Textbook Question
Consider a reaction A2(𝑔) + B2(𝑔) ⇌ 2 AB(𝑔), atoms of A shown in red in the diagram and atoms of B shown in blue. (a) If 𝐾𝑐 = 1, which box represents the system at equilibrium?
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Ch.19 - Chemical Thermodynamics
Chapter 19, Problem 11
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. (b) At what temperature will an equilibrium mixture of 1 atm total pressure contain twice as much NO2 as N2O4? (c) At what temperature will an equilibrium mixture of 10 atm total pressure contain twice as much NO2 as N2O4?
Verified step by step guidance1
Identify the equilibrium reaction: \( \text{N}_2\text{O}_4(g) \rightleftharpoons 2 \text{NO}_2(g) \). The equilibrium constant expression for this reaction is \( K_p = \frac{(P_{\text{NO}_2})^2}{P_{\text{N}_2\text{O}_4}} \).
For part (b), assume the partial pressure of \( \text{N}_2\text{O}_4 \) is \( x \) atm and \( \text{NO}_2 \) is \( 2x \) atm, given that \( 2x + x = 1 \) atm. Solve for \( x \) to find the partial pressures.
Substitute the partial pressures into the equilibrium constant expression to find \( K_p \) in terms of \( x \).
Use the relationship \( \Delta G^\circ = -RT \ln K_p \) and \( \Delta G^\circ = \Delta H^\circ - T \Delta S^\circ \) to set up an equation to solve for the temperature \( T \).
Repeat the process for part (c) with a total pressure of 10 atm, where \( 2x + x = 10 \) atm, and solve for the new temperature \( T \) using the same thermodynamic relationships.
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 partial pressures of N2O4 and NO2, allowing us to determine the conditions under which the specified ratio of gases is achieved.
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Chemical Equilibrium Concepts
Le Chatelier's Principle
Le Chatelier's Principle states that if a system at equilibrium is subjected to a change in concentration, temperature, or pressure, the system will adjust to counteract that change and restore a new equilibrium. This principle is crucial for predicting how changes in temperature or pressure will affect the equilibrium position of the reaction in question.
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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 is zero. Understanding how temperature affects ΔG is essential for determining the conditions under which the desired equilibrium concentrations are achieved.
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Related Practice
Textbook Question
Consider a reaction A2(𝑔) + B2(𝑔) ⇌ 2 AB(𝑔), atoms of A shown in red in the diagram and atoms of B shown in blue. (b) If 𝐾𝑐 = 1, which box represents the system at 𝑄 < 𝐾𝑐?
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Textbook Question
Which of the following processes are spontaneous and which are nonspontaneous: (a) the ripening of a banana
Textbook Question
Which of the following processes are spontaneous and which are nonspontaneous: (d) lightning
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Textbook Question
Which of the following processes are spontaneous and which are nonspontaneous: (e) formation of CH4 and O2 molecules from CO2 and H2O at room temperature and 1 atm of pressure?