Textbook Question
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.
Ch.19 - Free Energy & Thermodynamics
Chapter 19, Problem 93c
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?
Verified step by step guidance1
insert step 1> Determine the standard enthalpy change (\( \Delta H^\circ \)) and standard entropy change (\( \Delta S^\circ \)) for the reaction using standard thermodynamic tables.
insert step 2> Use the Gibbs free energy equation \( \Delta G^\circ = \Delta H^\circ - T \Delta S^\circ \) to find the standard Gibbs free energy change (\( \Delta G^\circ \)) at 298 K.
insert step 3> Determine if the reaction is spontaneous at 298 K by checking if \( \Delta G^\circ < 0 \).
insert step 4> To find the temperature at which the reaction becomes spontaneous, set \( \Delta G^\circ = 0 \) and solve for temperature \( T \) using the equation \( T = \frac{\Delta H^\circ}{\Delta S^\circ} \).
insert step 5> Analyze whether increasing or decreasing the temperature will make the reaction more spontaneous based on the signs of \( \Delta H^\circ \) and \( \Delta S^\circ \).
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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 (G) is a thermodynamic potential that helps predict the spontaneity of a reaction at constant temperature and pressure. A reaction is spontaneous if the change in Gibbs Free Energy (ΔG) is negative. The relationship between ΔG, enthalpy (ΔH), and entropy (ΔS) is given by the equation ΔG = ΔH - TΔS, where T is the temperature in Kelvin.
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Gibbs Free Energy of Reactions
Entropy and Enthalpy
Entropy (S) is a measure of the disorder or randomness in a system, while enthalpy (H) is a measure of the total energy of a system, including internal energy and the energy required to make room for it. For a reaction to be spontaneous, the increase in entropy must outweigh the enthalpy changes, particularly at higher temperatures, where the TΔS term becomes significant in the Gibbs Free Energy equation.
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Temperature's Effect on Spontaneity
The temperature of a system can significantly influence the spontaneity of a reaction. If a reaction has a positive ΔS (increase in entropy), increasing the temperature can make the reaction more spontaneous by lowering ΔG. Conversely, if ΔH is positive (endothermic reaction), a higher temperature may be required to achieve a negative ΔG, thus making the reaction spontaneous under standard conditions.
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Related Practice
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?
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.
Textbook Question
Consider this reaction occurring at 298 K: BaCO3(s) ⇌ BaO(s) + CO2( g) b. If BaCO3 is placed in an evacuated flask, what is the partial pressure of CO2 when the reaction reaches equilibrium?
Textbook Question
Consider this reaction occurring at 298 K: BaCO3(s) ⇌ BaO(s) + CO2(g) c. Can the reaction be made more spontaneous by an increase or decrease in temperature? If so, at what temperature is the partial pressure of carbon dioxide 1.0 atm?