Chapter 18, Problem 1PS

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.

1. (a) Was the process exothermic or endothermic?
2. (b) Was the process spontaneous?
3. (c) Did the entropy of the system increase?
4. (d) Did the entropy of the universe increase?

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.

Answer to Problem 1PS

The process of dissolution of solid ${\text{NH}}_{\text{4}}{\text{NO}}_{\text{3}}$ is endothermic.

Explanation of Solution

The chemical reaction is:

${\text{NH}}_{\text{4}}{\text{NO}}_{\text{3}}\left(\text{s}\right)\to {\text{NH}}_{\text{4}}{\text{NO}}_{\text{3}}\left(\text{aq}\right)$

The change in enthalpy $\Delta H^{\circ }$ is positive for the reaction. The value of $\Delta H^{\circ }$ is $+25.7\text{ kJ/mol}$. Since the value is positive, thus the reaction is endothermic.

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.

Answer to Problem 1PS

The process of dissolution of solid ${\text{NH}}_{\text{4}}{\text{NO}}_{\text{3}}$ is spontaneous.

Explanation of Solution

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 ${\text{Δ}}_{\text{r}}{S}^{\text{°}}$ value for aqueous ${\text{NH}}_{\text{4}}{\text{NO}}_{\text{3}}$ is greater than for solid ${\text{NH}}_{\text{4}}{\text{NO}}_{\text{3}}$. Thus, there is an increase in entropy.

Hence, the process is spontaneous. Also the change in free energy for the reaction ${\text{NH}}_{\text{4}}{\text{NO}}_{\text{3}}\left(\text{s}\right)\to {\text{NH}}_{\text{4}}{\text{NO}}_{\text{3}}\left(\text{aq}\right)$ is negative, which confirms the spontaneity.

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. ${\text{(ΔS}}^{\text{°}}{}_{\text{rxn}}\text{)}$ can be calculated by the following equation.

  ${\text{ΔS}}^{\text{°}}{}_{\text{rxn}}{\text{ = S}}^{\text{°}}{}_{\text{Products}}-{\text{ S}}^{\text{°}}{}_{\text{reactants}}$

Where,

  ${\text{S}}^{\text{°}}{}_{\text{reactants}}$ is the standard entropy of the reactants

  ${\text{S}}^{\text{°}}{}_{\text{Products}}$ 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. ${\text{ΔS}}_{\text{univ}}={\text{ΔS}}_{\text{sys}}+{\text{ΔS}}_{\text{surr}}$.

${\text{NH}}_{\text{4}}{\text{NO}}_{\text{3}}$ is a solid compound that dissolves readily in water. In a spontaneous process, energy goes from being concentrated to being dispersed.

Answer to Problem 1PS

The entropy of the system for the process of dissolution of ${\text{NH}}_{\text{4}}{\text{NO}}_{\text{3}}\left(\text{s}\right)$ increases.

Explanation of Solution

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

The $S^{\text{°}}$ value for ${\text{NH}}_{\text{4}}{\text{NO}}_{\text{3}}\left(\text{s}\right)$ is $\text{151}\text{.08 J/K}\cdot \text{mol}$ and the $S^{\text{°}}$ value for ${\text{NH}}_{\text{4}}{\text{NO}}_{\text{3}}\left(\text{aq}\right)$ is $\text{259}\text{.8 J/K}\cdot \text{mol}$. Thus, there is an increase in entropy of the system.

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. ${\text{(ΔS}}^{\text{°}}{}_{\text{rxn}}\text{)}$ can be calculated by the following equation.

  ${\text{ΔS}}^{\text{°}}{}_{\text{rxn}}{\text{ = S}}^{\text{°}}{}_{\text{Products}}-{\text{ S}}^{\text{°}}{}_{\text{reactants}}$

Where,

  ${\text{S}}^{\text{°}}{}_{\text{reactants}}$ is the standard entropy of the reactants

  ${\text{S}}^{\text{°}}{}_{\text{Products}}$ 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. ${\text{ΔS}}_{\text{univ}}={\text{ΔS}}_{\text{sys}}+{\text{ΔS}}_{\text{surr}}$.

${\text{NH}}_{\text{4}}{\text{NO}}_{\text{3}}$ is a solid compound that dissolves readily in water. In a spontaneous process, energy goes from being concentrated to being dispersed.

Answer to Problem 1PS

There is an increase in the entropy of the universe for the process of dissolution of ${\text{NH}}_{\text{4}}{\text{NO}}_{\text{3}}\left(\text{s}\right)$.

Explanation of Solution

${\text{NH}}_{\text{4}}{\text{NO}}_{\text{3}}$ 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.