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Chapter 4: Problem 23

The acid-base chemistry reaction of barium hydroxide \(\left(\mathrm{Ba}(\mathrm{OH})_{2}\right)\) with ammonium thiocyanate \(\left(\mathrm{NH}_{4} \mathrm{SCN}\right)\) in water creates barium thiocyanate, ammonia, and water. The reaction is highly favorable, but also so endothermic that the solutions cools to such an extent that a layer of frost forms on the reaction vessel. Explain how an endothermic reaction can be favorable.

Short Answer

Expert verified
Question: Explain how an endothermic reaction, such as the reaction of barium hydroxide with ammonium thiocyanate, can be favorable. Answer: An endothermic reaction like the one between barium hydroxide and ammonium thiocyanate can be favorable if the positive entropy change (ΔS) is significant enough to overcome the positive enthalpy change (ΔH). In this case, the release of ammonia gas contributes to a positive entropy change, making the reaction favorable despite being endothermic.

Step by step solution

01

Understanding endothermic reactions

An endothermic reaction is a chemical reaction in which the reactants absorb heat from the surroundings. In an endothermic reaction, the overall change in enthalpy (\(\Delta H\)) is positive. This means that the products have more energy than the reactants.
02

Understanding chemical reactions' favorability

A chemical reaction's favorability is determined by two factors: enthalpy change (\(\Delta H\)) and entropy change (\(\Delta S\)). The Gibbs free energy change (\(\Delta G\)) combines these factors and is calculated using the equation: \(\Delta G = \Delta H - T\Delta S\), where \(T\) is the temperature in Kelvin. A reaction is considered favorable (spontaneous) if \(\Delta G\) is negative. This can occur in a few ways: 1. Both \(\Delta H\) and \(\Delta S\) are negative, but the magnitude of \(T\Delta S\) is greater than \(\Delta H\). 2. Both \(\Delta H\) and \(\Delta S\) are positive, but the magnitude of \(T\Delta S\) is greater than \(\Delta H\). 3. \(\Delta H\) is negative, and \(\Delta S\) is positive.
03

Applying Gibbs free energy formula

In the case of the reaction between barium hydroxide and ammonium thiocyanate, the reaction is endothermic, so \(\Delta H\) is positive. For the reaction to be favorable, \(\Delta S\) must also be positive and the magnitude of \(T\Delta S\) must be greater than \(\Delta H\).
04

Reasons for positive entropy change

There are several factors that can contribute to a positive entropy change (\(\Delta S\)) in a reaction. These include an increase in the number of particles, a change in the physical state of the substances, or a release of gas molecules. In the reaction of barium hydroxide and ammonium thiocyanate, ammonia gas is released, leading to an increase in entropy.
05

Conclusion

An endothermic reaction, like the one between barium hydroxide and ammonium thiocyanate, can be favorable if the positive entropy change (\(\Delta S\)) is significant enough to overcome the positive enthalpy change (\(\Delta H\)). In this case, the release of ammonia gas contributes to a positive entropy change, making the reaction favorable despite being endothermic.

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Most popular questions from this chapter

Acetic acid, \(\mathrm{CH}_{3} \mathrm{COOH}\), is a weak organic acid, \(\mathrm{p} K_{\mathrm{a}} 4.76\). Write an equation for the equilibrium reaction of acetic acid with each base. Which equilibria lie considerably toward the left? Which lie considerably toward the right? (a) \(\mathrm{NaHCO}_{3}\) (b) \(\mathrm{NH}_{3}\) (c) \(\mathrm{H}_{2} \mathrm{O}\) (d) \(\mathrm{NaOH}\)

Following is a structural formula for the tert-butyl cation. (We discuss the formation, stability, and reactions of cations such as this one in Chapter 6 .) C[C+](C)C tert-Butyl cation (a carbocation) (a) Predict all \(\mathrm{C}-\mathrm{C}-\mathrm{C}\) bond angles in this cation. (b) What is the hybridization of the carbon bearing the positive charge? (c) Write a balanced equation to show its reaction as a Lewis acid with water. (d) Write a balanced equation to show its reaction as a Brønsted-Lowry acid with water.

Unless under pressure, carbonic acid \(\left(\mathrm{H}_{2} \mathrm{CO}_{3}\right)\) in aqueous solution breaks down into carbon dioxide and water, and carbon dioxide is evolved as bubbles of gas. Write an equation for the conversion of carbonic acid to carbon dioxide and water.

Each molecule or ion can function as a base. Write a structural formula of the conjugate acid formed by reaction of each with \(\mathrm{HCl}\). (a) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) (b) \(\mathrm{HCH}\) (c) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH}\) (d) \(\mathrm{HCO}_{3}{ }^{-}\)

Label the most acidic hydrogen in each molecule, and justify your choice by using appropriate \(\mathrm{p} K_{\mathrm{a}}\) values. (a) \(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\) (b) \(\mathrm{HSCH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\) (c) \(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{C} \equiv \mathrm{CH}\) (d) \(\mathrm{HOCCH}_{2} \mathrm{CH}_{2} \mathrm{SH}\) (e) \(\mathrm{CH}_{3} \mathrm{CHCOH}_{\mathrm{CH}}^{\mathrm{HO}}\) (f) \(\mathrm{H}_{3} \mathrm{NCH}_{2} \mathrm{CH}_{2} \|_{\mathrm{COH}}^{\mathrm{O}}\) (g) \(\mathrm{H}_{3} \mathrm{NCH}_{2} \mathrm{CH}_{2} \|_{\mathrm{CO}^{-}}\) (h) \(\mathrm{HSCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\)
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