Why the Enthalpy Change of Formation of Water is the Same as the Enthalpy Change of Combustion of Hydrogen

The relationship between the enthalpy change of formation and the enthalpy change of combustion of hydrogen is a fundamental concept in chemical thermodynamics. To understand this relationship, we need to carefully define and analyze the reactions involved.

Definition and Reactions

The enthalpy change of formation of a substance is defined as the enthalpy change when one mole of the substance is formed from its elements in their standard states. Similarly, the enthalpy change of combustion is the enthalpy change accompanying the complete combustion of one mole of the substance in the standard state. Let's explore these definitions and the specific reactions for water and hydrogen.

Formation of Water from Elements

The reaction of hydrogen gas with oxygen gas to form water can be written as:

H_{2}(g) frac{1}{2}O_{2}(g) rightarrow H_{2}O(l)

Here, the enthalpy change (ΔH) represents the enthalpy change when one mole of hydrogen reacts stoichiometrically with oxygen to form one mole of liquid water. This reaction defines the enthalpy change of formation of water.

Combustion of Hydrogen

The complete combustion of hydrogen involves the reaction of hydrogen gas with oxygen gas to form water:

H_{2}(g) frac{1}{2}O_{2}(g) rightarrow H_{2}O(l)

In this case, the enthalpy change (ΔH) represents the enthalpy change when one mole of hydrogen is combusted in the presence of oxygen to form one mole of liquid water. This defines the enthalpy change of combustion of hydrogen.

Comparison of Reaction Types

To compare the enthalpy changes, we need to understand the definitions of the two reaction types:

Formation Reaction: This is the reaction that produces one mole of a product from its elements in their standard states. For water, this is:

H_{2}(g) frac{1}{2}O_{2}(g) rightarrow H_{2}O(l)

Combustion Reaction: This is the complete combustion of one mole of the substance in the standard state. For hydrogen, this is:

H_{2}(g) frac{1}{2}O_{2}(g) rightarrow H_{2}O(l)

From these definitions, we can see that the reaction for both the formation of water and the combustion of hydrogen is the same. Therefore, the enthalpy change of the formation of water is the same as the enthalpy change of the combustion of hydrogen.

Thermochemical Equations

To further clarify this relationship, let's consider the following thermochemical equations:

Formation of Water:

H_{2}(g) frac{1}{2}O_{2}(g) rightarrow H_{2}O(l) quad Delta H -286 , text{kJ/mol}

Combustion of Hydrogen:

H_{2}(g) frac{1}{2}O_{2}(g) rightarrow H_{2}O(l) quad Delta H -286 , text{kJ/mol}

Both equations represent the same reaction, and the enthalpy change for each is -286 kJ/mol. This demonstrates that the enthalpy change of formation of water and the enthalpy change of combustion of hydrogen are indeed identical.

Conclusion

In conclusion, the reaction for the formation of water from its elements and the reaction for the combustion of hydrogen to form water are identical. As a result, the enthalpy change of formation of water is the same as the enthalpy change of combustion of hydrogen. This relationship is a key concept in chemical thermodynamics and highlights the importance of standard states in defining these thermodynamic properties.

Understanding this relationship is crucial for students and professionals in chemistry and related fields. By grasping the principles behind these reactions, one can better comprehend the fundamental aspects of thermodynamics and chemical reactions.