Chapter 9, Problem 9.24QP

Bond Enthalpy

When atoms of the hypothetical element X are placed together, they rapidly undergo reaction to form the X₂ molecule:

$\text{X}(g)+\text{X}(g)\to {\text{X}}_2(g)$

1. a Would you predict that this reaction is exothermic or endothermic? Explain.
2. b Is the bond enthalpy of X₂ a positive or a negative quantity? Why?
3. c Suppose ΔH for the reaction is −500 kJ/mol. Estimate the bond enthalpy of the X₂ molecule.
4. d Another hypothetical molecular compound, Y₂(g), has a bond enthalpy of 750 kJ/mol, and the molecular compound XY(g) has a bond enthalpy of 1500 kJ/mol. Using bond enthalpy information, calculate ΔH for the following reaction. ${\text{X}}_{\text{2}}(g)+{\text{Y}}_{\text{2}}(g)\to 2\text{XY}(g)$
5. e Given the following information, as well as the information previously presented, predict whether or not the hypothetical ionic compound AX is likely to form. In this compound, A forms the A⁺ cation, and X forms the X⁻ anion. Be sure to justify your answer. Reaction: $\text{A}(g)+\frac{1}{2}{\text{X}}_{\text{2}}(g)\to \text{AX}(s)$The first ionization energy of A(g) is 400 kJ/mol. The electron affinity of X(g) is 525 kJ/mol. The lattice energy of AX(s) is 100 kJ/mol.
6. f If you predicted that no ionic compound would form from the reaction in Part e, what minimum amount of AX(s) lattice energy might lead to compound formation?

Interpretation Introduction

Interpretation:

Explain for the given statement has to be given.

Concept introduction:

Bond enthalpy:

The measure of stability of molecule is bond enthalpy.  The change in enthalpy is related in breaking a specific bond of 1 mole of gaseous molecule.  In solids and liquids bond enthalpies are affected by neighboring molecules.  There is possibility to predict the enthalpy of reaction using the average bond enthalpies.  Energy is always needed for the breaking of chemical bonds and release of energy always takes place with the formation of chemical bonds.   The enthalpy of reaction is estimated by counting the total number of broken bonds and bonds formed in a reaction.

The enthalpy of reaction in gas phase is given by,

${\text{ΔH}}^{\text{o}}\text{=}{\displaystyle \sum {\text{BE}}_{\text{(reactants)}}\text{-}{\displaystyle \sum {\text{BE}}_{\text{(products)}}}}$

Lattice energy:

The amount of energy that is necessary for the conversion of one mole of ionic solid to its constituent ions in gaseous phase is called Lattice energy.

Explanation of Solution

The energy is released when the chemical bond formed, in this process also exothermic

Interpretation Introduction

Interpretation:

Explain for the given statement has to be given.

Concept introduction:

Bond enthalpy:

The measure of stability of molecule is bond enthalpy.  The change in enthalpy is related in breaking a specific bond of 1 mole of gaseous molecule.  In solids and liquids bond enthalpies are affected by neighboring molecules.  There is possibility to predict the enthalpy of reaction using the average bond enthalpies.  Energy is always needed for the breaking of chemical bonds and release of energy always takes place with the formation of chemical bonds.   The enthalpy of reaction is estimated by counting the total number of broken bonds and bonds formed in a reaction.

The enthalpy of reaction in gas phase is given by,

${\text{ΔH}}^{\text{o}}\text{=}{\displaystyle \sum {\text{BE}}_{\text{(reactants)}}\text{-}{\displaystyle \sum {\text{BE}}_{\text{(products)}}}}$

Lattice energy:

The amount of energy that is necessary for the conversion of one mole of ionic solid to its constituent ions in gaseous phase is called Lattice energy.

Explanation of Solution

We want to break a bond how much energy we have to spend that is called bond enthalpy

It is an endothermic process and quantity is positive

Interpretation Introduction

Interpretation:

Explain for the given statement has to be given.

Concept introduction:

Bond enthalpy:

The measure of stability of molecule is bond enthalpy.  The change in enthalpy is related in breaking a specific bond of 1 mole of gaseous molecule.  In solids and liquids bond enthalpies are affected by neighboring molecules.  There is possibility to predict the enthalpy of reaction using the average bond enthalpies.  Energy is always needed for the breaking of chemical bonds and release of energy always takes place with the formation of chemical bonds.   The enthalpy of reaction is estimated by counting the total number of broken bonds and bonds formed in a reaction.

The enthalpy of reaction in gas phase is given by,

${\text{ΔH}}^{\text{o}}\text{=}{\displaystyle \sum {\text{BE}}_{\text{(reactants)}}\text{-}{\displaystyle \sum {\text{BE}}_{\text{(products)}}}}$

Lattice energy:

The amount of energy that is necessary for the conversion of one mole of ionic solid to its constituent ions in gaseous phase is called Lattice energy.

Explanation of Solution

To calculate the Bond enthalpy

${\text{ΔH}}_{\text{rxn}}\cong {\text{BE }}_{\text{(reactant)}}\text{-}{\text{BE }}_{\text{(products)}}\text{=}\text{0}\text{-}\text{BE (X-X)}$

$\text{BE (X-X)}\text{= -}\text{ΔH}{}_{\text{rxn}}\text{ =}\text{- }\text{(}\text{-500kJ/mol)}\text{= 500kJ/mol }$

Interpretation Introduction

Interpretation:

Explain for the given statement has to be given.

