(a) Write the chemical equations that correspond to ΔG°f for NH3(g) and for CO(g). (b) For which of these formation reactions will the value of ΔG°f be more positive (less negative) than ΔH°f?

Verified step by step guidance

Step 1: Understand the concept of standard Gibbs free energy of formation (ΔG°f) and standard enthalpy of formation (ΔH°f). These values represent the change in Gibbs free energy and enthalpy, respectively, when one mole of a compound is formed from its elements in their standard states.

Step 2: Write the chemical equation for the formation of NH3(g) from its elements in their standard states. The elements involved are nitrogen (N2) and hydrogen (H2). The balanced chemical equation is: N2(g) + 3/2 H2(g) → NH3(g).

Step 3: Write the chemical equation for the formation of CO(g) from its elements in their standard states. The elements involved are carbon (C) and oxygen (O2). The balanced chemical equation is: C(s) + 1/2 O2(g) → CO(g).

Step 4: Consider the relationship between ΔG°f and ΔH°f. The difference between these values is related to the entropy change (ΔS°) of the reaction at standard conditions, as given by the equation: ΔG°f = ΔH°f - TΔS°.

Step 5: Analyze which formation reaction will have a more positive (or less negative) ΔG°f compared to ΔH°f. This occurs when the entropy change (ΔS°) is negative, meaning the system becomes more ordered. Consider the molecular complexity and phase changes involved in each reaction to determine the likely sign of ΔS°.

Key Concepts

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

Gibbs Free Energy (ΔG°f)

Gibbs Free Energy (ΔG°f) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. It indicates the spontaneity of a reaction; a negative ΔG°f suggests that the formation of a compound is spontaneous, while a positive value indicates non-spontaneity. The standard formation free energy change (ΔG°f) specifically refers to the change when one mole of a compound is formed from its elements in their standard states.

Enthalpy (ΔH°f)

Enthalpy (ΔH°f) is a measure of the total heat content of a system and is used to describe the heat changes during chemical reactions. The standard enthalpy of formation (ΔH°f) is the change in enthalpy when one mole of a compound is formed from its elements in their standard states. Understanding the relationship between ΔH°f and ΔG°f is crucial, as it helps predict whether a reaction is exothermic or endothermic and its spontaneity under standard conditions.

Relationship between ΔG°f and ΔH°f

The relationship between Gibbs Free Energy (ΔG°f) and Enthalpy (ΔH°f) is described by the equation ΔG°f = ΔH°f - TΔS°, where T is the temperature in Kelvin and ΔS° is the change in entropy. This equation indicates that at higher temperatures, the entropy term (TΔS°) can significantly influence the value of ΔG°f. If ΔH°f is negative (exothermic reaction) and ΔS° is positive, ΔG°f will be more negative, indicating a spontaneous reaction, while a positive ΔH°f with a negative ΔS° can lead to a less negative or positive ΔG°f.

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Relationship between ∆E°, ∆G°, and K

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. (c) In a central air-conditioning system, one chamber is inside the home and the other is outside. Which chamber is where, and why?

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Textbook Question

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?

Textbook Question

(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.

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.

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?