   Chapter 18, Problem 1PS

Chapter
Section
Textbook Problem

Solid NH4NO3 is placed in a beaker containing water at 25 °C. When the solid has completely dissolved, the temperature of the solution is 23.5 °C. (a) Was the process exothermic or endothermic? (b) Was the process spontaneous? (c) Did the entropy of the system increase? (d) Did the entropy of the universe increase?

(a)

Interpretation Introduction

Interpretation: Considering the given reaction and its conditions it should be identified that the process is exothermic or endothermic.

Concept introduction: A process is referred to as spontaneous if the change occurs without any outside interference. The spontaneous change occurs in the direction of equilibrium.

Exothermic reaction: Exothermic reactions are those in which evolution of heat takes place during any chemical reaction. They release heat because the reactant molecules require less heat for breakage of bonds than the product molecules hence the reaction enthalpy will be negative value.

Endothermic reaction: Endothermic reactions are those in which heat is absorbed during any chemical reaction. In such type of reactions, external energy is needed hence reaction enthalpy will be positive value.

The process of dissolution of solid NH4NO3 is endothermic.

Explanation

The chemical reaction is:

NH4NO3(s)NH4NO3(aq)

The change in enthalpy ΔH is positive for the reaction. The value of ΔH is +25.7 kJ/mol. Since the value is positive, thus the reaction is endothermic.

(b)

Interpretation Introduction

Interpretation: Considering the given reaction and its conditions it should be identified that the process is spontaneous or not.

Concept introduction: A process is referred to as spontaneous if the change occurs without any outside interference. The spontaneous change occurs in the direction of equilibrium.

Exothermic reaction: Exothermic reactions are those in which evolution of heat takes place during any chemical reaction. They release heat because the reactant molecules require less heat for breakage of bonds than the product molecules hence the reaction enthalpy will be negative value.

Endothermic reaction: Endothermic reactions are those in which heat is absorbed during any chemical reaction. In such type of reactions, external energy is needed hence reaction enthalpy will be positive value.

The process of dissolution of solid NH4NO3 is spontaneous.

Explanation

In a spontaneous process, energy goes from being concentrated to being dispersed. The second law of thermodynamic state that a spontaneous process results in increase in entropy.

The ΔrS° value for aqueous NH4NO3 is greater than for solid NH4NO3. Thus, there is an increase in entropy.

Hence, the process is spontaneous. Also the change in free energy for the reaction NH4NO3(s)NH4NO3(aq) is negative, which confirms the spontaneity.

(c)

Interpretation Introduction

Interpretation: Considering the given reaction and its conditions it should be identified that whether the entropy of the system increase.

Concept introduction: A process is referred to as spontaneous if the change occurs without any outside interference. The spontaneous change occurs in the direction of equilibrium.

Exothermic reaction: Exothermic reactions are those in which evolution of heat takes place during any chemical reaction. They release heat because the reactant molecules require less heat for breakage of bonds than the product molecules hence the reaction enthalpy will be negative value.

Endothermic reaction: Endothermic reactions are those in which heat is absorbed during any chemical reaction. In such type of reactions, external energy is needed hence reaction enthalpy will be positive value.

Entropy is the measure of randomness in the system.  Standard entropy change in a reaction is the difference in entropy of the products and reactants. (ΔS°rxn) can be calculated by the following equation.

ΔS°rxn = S°Products- S°reactants

Where,

S°reactants is the standard entropy of the reactants

S°Products is the standard entropy of the products

Standard entropy change in a reaction and entropy change in the system are same.

It is the amount of arrangements possible in a system at a particular state. ΔSuniv=ΔSsys+ΔSsurr.

NH4NO3 is a solid compound that dissolves readily in water. In a spontaneous process, energy goes from being concentrated to being dispersed.

The entropy of the system for the process of dissolution of NH4NO3(s) increases.

Explanation

In a spontaneous process, energy goes from being concentrated to being dispersed.

The S° value for NH4NO3(s) is 151.08 J/Kmol and the S° value for NH4NO3(aq) is 259.8 J/Kmol. Thus, there is an increase in entropy of the system.

(d)

Interpretation Introduction

Interpretation: Considering the given reaction and its conditions it should be identified that the whether the entropy of the universe increase.

Concept introduction: A process is referred to as spontaneous if the change occurs without any outside interference. The spontaneous change occurs in the direction of equilibrium.

Exothermic reaction: Exothermic reactions are those in which evolution of heat takes place during any chemical reaction. They release heat because the reactant molecules require less heat for breakage of bonds than the product molecules hence the reaction enthalpy will be negative value.

Endothermic reaction: Endothermic reactions are those in which heat is absorbed during any chemical reaction. In such type of reactions, external energy is needed hence reaction enthalpy will be positive value.

Entropy is the measure of randomness in the system.  Standard entropy change in a reaction is the difference in entropy of the products and reactants. (ΔS°rxn) can be calculated by the following equation.

ΔS°rxn = S°Products- S°reactants

Where,

S°reactants is the standard entropy of the reactants

S°Products is the standard entropy of the products

Standard entropy change in a reaction and entropy change in the system are same.

It is the amount of arrangements possible in a system at a particular state. ΔSuniv=ΔSsys+ΔSsurr.

NH4NO3 is a solid compound that dissolves readily in water. In a spontaneous process, energy goes from being concentrated to being dispersed.

There is an increase in the entropy of the universe for the process of dissolution of NH4NO3(s).

Explanation

NH4NO3 is a solid compound that dissolves readily in water. In a spontaneous process, energy goes from being concentrated to being dispersed.

The second law of thermodynamic state that a spontaneous process results in increase in entropy of the universe. The entropy of the universe is always greater than zero for a spontaneous process.

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