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
-
Investigate Hess’s Law in quantifying the enthalpy change for a stepped reaction using standard enthalpy change data and bond energy data, for example:
– Carbon reacting with oxygen to form carbon dioxide via carbon monoxide
- Apply Hess’s Law to simple energy cycles and solve problems to quantify enthalpy changes within reactions, including but not limited to:
– Enthalpy changes involved in photosynthesis
– Enthalpy changes involved in respiration
Hess's Law Explained
This video will introduce Hess's Law and explore how the principles of Hess's Law apply to help determine the enthalpy change of particular reactions.
Enthalpy Change Formula
The formula for enthalpy change can be given by
$$\Delta H = \Sigma \Delta H_f^{\circ} \text{(products)} – \Sigma \Delta H_f^{\circ} \text{(reactants)} $$
where:
$$\text{Bonds of reactants that are broken = } –\Sigma \Delta H_f^{\circ} \text{(reactants)}$$
$$\text{Bonds of products that are formed = } \Sigma \Delta H_f^{\circ} \text{(products)}$$
`\Delta H` is largely equal to the difference in energy absorbed when breaking bonds (endothermic) and energy released when forming bonds (exothermic).
There are relatively small contributions to `Delta H` from energy changes involved in other processes in a chemical reaction such as state changes. This is discussed in more detail here. For the sake of simplicity, we will assume these energy changes are negligible when explaining Hess's law.
Hess's Law
The diagram above demonstrates the concept of Hess's Law
“The total enthalpy change of a chemical reaction is the same, regardless of the pathway taken provided the initial and final conditions are the same”
It can also be summarised by the following diagram
The importance of Hess's Law stems from its use in calculating enthalpy change values where direct measurement is difficult.
In the previous example demonstrated by the diagram, the enthalpy of formation for carbon monoxide (`\Delta H_f = -110 \text{ kJ}`) is difficult to measure directly because the combustion of carbon often produces both carbon monoxide and carbon dioxide. However by using Hess's Law, the enthalpy of formation of carbon monoxide can be calculated by calculating the difference between the enthalpy of formation of carbon dioxide (`\Delta H_f = -395 \text{ kJ}`) and combustion of carbon monoxide (`\Delta H = -285 \text{ kJ}`).
Hess's Law also demonstrates how chemical reactions abide by the Law of Conservation of Energy.
Hess's Law Formula
Hess's law demonstrates that enthalpy change is independent of the reaction pathway.
Using Hess's Law the formula for `\Delta H` can be derived to be
$$\Delta H _\text{overall} = \Delta H_1 + \Delta H_2 + \Delta H_3 + ...$$
Although `\Delta H` remains unchanged, the overall activation energy would theoretically be higher if reactants are converted to products via multiple reactions compared to a single reaction.
Consider the following diagram:
-
Two-Step Reaction to Form `CO_2`
The blue arrows represent the formation of `CO_2` in a two-step process – first producing `CO` by oxidising carbon, then oxidising `CO` to form `CO_2`.
-
Direct Combustion
The black arrow shows the direct combustion of carbon to create `CO_2`
Note: The enthalpy change values of both pathways are identical as they produce the same product from the same starting reactants.
Applying Hess's Law: Practical Examples
Heat of Combustion
Combustion is exohermic, indicating that more energy is released than absorbed. We can consider the combustion of an alcohol to illustrate this. When an alcohol has been combusted, energy was first absorbed to break C-C and C-H bonds, then energy was released to form C=O double bonds and O-H bonds. The formation particularly of the C=O double bond leads to a relatively large amount of energy in comparison to the energy used to break the C-C and C-H bonds. This is discussed in greater detail here.
Respiration and Photosynthesis
These are two complex biological processes to which enthalpy change and Hess's law also apply. Both processes involve multiple chemical reactions and thus the overall enthalpy change is difficult to measure directly. Hess's law can be used to determine the `\Delta H` value. This is discussed in greater detail here.
Calculation Examples of Hess's Law
Example 1
Enthalpy changes of the following reactions are shown.
$$C(s) + \frac{1}{2}O_2(g) \rightarrow CO(g) \hspace{1cm} \Delta H = -111 \text{ kJ/mol}$$
$$CO(g) + \frac{1}{2}O_2(g) \rightarrow CO_2(g) \hspace{1cm} \Delta H = -282 \text{ kJ/mol}$$
Calculate the enthalpy of formation value for carbon dioxide.
Example 2
Enthalpy changes of the following reactions are shown.
$$SO_2(g) \rightarrow S(s) + O_2(g) \hspace{1cm} \Delta H = 297 \text{ kJ}$$
$$2SO_2(g) + O_2(g) \rightarrow 2SO_3(g) \hspace{1cm} \Delta H = -198 \text{ kJ}$$
Calculate the enthalpy of formation value for sulfur trioxide.
Example 3
Enthalpy changes of the following reactions are shown.
$$O_2 \rightarrow 2O \hspace{1cm} \Delta H = 495 \text{ kJ}$$
$$2O_3 \rightarrow 3O_2 \hspace{1cm} \Delta H = -427 \text{ kJ}$$
$$NO + O_3 \rightarrow NO_2 + O_2 \hspace{1cm} \Delta H = -199 \text{ kJ}$$
Calculate the enthalpy change of the following reaction:
$$NO + O \rightarrow NO_2$$
Example 4
Enthalpy changes of the following reactions are shown.
$$CO(g) + \frac{1}{2}O_2(g) \rightarrow CO_2(g) \hspace{1cm} \Delta H = -283 \text{ kJ}$$
$$N_2(g) + O_2(g) \rightarrow 2NO_2(g) \hspace{1cm} \Delta H = 181 \text{ kJ}$$
Calculate the enthalpy change for the following reaction:
$$CO(g) + NO(g) \rightarrow CO_2(g) + \frac{1}{2}N_2(g)$$
Previous Section: Calculating the Enthalpy of Formation
Next Section: Entropy and Gibbs Free Energy ( ΔG)