Ch.19 - Chemical Thermodynamics

Problem 66

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Chapter 19, Problem 66

A certain constant-pressure reaction is barely nonspontaneous at 45 °C. The entropy change for the reaction is 72 J/K. Estimate ΔH.

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1. The spontaneity of a reaction is determined by the Gibbs free energy change (ΔG). If ΔG is negative, the reaction is spontaneous. If ΔG is positive, the reaction is nonspontaneous. In this case, we know the reaction is barely nonspontaneous, so ΔG is slightly positive.

2. The Gibbs free energy change is given by the equation ΔG = ΔH - TΔS, where ΔH is the enthalpy change, T is the temperature in Kelvin, and ΔS is the entropy change. We need to solve this equation for ΔH, which gives us ΔH = ΔG + TΔS.

3. We know that ΔG is slightly positive, but we don't know its exact value. However, because the reaction is barely nonspontaneous, we can assume that ΔG is very close to zero. This simplifies our equation to ΔH ≈ TΔS.

4. Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature. So, T = 45°C + 273.15 = 318.15 K.

5. Substitute the values of T and ΔS into the equation from step 3 to estimate ΔH. Remember to keep the units consistent, so convert the entropy change from J/K to kJ/K by dividing by 1000 if necessary.

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Key Concepts

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

Gibbs Free Energy

Gibbs Free Energy (ΔG) is a thermodynamic potential that helps predict the spontaneity of a reaction. A reaction is spontaneous when ΔG is negative. At equilibrium, ΔG equals zero, and for a reaction to be barely nonspontaneous, ΔG is close to zero, indicating that the enthalpy and entropy changes are in a delicate balance.

Entropy Change (ΔS)

Entropy change (ΔS) measures the degree of disorder or randomness in a system. In this context, a positive ΔS of 72 J/K suggests that the reaction increases the disorder of the system. This increase in entropy can drive a reaction towards spontaneity, but it must be balanced with the enthalpy change (ΔH) to determine the overall spontaneity through Gibbs Free Energy.

Enthalpy Change (ΔH)

Enthalpy change (ΔH) represents the heat content of a system at constant pressure. It is a crucial factor in determining the energy required or released during a reaction. In the context of the question, we can use the relationship ΔG = ΔH - TΔS to estimate ΔH, knowing that the reaction is barely nonspontaneous at a specific temperature (45 °C).

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Related Practice

Textbook Question

Classify each of the following reactions as one of the four possible types summarized in Table 19.3: (i) spontaneous at all temperatures; (ii) not spontaneous at any temperature; (iii) spontaneous at low T but not spontaneous at high T; (iv) spontaneous at high T but not spontaneous at low T. (c) N₂F₄(g) ⟶ 2 NF₂(g) ΔH° = 85 kJ; ΔS° = 198 J/K

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Textbook Question

From the values given for ΔH° and ΔS°, calculate ΔG° for each of the following reactions at 298 K. If the reaction is not spontaneous under standard conditions at 298 K, at what temperature (if any) would the reaction become spontaneous? a. 2 PbS(s) + 3 O₂(g) → 2 PbO(s) + 2 SO₂(g) ΔH° = −844 kJ; ΔS° = −165 J/K

A particular constant-pressure reaction is barely spontaneous at 390 K. The enthalpy change for the reaction is +23.7 kJ. Estimate ΔS for the reaction.

Open Question

For a particular reaction, ΔH = -32 kJ and ΔS = -98 J>K. Assume that ΔH and ΔS do not vary with temperature. (a) At what temperature will the reaction have ΔG = 0? (b) If T is increased from that in part (a), will the reaction be spontaneous or nonspontaneous?

Textbook Question

Reactions in which a substance decomposes by losing CO are called decarbonylation reactions. The decarbonylation of acetic acid proceeds according to: CH₃COOH(l) → CH₃OH(g) + CO(g) By using data from Appendix C, calculate the minimum temperature at which this process will be spontaneous under standard conditions. Assume that ΔH° and ΔS° do not vary with temperature.

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Textbook Question

Consider the following reaction between oxides of nitrogen: NO₂(g) + N₂O(g) → 3 NO(g) (a) Use data in Appendix C to predict how ΔG for the reaction varies with increasing temperature.

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