# Bond enthalpy

### Bond enthalpy

#### Lessons

In this lesson, we will learn:

• To understand what is meant by mean bond enthalpy.
• To use mean bond enthalpy as a method to calculate the enthalpy change of a reaction.
• To understand the limitation of using it to find reaction enthalpies precisely.

Notes:

• When a chemical reaction occurs, what is actually happening to the reactants?

• Heat energy gets put in to break bonds in the reactants.
• Heat energy is released when products form by new bonds being created.

In short, bond enthalpy finds the enthalpy change of a reaction by:

• Finding the energy needed to break all the reactant bonds that need breaking. This is the endothermic part of the reaction.
• Finding the energy released from all the product bonds that get made. This is the exothermic part of the reaction.

…and finding the difference between them!

• If the energy needed is greater than the energy released, it is an overall endothermic reaction.
• If the energy released is greater than the energy needed, it is an overall exothermic reaction.

• Mean bond enthalpy is the energy required to break one mole of a chemical bond in the gas phase, taken as an average across different compounds.
Because the definition is about breaking chemical bonds, which always requires energy, mean bond enthalpy is ALWAYS a positive value.
As well as the mean bond enthalpy, you will need to know (or be told) the structure of the reactants and products; you need to know what bonds are being broken and made!

With mean bond enthalpy values, you can find the enthalpy change of a reaction with the following equation:

$\triangle H$r = $\sum$H(bonds broken) - $\sum$H(bonds formed)

Like using Hess’s law, this calculation lets you make a conclusion based on the sign of your value.
• A negative enthalpy change shows an exothermic reaction, as the chemical substances gave out more energy than they absorbed.
• A positive enthalpy change shows an endothermic reaction, as the chemical substances absorbed more energy than they gave out.

• WORKED EXAMPLE:
The reaction of ethene with hydrogen to produce ethane is described by the equation below:

C2H4 (g) + H2 (g) $\,$$\,$ C2H6 (g)

The mean bond enthalpy data1 for the bonds in these compounds are as follows:
C-C: 348 kj mol-1; C=C: 612 kJ mol-1; C-H: 412 kJ mol-1; H-H: 436 kJ mol-1;

Use this data to find the enthalpy change of the reaction, $\triangle H$r.

We first need to look at the structure of the molecules and see what bonds are in the reactants and products. See the image below:

Draw out the structure of the molecules involved so you can see what bonds are being broken and made. Sum the bond enthalpies in two categories: ‘bonds broken’ and ‘bonds made’, remembering to multiply by the number of bonds there.
 Bond type: Bonds broken Bonds formed C-C 0 348 * 1 C=C 612 * 1 0 C-H 412 * 4 412 * 6 H-H 436 * 1 0 TOTAL: 2696 kJ mol-1 2820 kJ mol-1

Then apply the equation:

$\triangle H$r = $\sum$H(bonds broken) - $\sum$H(bonds formed)

Which gives us the calculation:

$\triangle H$r = 2696 - 2820 = -124 kJ mol-1

• Using bond enthalpy to find the enthalpy change of reaction is not always very precise. This is because for any type of bond, its precise strength depends on its surroundings.
• For example, ammonia, NH3, has three identical N-H bonds. You would expect this to mean all three bonds need the same amount of energy to be broken, but as the molecule breaks up its stability is going to change, affecting the remaining N-H bonds and their strength. The three N-H bonds will not all require the exact same energy to be overcome.
• In the same way, with a different electronic environment the N-H bonds in NH3 (ammonia) will have slightly different strength than the lone N-H bond in (CH3)2NH (dimethylamine).
This is why bond enthalpy is normally quoted as mean bond enthalpy. Because the specific type of bond will vary in strength across different compounds, we just take an average.

1 Source for mean bond enthalpy data: ATKINS, P. W., & DE PAULA, J. (2006). Atkins' Physical chemistry. Oxford, Oxford University Press.
• Introduction
Another method of calculating enthalpy: Bond enthalpy.
a)
Bond enthalpy: introduction.

b)
How to use bond enthalpy to find enthalpy change.

c)
Example: Using bond enthalpy to find enthalpy change.

• 1.
Use the mean bond enthalpy values to find the enthalpy change in chemical reactions.
The combustion of propane to make carbon dioxide and water vapour is described in this equation:

C3H8 (g) + O2 (g) $\,$$\,$ CO2 (g) + H2O (g)

The table below shows relevant bond enthalpy data:
 Bond: Mean bond enthalpy1 (kJ mol-1) C-C 348 C-H 412 O=O 497 C=O 743 O-H 463

Balance the equation and find the enthalpy change of the reaction.

• 2.
Calculate the mean bond enthalpy from enthalpy of reaction data.
The combustion reaction of butene is described below, with the enthalpy of reaction provided:

C4H8 (g) + 6O2 (g) $\,$$\,$ 4CO2 (g) + 4H2O $\qquad$ $\triangle H$r = -2062 kJ mol-1

 Bond: Mean bond enthalpy1 (kJ mol-1) C-C 348 C-H 412 O=O 497 C=O x O-H 463

Use this information and the data to find the mean bond enthalpy of the C=O bond.