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# Bond Enthalpy

## Introduction: What is Bond Enthalpy?

Bond Enthalpy, also known as bond energy, is a quantity that offers insight into the strength of a chemical bond and, by extension, its stability. The bond enthalpy of a chemical bond can be defined as the total amount of energy required to break 1 mole of that chemical bond. For example, the bond enthalpy of the oxygen-hydrogen single bond is equal to 463 kJ/mol. This implies that a total of 463 kilojoules of energy is required to break 1 mole of hydrogen-oxygen single bonds.

It is important to note that the breaking of a chemical bond is always an endothermic process (because energy must be supplied to the molecule in order to break the chemical bonds that constitute it). Thus, the enthalpy change associated with the breaking of a chemical bond is always positive (ΔH > 0). On the other hand, the formation of a chemical bond is almost always an endothermic process. In such cases, the enthalpy change will have a negative value (ΔH < 0).

To express the strength of a single, specific bond in a molecule, the quantity ‘mean bond enthalpy’ or ‘average bond enthalpy’ can be used. The mean bond energy of a chemical bond (in a molecule) can be determined by calculating the average value of all the bond dissociation energies of that type of bond in the molecule. Thus, mean bond enthalpy is different from bond dissociation energy (except for diatomic molecules).

It can also be noted that some definitions specifically define bond enthalpy as the amount of energy required to break one mole of a chemical bond at 298K at gas phase. The higher the value, the stronger the bond and high energy required to break the bond. An illustration detailing how the chemical bond between atoms A & B is broken when energy equal to the bond enthalpy is supplied to molecule AB is provided below.

Example Bond dissociation energy required to break 1 mole of gaseous hydrogen chloride molecule to gaseous hydrogen and chlorine atom requires 432kJ, bond dissociation enthalpy of gaseous HCl is +432kJ per mol.

If a molecule has several bonds, bond enthalpy is calculated for each bond and the average value has been considered. For example, methane (CH4) has four C-H bonds, and average bond energy is +1652 kJ and +415.5kJ per mole of the bond.

Note: Bond enthalpy can be calculated directly if everything your working is in a gaseous state. If it is in the liquid state need extra energy to convert it from liquid state to gaseous state

## Average Bond Enthalpies

Bond enthalpy to estimate the enthalpy of the reaction

Consider an example of hydrogenation of propene which has the following steps.

• Breaking of carbon-carbon double bond and H-H bond

Using reference table bond enthalpy of C double bond C is 610kJ/mol, while H-H bond is 436kJ/mol

• Calculate the energy required to break C-C double bond and H-H bond and addition of this gives the total amount of energy required to break the desired bonds in propene and hydrogen gas that is 1046kJ/mol(610kJ/mol+ 436 Kj/mol= 1046 kJ/mol)
• The reaction gives the new molecule forming one C-C bond and two C-H bonds

In order to understand how much energy is released during the process, calculate the bond enthalpy of C-C bond and multiply by -1 and bond enthalpy of C-H bond by 2, combining the bond enthalpy gives the amount of energy released during the process.

Energy released to make product bond = -346kJ/mol + (2* -413kJ/mol) = -1172kJ/mol

• From the energy of the above step required to break the bond and energy released in the formation of new bonds gives the change in enthalpy during the reaction.

= Energy required to break the bond + Energy released in the formation of new bond

= 1046 kJ/mol+ (-1172/ kJ/mol)

= -126 kJ/mol

## Endothermic and Exothermic Process

During the reaction energy is absorbed to break the bond which is called endothermic process and energy is released to form a new bond is called exothermic process. The two processes can be explained in the energy diagram as follows

• In exothermic reactions reactants are in higher energy than products and energy difference between them is called change in enthalpy of the reaction (∆H) is always negative
• In endothermic reactions products are in higher energy than reactants and energy difference((∆H) between them is always positive.

### Summary

• Bond enthalpy describes how much energy is required to break or form the bond.
• Combined bond enthalpy for all broken and formed bonds during the process gives the idea about a total change in the energy of the system which is called change in enthalpy.
• Depending on whether the change in enthalpy is positive or negative, can determine whether the reaction is endothermic or exothermic.

## Solved Examples

Calculate the Change in enthalpy of the following reactions

1. $$\begin{array}{l}CH_{4}+Cl_{2}\rightarrow CHCl_{3}+HCl\end{array}$$
(Exothermic reactions)

Solution:

Energy is required to break or make one mole of particular bond in kJ/mol

C-H = 412kJ/mol, Cl-Cl = 242kJ/mol, C-Cl = 331kJ/mol, H-Cl = 432kJ/mol

Step 1:

Total energy required to break one C-H and Cl-Cl bond is

412kJ/mol +241kJ/mol = 654kJ/mol

Step 2:

Energy released during the formation of new C-Cl and H-Cl bond is

331kJ/mol + 432kJ/mol = 763kJ/mol

Step 3:

Energy change = Energy absorbed while breaking the bond – Energy released while forming the bond

Energy change = 654kJ/mol – 763kJ/mol

= -109kJ/mol

1. HBr(g) ==> H2(g) + Br2(g)( Endothermic reactions)

Solution:

Energy is required to break or make one mole of particular bond in kJ/mol

H–Br = 366kJ/mol, H–H = 436kJ/mol, Br–Br = 193kJ/mol

Step 1:

Energy need to break the bonds = 366kJ/mol +366kJ/mol = 732kJ/mol

Step 2:

Energy released on bond formation = 436kJ/mol + 193kJ/mol = 629kJ/mol

Step 3:

Change in enthalpy = 366kJ/mol – 629kJ/mol = +103kJ/mol

1. methane + oxygen ==> carbon dioxide + water(Exothermic process)

CH4(g) + 2O2(g) ==> CO2(g) + 2H2O(g)

Bond energies in kJ/mol

C-H single bond = 412 kJ/mol, O=O double bond = 496 kJ/mol, C=O double bond = 803kJ/mol, H-O single bond = 463 kJ/mol

Solution

Step 1:

Energy required to break the bonds = 4*(C-H) + 2*(1* O=O)

= (4*412) + (2*496)

= 1648 + 992

= 2640kJ/mol

Step 2:

Energy released while forming bonds = (2*C=O) + 2*(2*O-H)

= (2*208) + 2*(2*463)

= 1606 + 1852

= 3458 kJ/mol

Step 3:

Change in enthalpy = Step 1 – step 2

= 2640kJ/mol – 3458 kJ/mol

= -818 kJ/mol

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