# Calculating the Enthalpy of Formation

This is part of Year 11 HSC Chemistry course under the topic of Enthalpy and Hess's Law

### HSC Chemistry Syllabus

• Explain the enthalpy changes in a reaction in terms of breaking and reforming bonds, and relate this to:

– The Law of Conservation of Energy

### Calculating the Enthalpy of Formation

This video will discuss ideas relating to the Law of Conservation of Energy, and also demonstrate how the enthalpy of formation can be determined given the bond energy values for various types of bonds which exist within a compound.

### Enthalpy in Chemical Reactions

Contrary to what might seem intuitive, the breaking of chemical bonds is an energy absorbing (endothermic) process, while the formation of bonds is an energy-releasing (exothermic) process. This fundamental concept is key to understanding how chemical reactions store or release energy.

The Law of conservation of energy:

The law of conservation of energy tells us that energy cannot be created nor destroyed, only transformed from one form to another. This principle is crucial in understanding why not all energy absorbed in endothermic reactions leads to an increase in temperature. Instead this energy can be converted into various other forms, either kinetic or potential energy.

### Bond Energy and Enthalpy of Formation

Bond energy is s term which refers to the amount of energy required to break a chemical bond. Take methane (CH_4) as an example. It contains four C-H bonds. With a bond energy of 415.5 kJ mol^{–1} per C-H bond, breaking all bonds in one mole of CH_4 would require 1662 kJ (4 \times 415.5 kJ mol^{–1}).

The enthalpy of formation is the amount of energy that is required to reverse the breaking of bonds. Because it is bond formation, typically the formation of bonds are an inherently exothermic process. If we reused the example of methane CH_4, we know that forming all the C-H bonds is the opposite of the energy required to break all the C-H bonds. The formation of methane's bonds thus releases 1662 kJ which is the same amount that would be required to break them. To represent that this enthalpy change is an exothermic release of energy, we add a negative sign to give a value of –1662  kJ mol^{–1} for the formation of methane's bonds.

The general formula for calculating the standard enthalpy of formation is:

$$\Delta H_{reaction} = \Sigma \Delta H_f(products) – \Sigma \Delta H_f(reactants)$$

### Elemental Substances and Their Enthalpy Values

Elemental forms of substances such as hydrogen, oxygen, nitrogen, chlorine, carbon, copper, and sodium exhibit an enthalpy change of zero. This is an important consideration when calculating the enthalpy changes in reactions involving these elements.

Consider the formation of water (H_2O) from hydrogen gas (H_2) and oxygen gas (O_2). The reaction can be represented as:

$$2H_2(g) + O_2(g) \rightarrow 2H_2O(l)$$

Here the ΔH_f of H_2 and O_2 is considered zero because they are in their elemental forms. The standard enthalpy of formation of liquid water is approximately -285.8 kJ mol^{–1}

Since the above reaction produces 2 moles of H_2O, the enthalpy change for the reaction can be calculated using the standard enthalpies of formation. If we use the formula we previously looked at for calculating the enthalpy of formation.

$$\Delta H_{reaction} = \Sigma \Delta H_f(products) – \Sigma \Delta H_f(reactants)$$

we get:

$$\Delta H_{\text{reaction}} = \left[ (2 \times -285.8 \text{ kJ/mol}) \right] - \left[ 2 \times (0 \text{ kJ/mol}) + 0 \text{ kJ/mol} \right]$$

$$= -571.6 \text{ kJ/mol}$$

### Calculating Reaction Enthalpy Example (answered in video)

Consider a reaction involving the formation of carbon monoxide (CO) and carbon dioxide (CO_2) from elemental forms. If 222 kJ is released in forming 2 moles of CO, then forming the bonds of one mole of CO releases 111 kJ. Subtracting 222 kJ from –564 kJ and dividing by 2 (the stoichiometric ratio), we can find the enthalpy change of CO_2 formation as –393 kJ/mol.

Previous Section: Enthalpy Change (ΔH) in Ionic Compound Dissolution

Next Section: Hess's Law