Chapter U5.105, Problem 4E

(a)

Interpretation Introduction

Interpretation: The diagram which represents endothermic reaction needs to be identified.

Concept Introduction : Endothermic reaction is the reaction in which the energy is consumed by the reaction and exothermic reaction is the reaction in which energy is released by the reaction. For endothermic reaction heat is expressed as positive value and for exothermic reaction heat is expressed as negative value.

Answer to Problem 4E

The diagram which represents endothermic reaction is,

  

Explanation of Solution

Two diagrams are given. One is for the reaction of methane and oxygen to form carbon dioxide and water and $\Delta H$ for the reaction is $-814\text{kJ}$ . The another diagram is the reverse reaction to form methane and oxygen from carbon dioxide and water and $\Delta H$ for the reaction is $814\text{kJ}$ . The positive $\Delta H$ value indicates endothermic reaction. So, reaction of water and carbon dioxide to form methane and oxygen is endothermic process.

(b)

Interpretation Introduction

Interpretation: The substances having lowest potential energy are to be identified.

Concept Introduction : The energy in a system is a combination of potential and kinetic energy. The energy of motion is the kinetic energy and the stored energy within a physical energy is termed as potential energy.

Answer to Problem 4E

  ${\text{CO}}_{\text{2}}$ and ${\text{H}}_2\text{O}$ have lowest potential energy.

Explanation of Solution

For an exothermic reaction, potential energy of the system decreases as conversion of reactants to product occurs which results increase of kinetic energy. So for combustion reaction, products, that is,

  ${\text{CO}}_{\text{2}}$ and ${\text{H}}_2\text{O}$ have lowest potential energy.

(c)

Interpretation Introduction

Interpretation: What happens to kinetic energy when methane undergoes combustion reaction to form water and carbon dioxide needs to be explained.

Concept Introduction : The energy in a system is a combination of potential and kinetic energy. The energy of motion is the kinetic energy and the stored energy within a physical energy is termed as potential energy.

Answer to Problem 4E

Kinetic energy increases when methane undergoes combustion reaction to form water and carbon dioxide.

Explanation of Solution

Energy is conserved in every chemical reaction. Law of conservation of energy states that for an isolated system, total energy remains constant. In the reaction of methane and oxygen to form carbon dioxide and water, potential energy decreases. As the energy is conserved, the sum of potential and kinetic energy must remain the same. So, kinetic energy increases.

(d)

Interpretation Introduction

Interpretation: The need of constant input of energy in the reverse reaction needs to be explained.

Concept Introduction: In a chemical process, energy is conserved. This means, net exchange of energy in a forward process is equal and opposite to exchange of net energy in the reverse process. If a forward reaction exothermic, the reverse reaction is endothermic.

Answer to Problem 4E

Reverse reaction is endothermic reaction. So, constant amount of energy must be supplied.

Explanation of Solution

The reaction of methane and oxygen to produce carbon dioxide and water is an exothermic reaction. As the energy is conserved, the reverse reaction to form methane and oxygen from carbon dioxide and water is an endothermic reaction. An endothermic reaction always required supply of energy to result the reaction. So, there is need of constant input of energy in the reverse reaction.

(e)

Interpretation Introduction

Interpretation: The heat of the reaction needs to be calculated using the bond energies and the calculated value is to be compared with the value given the energy diagram.

Concept Introduction: To estimate the energy of an entire chemical reaction, the reaction is to considered as it takes place in two parts, that is, energy in for bond breaking and energy out for bond making. The energy of bond breaking is positive and bond making is negative.

Answer to Problem 4E

The calculated value of heat energy for the reaction is $-824\text{kJ/}\text{mol}$ and the value given in the energy diagram is $-814\text{kJ/}\text{mol}$ .

Explanation of Solution

The combustion reaction of methane is,

  ${\text{CH}}_4\text{+}{\text{2O}}_{\text{2}}\to {\text{CO}}_{\text{2}}+2{\text{H}}_{\text{2}}\text{O}$

Here, $4\text{C}-\text{H}$ and $2\text{O=O}$ are broken and $2\text{C=O}$ and 4O-H bonds formed.

Taking values from chapter 104,

  $\begin{array}{l}\text{Bond}\text{enthalpy}\text{of}\text{C}-\text{H}\text{=}\text{413}\text{kJ/}\text{mol}\\ \text{Bond}\text{enthalpy}\text{of}\text{O}=\text{O}\text{=}\text{495}\text{kJ/}\text{mol}\end{array}$

  $\begin{array}{c}\text{Energy}\text{in}\text{bond}\text{breaking}\text{=}\text{4}\left(\text{C}-\text{H}\right)+2\left(\text{O}=\text{O}\right)\\ =4\left(413\text{kJ}\text{/}\text{mol}\right)+2\left(495\text{kJ}\text{/}\text{mol}\right)\\ =1652\text{kJ}\text{/}\text{mol}+990\text{kJ}\text{/}\text{mol}\\ =2642\text{kJ}\text{/}\text{mol}\end{array}$

  $2\text{C=O}$ and 4O-H bonds formed in the reaction.

  $\begin{array}{l}\text{Bond}\text{enthalpy}\text{of}\text{O}-\text{H}\text{=}\text{467}\text{kJ/}\text{mol}\\ \text{Bond}\text{enthalpy}\text{of}\text{C}=\text{O}\text{=}799\text{kJ/}\text{mol}\end{array}$

In bond making bond energies are taken as negative values as energy added from system to the surroundings.

  $\begin{array}{c}\text{Energy}\text{in}\text{bond}\text{making}\text{=}2\left(\text{C}=\text{O}\right)+4\left(\text{O}-\text{H}\right)\\ =2\left(-799\text{kJ/}\text{mol}\right)+4\left(-\text{467}\text{kJ/}\text{mol}\right)\\ =-1598\text{kJ/}\text{mol}-1868\text{kJ/}\text{mol}\\ =-3466\text{kJ/}\text{mol}\end{array}$

Net energy is the summation of energy of bond breaking and bond making.

  $\begin{array}{c}\text{Net}\text{energy}\text{=}-\text{3466}\text{kJ/}\text{mol+2642}\text{kJ/}\text{mol}\\ =-824\text{kJ/}\text{mol}\end{array}$

The heat energy for the reaction given in the diagram is $-814\text{kJ/}\text{mol}$ and the calculated value is $-824\text{kJ/}\text{mol}$ s.