Bond enthalpy and enthalpy of reaction

Chemical bonds represent potential energy. Quantifying the energy represented by the bonds in different molecules is an important part of understanding the overall energy implications of a reaction. In this article, we'll explore two different concepts that help describe that energy: enthalpy of reaction and bond enthalpy.

During chemical reactions, the bonds between atoms may break, reform or both to either absorb or release energy. The result is a change to the potential energy of the system. The heat absorbed or released from a system under constant pressure is known as enthalpy, and the change in enthalpy that results from a chemical reaction is the enthalpy of reaction. The enthalpy of reaction is often written as $\mathrm{\Delta }{\text{H}}_{\text{rxn}}$‍.

To better understand enthalpy of reaction, let's consider the hydrogenation of propene, ${\text{C}}_3{\text{H}}_6$‍, to form propane, ${\text{C}}_3{\text{H}}_8$‍. In this reaction, propene gas reacts with hydrogen gas, ${\text{H}}_2(g)$‍, to form propane gas:

What is happening in this reaction? First we have to break the carbon $\text{C}=\text{C}$‍ bond and the hydrogen $\text{H}-\text{H}$‍ bond of the reactants. As a rule, breaking bonds between atoms requires adding energy. The stronger the bond, the more energy it takes to break the bond. To make the product propane, a new $\text{C-C}$‍ bond and two new $\text{C-H}$‍ bonds are then formed. Since breaking bonds requires adding energy, the opposite process of forming new bonds always releases energy. The stronger the bond formed, the more energy is released during the bond formation process. In this particular reaction, because the newly formed bonds release more energy than was needed to break the original bonds, the resulting system has a lower potential energy than the reactants. This means the enthalpy of reaction is negative.

Mathematically, we can think of the enthalpy of reaction as the difference between the potential energy from the product bonds and the potential energy of the reactant bonds:

Reactions where the products have a lower potential energy than the reactants, such as the hydrogenation of propene described above, are exothermic. Reactions where the products have a higher potential energy than the reactants are endothermic.

In an exothermic reaction, the released energy doesn't simply disappear. Instead it is converted to kinetic energy, which produces heat. This is observed as an increase in temperature as the reaction progresses. On the other hand, endothermic reactions often require the addition of energy to favor the formation of products. In practice, this often means running a reaction at a higher temperature with a heat source.

In order to quantify the enthalpy of reaction for a given reaction, one approach is to use the standard enthalpies of formation for all of the molecules involved. These values describe the change in enthalpy to form a compound from its constituent elements. Subtracting the standard enthalpies of formation for the reactants from the standard enthalpies of the products approximates the enthalpy of reaction for the system. To learn more about enthalpies of formation (which are also called heats of formation) and how to use them to calculate the enthalpy of reaction, you can check out our video on standard heat of formation and the video on using heats of formation to calculate reaction enthalpies.

An alternative approach is to estimate the enthalpy of reaction by looking at the individual bonds involved. If we know how much energy we need to make and break each of the bonds, then we can add those values to find the enthalpy of reaction. We will discuss this method in more detail in the remainder of this article.

Bond enthalpy (which is also known as bond-dissociation enthalpy, average bond energy, or bond strength) describes the amount of energy stored in a bond between atoms in a molecule. Specifically, it's the energy that needs to be added for the homolytic or symmetrical cleavage of a bond in the gas phase. A homolytic or symmetrical bond breaking event means that when the bond is broken, each atom that originally participated in the bond gets one electron and becomes a radical, as opposed to forming an ion.

Chemical bonds form because they're thermodynamically favorable, and breaking them inevitably requires adding energy. For this reason, bond enthalpy values are always positive, and they usually have units of $\text{kJ/mol}$‍ or $\text{kcal/mol}$‍. The higher the bond enthalpy, the more energy is needed to break the bond and the stronger the bond. To determine how much energy will be released when we form a new bond rather than break it, we simply make the bond enthalpy value negative.

Because bond enthalpy values are so useful, average bond enthalpies for common bond types are readily available in reference tables. While in reality the actual energy change when forming and breaking bonds depends on neighboring atoms in a specific molecule, the average values available in the tables can still be used as an approximation.

Tip: The bond values listed in tables are for a mole of reaction for a single bond. This means that if there are multiples of the same bond breaking or forming in a reaction, you will need to multiply the bond enthalpy in your calculation by how many of that type of bond you have in the reaction. This also means it's important to make sure the equation is balanced and that the coefficients are written as the smallest possible integer values so the correct number of each bond is used.

Once we understand bond enthalpies, we use them to estimate the enthalpy of reaction. To do this, we can use the following procedure:

Krok 1. Identify which bonds in the reactants will break and find their bond enthalpies.

Krok 2. Add up the bond enthalpy values for the broken bonds.

Krok 3. Identify which new bonds form in the products and list their negative bond enthalpies. Remember we have to switch the sign for the bond enthalpy values to find the energy released when the bond forms.

Krok 4. Add up the bond enthalpy values for the formed product bonds.

Krok 5. Combine the total values for breaking bonds (from Krok 2) and forming bonds (from Krok 4) to get the enthalpy of reaction.

Let's find the enthalpy of reaction for the hydrogenation of propene, our example from the beginning of the article.

This reaction breaks one $\text{C}=\text{C}$‍ bond and one $\text{H}-\text{H}$‍ bond.

Using a reference table, we find that the bond enthalpy of a $\text{C}=\text{C}$‍ bond is $610\text{kJ/mol}$‍, while the bond enthalpy of a $\text{H}-\text{H}$‍ bond is $436\text{kJ/mol}$‍.

Combining the values from Krok 1 gives us:

as the total energy required to break the necessary bonds in propene and hydrogen gas.

This reaction forms one new $\text{C}-\text{C}$‍ bond and two new $\text{C}-\text{H}$‍ bonds.

Using a reference table, we find that the bond enthalpy of a $\text{C}-\text{C}$‍ bond is $346\text{kJ/mol}$‍, while the bond enthalpy of a $\text{C}-\text{H}$‍ bond is $413\text{kJ/mol}$‍. To find how much energy is released when these bonds are formed, we'll need to multiply each bond enthalpy by $-1$‍. Also, since two new $\text{C}-\text{H}$‍ bonds are formed, we'll need to multiply the $\text{C}-\text{H}$‍ bond enthalpy by $2$‍.

Combining the values from Krok 3 gives us:

for the total energy that will be released by forming the new bonds.

From Krok 2 and Krok 4, we have $1046\text{kJ}$‍ of energy required to break bonds and $-1172\text{kJ}$‍ of energy released from forming bonds. Combining these values, we get for the enthalpy of reaction:

Since the enthalpy of reaction for the hydrogenation of propene is negative, we know that the reaction is exothermic.

Bond enthalpy and enthalpy of reaction help us understand how a chemical system uses energy during reactions. The bond enthalpy describes how much energy is needed to break or form a bond, and it is also a measure of bond strength. By combining the bond enthalpy values for all of the bonds broken and formed during a reaction, it's possible to estimate the total change in potential energy of the system, which is $\mathrm{\Delta }{\text{H}}_{\text{rxn}}$‍ for a reaction at constant pressure. Depending on whether the enthalpy of reaction is positive or negative, we can determine whether a reaction will be endothermic or exothermic.