction is not spontaneous under standard conditions by calculating ΔG°rxn.

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1
<insert step 1> Calculate the standard Gibbs free energy of formation (ΔG°f) for each species involved in the reaction using a standard table of thermodynamic values.>
<insert step 2> Use the equation ΔG°rxn = ΣΔG°f(products) - ΣΔG°f(reactants) to find the standard Gibbs free energy change for the reaction.>
<insert step 3> Substitute the ΔG°f values for NO, N2O, and NO2 into the equation. Remember to multiply the ΔG°f of NO by 3, as there are 3 moles of NO produced.>
<insert step 4> Calculate the sum of the ΔG°f values for the products and the reactants separately.>
<insert step 5> Subtract the sum of the reactants' ΔG°f from the sum of the products' ΔG°f to find ΔG°rxn. If ΔG°rxn is positive, the reaction is not spontaneous under standard conditions.>

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Key Concepts

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

Gibbs Free Energy (ΔG)

Gibbs Free Energy (ΔG) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. A negative ΔG indicates that a reaction is spontaneous, while a positive ΔG suggests non-spontaneity. The standard Gibbs free energy change (ΔG°) is calculated using standard state conditions, which allows for the comparison of different reactions.
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Standard Conditions

Standard conditions refer to a set of specific conditions used to measure and compare the properties of substances, typically defined as 1 bar of pressure and a specified temperature, usually 298 K (25 °C). Under these conditions, the standard enthalpy, entropy, and Gibbs free energy values are determined, providing a consistent basis for evaluating the spontaneity of reactions and their thermodynamic favorability.
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Equilibrium Constant (K)

The equilibrium constant (K) is a dimensionless value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. It is related to the Gibbs free energy change by the equation ΔG° = -RT ln(K), where R is the universal gas constant and T is the temperature in Kelvin. A K value less than 1 indicates that reactants are favored at equilibrium, which correlates with a positive ΔG°, suggesting the reaction is not spontaneous under standard conditions.
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Related Practice
Textbook Question

Nitrogen dioxide, a pollutant in the atmosphere, can combine with water to form nitric acid. One of the possible reactions is shown here. Calculate ΔG° and Kp for this reaction at 25 °C and comment on the spontaneity of the reaction. 3 NO2(g) + H2O(l)→ 2 HNO3(aq) + NO(g)

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Open Question

Ethene (C2H4) can be halogenated by the reaction: C2H4(g) + X2(g) → C2H4X2(g) where X2 can be Cl2, Br2, or I2. Use the thermodynamic data given to calculate ΔH°, ΔS°, ΔG°, and Kp for the halogenation reaction by each of the three halogens at 25 °C. Which reaction is most spontaneous? Least spontaneous? What is the main factor responsible for the difference in the spontaneity of the three reactions? Does higher temperature make the reactions more spontaneous or less spontaneous?

Compound ΔH°f (kJ/mol) S° (J/mol·K)

C2H4Cl2(g) -129.7 308.0

C2H4Br2(g) +38.3 330.6

C2H4I2(g) +66.5 347.8

Open Question

H2 reacts with the halogens (X2) according to the reaction: H2(g) + X2(g) → 2 HX(g) where X2 can be Cl2, Br2, or I2. Use the thermodynamic data in Appendix IIB to calculate ΔH°, ΔS°, ΔG°, and Kp for the reaction between hydrogen and each of the three halogens. Which reaction is most spontaneous? Least spontaneous? What is the main factor responsible for the difference in the spontaneity of the three reactions? Does higher temperature make the reactions more spontaneous or less spontaneous?

Textbook Question

Consider this reaction occurring at 298 K: N2O(g) + NO2(g) ⇌ 3 NO(g) b. If a reaction mixture contains only N2O and NO2 at partial pressures of 1.0 atm each, the reaction will be spontaneous until some NO forms in the mixture. What maximum partial pressure of NO builds up before the reaction ceases to be spontaneous?

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Textbook Question

Consider this reaction occurring at 298 K: N2O(g) + NO2(g) ⇌ 3 NO(g) c. Can the reaction be made more spontaneous by an increase or decrease in temperature? If so, what temperature is required to make the reaction spontaneous under standard conditions?

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Textbook Question

Consider this reaction occurring at 298 K: BaCO3(s) ⇌ BaO(s) + CO2(g) a. Show that the reaction is not spontaneous under standard conditions by calculating ΔG°rxn.

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