Concept introduction:

Bond enthalpy:

The measure of stability of molecule is bond enthalpy.  The change in enthalpy is related in breaking a specific bond of 1 mole of gaseous molecule.  In solids and liquids bond enthalpies are affected by neighboring molecules.  There is possibility to predict the enthalpy of reaction using the average bond enthalpies.  Energy is always needed for the breaking of chemical bonds and release of energy always takes place with the formation of chemical bonds.   The enthalpy of reaction is estimated by counting the total number of broken bonds and bonds formed in a reaction.

The enthalpy of reaction in gas phase is given by,

${\text{ΔH}}^{\text{o}}\text{=}{\displaystyle \sum {\text{BE}}_{\text{(reactants)}}\text{-}{\displaystyle \sum {\text{BE}}_{\text{(products)}}}}$

Lattice energy:

The amount of energy that is necessary for the conversion of one mole of ionic solid to its constituent ions in gaseous phase is called Lattice energy.

Explanation of Solution

To calculate the enthalpy

${\text{ΔH}}_{\text{rxn}}\cong {\text{BE }}_{\text{(reactant)}}\text{-}{\text{BE }}_{\text{(products)}}\text{=}\text{BE (X-X)}\text{+}\text{BE}\text{(Y-Y)}\text{-}\text{2BE}\text{(X-Y)}$

$\cong \text{500}\text{kJ/mol}\text{+}\text{750}\text{kJ/mol-2}\text{(1500}\text{kJ/mol)=-1750}\text{kJ/mol}$

Interpretation Introduction

Interpretation:

Explain for the given statement has to be given.

Concept introduction:

Bond enthalpy:

The measure of stability of molecule is bond enthalpy.  The change in enthalpy is related in breaking a specific bond of 1 mole of gaseous molecule.  In solids and liquids bond enthalpies are affected by neighboring molecules.  There is possibility to predict the enthalpy of reaction using the average bond enthalpies.  Energy is always needed for the breaking of chemical bonds and release of energy always takes place with the formation of chemical bonds.   The enthalpy of reaction is estimated by counting the total number of broken bonds and bonds formed in a reaction.

The enthalpy of reaction in gas phase is given by,

${\text{ΔH}}^{\text{o}}\text{=}{\displaystyle \sum {\text{BE}}_{\text{(reactants)}}\text{-}{\displaystyle \sum {\text{BE}}_{\text{(products)}}}}$

Lattice energy:

The amount of energy that is necessary for the conversion of one mole of ionic solid to its constituent ions in gaseous phase is called Lattice energy.

Explanation of Solution

The Born-Haber cycle to calculate $\text{ΔH}$ for the reaction

$\begin{array}{l}\text{A(g)}\to {\text{A}}_{{}^{\text{(g)}}}^{\text{+}}{\text{+e}}^{\text{-}}{\text{ΔH}}_{\text{1}}{\text{=I}}_{\text{1}}\text{=400}\text{kJ}\\ \frac{\text{1}}{\text{2}}{\text{X}}_{\text{2(g)}}\to {\text{X}}_{\text{(g)}}{\text{ΔH}}_{\text{2}}\text{=}\frac{\text{1}}{\text{2}}\text{BE=}\frac{\text{1}}{\text{2}}\text{(500}\text{kJ)=250}\text{kJ}\\ {\text{X(g)+e}}^{\text{-}}\to {\text{X}}_{\text{(g)}}^{\text{-}}{\text{ΔH}}_{\text{3}}\text{=}\text{EA}\text{=}\text{-525kJ}\\ \underset{\_}{{\text{A}}_{\text{(g)}}^{\text{+}}{\text{+X}}_{\text{(g)}}^{\text{-}}\to {\text{AX}}_{\text{(s)}}{\text{ΔH}}_{\text{4}}\text{=-U=-(100}\text{kJ)=-100kJ}}\\ {\text{A}}_{\text{(g)}}\text{+}\frac{\text{1}}{\text{2}}{\text{X}}_{\text{2(g)}}\to {\text{AX}}_{\text{(s)}}{\text{ΔH}}_{\text{rxn}}\text{=}{\text{ΔH}}_{\text{1}}{\text{+ΔH}}_{\text{2}}{\text{+ΔH}}_{\text{3}}{\text{+ΔH}}_{\text{4}}\end{array}$

The reaction is endothermic

Interpretation Introduction

Interpretation:

Explain for the given statement has to be given.

Concept introduction:

Bond enthalpy:

The measure of stability of molecule is bond enthalpy.  The change in enthalpy is related in breaking a specific bond of 1 mole of gaseous molecule.  In solids and liquids bond enthalpies are affected by neighboring molecules.  There is possibility to predict the enthalpy of reaction using the average bond enthalpies.  Energy is always needed for the breaking of chemical bonds and release of energy always takes place with the formation of chemical bonds.   The enthalpy of reaction is estimated by counting the total number of broken bonds and bonds formed in a reaction.

The enthalpy of reaction in gas phase is given by,

${\text{ΔH}}^{\text{o}}\text{=}{\displaystyle \sum {\text{BE}}_{\text{(reactants)}}\text{-}{\displaystyle \sum {\text{BE}}_{\text{(products)}}}}$

Lattice energy:

The amount of energy that is necessary for the conversion of one mole of ionic solid to its constituent ions in gaseous phase is called Lattice energy.

Explanation of Solution

The formation of AX(s) the reaction were exothermic, hence ${\text{ΔH}}_{\text{rxn}}$ must be negative.  As a result, the lowest amount of ${\text{AX}}_{\text{(s)}}$ lattice energy required would be $\text{100 kJ + 25 kJ = 125 kJ}$.