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Ch.19 - Chemical Thermodynamics
Chapter 19, Problem 94c

(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.

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Understand the relationship between Gibbs free energy (\( \Delta G^\circ \)) and enthalpy (\( \Delta H^\circ \)) using the equation: \( \Delta G^\circ = \Delta H^\circ - T\Delta S^\circ \).
Identify the condition where \( \Delta G^\circ \) is more positive (or less negative) than \( \Delta H^\circ \). This occurs when the term \( -T\Delta S^\circ \) is positive, which means \( \Delta S^\circ \) must be negative.
Consider the effect of temperature (\( T \)) on the equation. A higher temperature would increase the magnitude of the \( -T\Delta S^\circ \) term, making \( \Delta G^\circ \) more positive if \( \Delta S^\circ \) is negative.
Evaluate the options given: (i) High temperature would make \( \Delta G^\circ \) more positive if \( \Delta S^\circ \) is negative. (ii) Reversibility of the reaction does not directly affect the relationship between \( \Delta G^\circ \) and \( \Delta H^\circ \). (iii) A negative \( \Delta S^\circ \) would directly contribute to \( \Delta G^\circ \) being more positive.
Conclude that the condition where \( \Delta G^\circ \) is more positive than \( \Delta H^\circ \) is when \( \Delta S^\circ \) is negative, especially at high temperatures.

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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. It combines the system's enthalpy (ΔH°) and entropy (ΔS°) to determine spontaneity; a negative ΔG° indicates a spontaneous process. Understanding how ΔG° relates to temperature and entropy is crucial for predicting reaction behavior.
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Enthalpy (ΔH°)

Enthalpy (ΔH°) is a measure of the total heat content of a system, reflecting the energy required to create a system at constant pressure. It is a key factor in determining the heat absorbed or released during a chemical reaction. The relationship between ΔH° and ΔG° is essential for understanding how temperature influences reaction spontaneity, particularly when considering the signs of ΔH° and ΔS°.
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Entropy (ΔS°)

Entropy (ΔS°) is a measure of the disorder or randomness in a system. It plays a critical role in thermodynamics, as it influences the spontaneity of reactions. A negative ΔS° indicates a decrease in disorder, which can lead to a more positive ΔG° at high temperatures, affecting the overall feasibility of a reaction. Understanding the interplay between ΔS° and temperature is vital for analyzing the conditions under which ΔG° becomes less negative.
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Related Practice
Textbook Question

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?

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Textbook Question

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?

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Textbook Question

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.

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Textbook Question

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?

Textbook Question

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.

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