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Chapter 19: Problem 22

Explain why you would expect a reaction of the type $\mathrm{AB}(\mathrm{g}) \longrightarrow \mathrm{A}(\mathrm{g})+\mathrm{B}(\mathrm{g})$ always to be spontaneous at high rather than at low temperatures.

Short Answer

Expert verified
A reaction of the type AB(g) -> A(g) + B(g) is expected to be more spontaneous at higher temperatures because the positive entropy change (due to increase in number of gas molecules) leads to a greater decrement in Gibbs Free Energy at higher temperatures, making the reaction more spontaneous as per the definition of spontaneity based on Gibbs Free Energy change.

Step by step solution

01

Recognize the Reaction

This is a chemical reaction which describes the process of an AB molecule breaking down into individual A and B atoms. The process increases the number of gas molecules and hence, increases the entropy, making \( \Delta S \) positive.
02

Identify the Factors Involved in Spontaneity of Reaction

The spontaneity of a reaction is determined by the sign of the Gibbs Free Energy change, \( \Delta G \). According to the Gibbs Free Energy equation, \( \Delta G = \Delta H - T\Delta S \), where 'Delta H' is the enthalpy change, 'Delta S' is the entropy change, and 'T' is the temperature in Kelvin.
03

Analyzing the Impact of Temperature

From the Gibbs Free Energy equation, it can be noticed that for a given positive \( \Delta S \), as temperature 'T' increases, the value of \( T\Delta S \) also increases. Since\( \Delta G = \Delta H - T\Delta S \), an increase in \( T\Delta S \) means a decrease in \( \Delta G \). As a result, the reaction becomes more spontaneous with higher temperatures.

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Most popular questions from this chapter

The following standard Gibbs energy changes are given for \(25^{\circ} \mathrm{C}\) (1) \(\mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{g})\) \(\Delta G^{\circ}=-33.0 \mathrm{kJ}\) (2) \(4 \mathrm{NH}_{3}(\mathrm{g})+5 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(1)\) \(\Delta G^{\circ}=-1010.5 \mathrm{kJ}\) (3) \(\mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}(\mathrm{g})\) \(\Delta G^{\circ}=+173.1 \mathrm{kJ}\) (4) \(\mathrm{N}_{2}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{g})\) \(\Delta G^{\circ}=+102.6 \mathrm{kJ}\) (5) \(2 \mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{N}_{2} \mathrm{O}(\mathrm{g})\) \(\Delta G^{\circ}=+208.4 \mathrm{kJ}\) Combine the preceding equations, as necessary, to obtain \(\Delta G^{\circ}\) values for each of the following reactions. (a) \(\mathrm{N}_{2} \mathrm{O}(\mathrm{g})+\frac{3}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{g}) \quad \Delta G^{\circ}=?\) (b) \(2 \mathrm{H}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(1) \quad \Delta G^{\circ}=?\) (c) \(2 \mathrm{NH}_{3}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{N}_{2} \mathrm{O}(\mathrm{g})+3 \mathrm{H}_{2} \mathrm{O}(1)\) \(\Delta G^{\circ}=?\) Of reactions (a), (b), and (c), which would tend to go to completion at \(25^{\circ} \mathrm{C}\), and which would reach an equilibrium condition with significant amounts of all reactants and products present?

Explain briefly why (a) the change in entropy in a system is not always a suitable criterion for spontaneous change; (b) \(\Delta G^{\circ}\) is so important in dealing with the question of spontaneous change, even though the conditions employed in a reaction are very often nonstandard.

Indicate whether each of the following changes represents an increase or a decrease in entropy in a system, and explain your reasoning: (a) the freezing of ethanol; (b) the sublimation of dry ice; (c) the burning of a rocket fuel.

Which of the following changes in a thermodynamic property would you expect to find for the reaction \(\mathrm{Br}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{Br}(\mathrm{g})\) at all temperatures: \((\mathrm{a}) \Delta H<0\) (b) \(\Delta S>0 ;\) (c) \(\Delta G<0 ;\) (d) \(\Delta S<0 ?\) Explain.

Briefly describe each of the following ideas, methods, or phenomena: (a) absolute molar entropy; (b) coupled reactions; (c) Trouton's rule; (d) evaluation of an equilibrium constant from tabulated thermodynamic data.
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