Question

Part A

Calculate the bond energy per mole for breaking all the bonds in methane, CH4.

Express your answer to four significant figures and include the appropriate units.

ΔHCH4 =

1656 kJmol

Correct

In CH4, the energy required to break one C−H bond is 414 kJ/mol. Since there are four C−H bonds in CH4, the energy ΔHCH4 for breaking all the bonds is calculated as

ΔHCH4	=	4×bond energy of C−H bond
	=	4×414 kJ/mol
	=	1656 kJ/mol CH4 molecules

Part B

Calculate the bond energy per mole for breaking all the bonds of oxygen, O2?

Express your answer to three significant figures and include the appropriate units.

ΔHO2 =

498 kJmol

Correct

There is only one O=O bond in an O2 molecule, so the energy ΔHO2 required for breaking all the bonds in a mole of O2 molecules is 498 kJ/mol O2 molecules.

Part C

Calculate the bond energy per mole for forming all the bonds of water molecules, H2O.

Express your answer to three significant figures and include the appropriate units.

ΔHH2O =

-928 kJmol

Correct

In H2O, the energy required for the formation of one O−H bond is 464 kJ/mol. Since there are two O−H bonds in H2O, the energy ΔHH2O for forming all the bonds is calculated as

ΔHH2O	=	−2×bond energy of O−H bond
	=	−2×464 kJ/mol
	=	−928 kJ/mol H2O molecules

Part D

Calculate the bond energy per mole for forming all the bonds of carbon dioxide, CO2.

Express your answer to four significant figures and include the appropriate units.

ΔHCO2 =

-1598 kJmol

Correct

In CO2, the energy required for the formation one C=O bond is 799 kJ/mol. Since there are two C=O bonds in CO2, the energy for forming all the bonds is calculated as

ΔHCO2	=	−2×bond energy of  C=O bond
	=	−2×799 kJ/mol
	=	−1598 kJ/mol CO2 molecules

Part E

Calculate the approximate enthalpy change, ΔHrxn, for the combustion of one mole of methane a shown in the balanced chemical equation:

CH4+2O2→2H2O+CO2

Use the values you calculated in Parts A, B, C, and D, keeping in mind the stoichiometric coefficients.

Express your answer to three significant figures and include the appropriate units.

ΔHrxn = _______ 

Answer 1

Concepts and reason

Calculate the bond energy per mole for breaking and forming the bonds of following molecules using the energy values.

Fundamentals

Atom and molecules possess some amount of energies, but when they are suitably bonded they releases energy and acquires low energy.

Bond energy is the measure of the bond strength, it is defined as the average gas-phase bond dissociation energy for all identical bonds at 298 kelvin temperature.

Energy is released when bonds are formed, and energy is absorbed when the bonds break.

Heat of the reaction is the energy change that took place when the reactants changes to products.

A

Each ${\rm{C}} - {\rm{H}}$ bond requires 414 kJ/mol of energy to dissociate it from the compound.

Therefore, the bond energy of methane is calculated as follows:

$\begin{array}{c}\\\Delta {{\rm{H}}_{{\rm{C}}{{\rm{H}}_{\rm{4}}}}} = {\rm{4}} \times {\rm{414}}\,{\rm{kJ/mol}}\\\\{\rm{ = 1656}}\,{\rm{kJ/mol}}\\\end{array}$

B

Each ${\rm{O = O}}$ bond requires 498 kJ/mol of energy to dissociate.

Therefore, bond dissociation energy is calculated as follows:

$\begin{array}{c}\\\Delta {{\rm{H}}_{{{\rm{O}}_2}}} = \Delta {{\rm{H}}_{{\rm{O = O}}}}\\\\{\rm{ = }}\;{\rm{498}}\,{\rm{kJ/mol}}\\\end{array}$

C

Each ${\rm{H}} - {\rm{O}}$ bond requires 464 kJ/mol of energy.

Therefore, bond dissociation energy of water molecule is calculated as follows:

$\begin{array}{c}\\\Delta {{\rm{H}}_{{{\rm{H}}_2}{\rm{O}}}} = - 2 \times \Delta {{\rm{H}}_{{\rm{H}} - {\rm{O}}}}\\\\{\rm{ = }}\; - {\rm{2}} \times {\rm{464}}\,{\rm{kJ/mol}}\\\\{\rm{ = }} - \;{\rm{928}}\,{\rm{kJ/mol}}\\\end{array}$

D

Each ${\rm{C}} - {\rm{O}}$ bond requires 799 kJ/mol of energy to dissociate.

Therefore, bond dissociation energy of ${\rm{C}}{{\rm{O}}_2}$ molecule is calculated as follows:

$\begin{array}{c}\\\Delta {{\rm{H}}_{{\rm{C}}{{\rm{O}}_2}}} = - 2 \times \Delta {{\rm{H}}_{{\rm{C}} - {\rm{O}}}}\\\\{\rm{ = }} - {\rm{2}} \times {\rm{799}}\,{\rm{kJ/mol}}\\\\{\rm{ = }} - {\rm{1598}}\,{\rm{kJ/mol}}\\\end{array}$

E

Consider the reaction as follows:

${\rm{C}}{{\rm{H}}_{\rm{4}}} + {\rm{2}}{{\rm{O}}_{\rm{2}}} \to {\rm{2}}{{\rm{H}}_{\rm{2}}}{\rm{O}} + {\rm{C}}{{\rm{O}}_{\rm{2}}}$

Heat change of the reaction is calculated as follows:

$\Delta {\rm{H}}_{{\rm{rxn}}}^{\rm{o}} = \Delta {\rm{H}}^\circ \left( {{\rm{bonds}}\;{\rm{broken}}} \right) + \Delta {\rm{H}}^\circ \left( {{\rm{bonds}}\;{\rm{formed}}} \right)$

Substitute the values in the above equation as follows:

$\begin{array}{c}\\\Delta {\rm{H}}_{{\rm{rxn}}}^{\rm{o}} = \Delta {\rm{H}}^\circ \left( {{\rm{bonds}}\;{\rm{broken}}} \right) + \Delta {\rm{H}}^\circ \left( {{\rm{bonds}}\;{\rm{formed}}} \right)\\\\ = \left( {\Delta {\rm{H}}_{{\rm{C}}{{\rm{H}}_4}}^{\rm{o}} + 2\Delta {\rm{H}}_{{{\rm{O}}_{\rm{2}}}}^{\rm{o}}} \right) + \left( {\Delta {\rm{H}}_{{\rm{C}}{{\rm{O}}_{\rm{2}}}}^{\rm{o}} + 2\Delta {\rm{H}}_{{{\rm{H}}_{\rm{2}}}{\rm{O}}}^{\rm{o}}} \right)\\\\ = \;\left( {1656\;{\rm{kJ/mol}} + 2 \times 498\;{\rm{kJ/mol}}} \right) + \left( { - 1598\;{\rm{kJ/mol}} + 2\left( { - 928\;{\rm{kJ/mol}}} \right)} \right)\\\\ = - 802\,\,{\rm{kJmo}}{{\rm{l}}^{ - 1}}\\\end{array}$

[Part E]

Part E

Ans: Part A

The energy required to break all bonds in a methane (${\rm{C}}{{\rm{H}}_{\rm{4}}}$) is .

Part B

The energy required to break all bonds in an oxygen molecule is .

Part C

The energy required to form all bonds in a water molecule is .

Part D

The energy required to form all bonds in carbon dioxide is .

Part E

The change in enthalpy of the reaction is .