Question

The standard enthalpy change for the following reaction is \(436.4 \mathrm{~kJ} / \mathrm{mol}\) : $$\mathrm{H}_{2}(g) \longrightarrow \mathrm{H}(g)+\mathrm{H}(g)$$ Calculate the standard enthalpy of formation of atomic hydrogen (H).

Short answer

The standard enthalpy of formation of atomic hydrogen is \(218.2 \, \mathrm{kJ/mol}\).

Step-by-step solution

Understand the Problem

The problem requires us to find the standard enthalpy of formation of atomic hydrogen from the given standard enthalpy change of the reaction: \(\mathrm{H}_{2}(g) \longrightarrow \mathrm{H}(g)+\mathrm{H}(g)\). This means we need to determine how much energy is required to form atomic hydrogen from diatomic hydrogen gas.

Interpret the Given Reaction

The reaction \(\mathrm{H}_{2}(g) \longrightarrow \mathrm{H}(g)+\mathrm{H}(g)\) represents the dissociation of one mole of diatomic hydrogen into two moles of atomic hydrogen. The provided standard enthalpy change of the reaction is \(436.4\, \mathrm{kJ/mol}\). This is the energy required to break the bond in \(1\, \text{mole}\) of \(\mathrm{H}_2\) to form \(2\, \text{moles}\) of atomic \(\mathrm{H}\).

Define Enthalpy of Formation

The standard enthalpy of formation for a substance is the energy change when one mole of a substance is formed from its elements in their standard states. We want to find the enthalpy change to form 1 mole of atomic hydrogen \(\mathrm{H}(g)\) from its standard state, which is \(\mathrm{H}_{2}(g)\).

Calculate the Enthalpy of Formation for Atomic Hydrogen

Since the enthalpy change given is for \(1\, \text{mole}\) of \(\mathrm{H}_2\) forming \(2\, \text{moles}\) of \(\mathrm{H}(g)\), the enthalpy of formation for one mole of atomic \(\mathrm{H}(g)\), is half of this value. Therefore, the enthalpy of formation of \(\mathrm{H}(g)\) is:\[\Delta H_f^{\circ}(\mathrm{H}) = \frac{436.4\, \mathrm{kJ/mol}}{2} = 218.2\, \mathrm{kJ/mol}.\]

Verify Calculation

Review the calculations to ensure they align with the definition and setup provided. One mole of \(\mathrm{H}_2\) creates two moles of \(\mathrm{H}(g)\), so dividing the enthalpy change equally is consistent with the problem statement.

Key concepts

Standard Enthalpy Change

The standard enthalpy change refers to the heat exchange that accompanies a chemical reaction conducted under standard conditions. These conditions typically include a temperature of 298 K and a pressure of 1 atm. In the context of the given exercise, the standard enthalpy change of 436.4 kJ/mol corresponds to the dissociation of molecular hydrogen (\(\mathrm{H}_2\)) into atomic hydrogen (\(\mathrm{H}\)).

• Standard conditions ensure that results are comparable and consistent across different experiments.
• The symbol for standard enthalpy change is often \(\Delta H^\circ\), where the degree symbol represents the standard states of the reactants and products.

Understanding this concept helps clarify why we use the given values and how they relate to real-world chemical processes.

Dissociation Energy

Dissociation energy is the amount of energy required to break a chemical bond in a molecule and separate its atoms. Specifically, in our problem, it refers to the energy needed to break the bond between two hydrogen atoms in a diatomic hydrogen molecule (\(\mathrm{H}_2\)) to form two individual hydrogen atoms (\(\mathrm{H}(g)\)).

• This energy is vital in reactions because it dictates how much energy is needed to initiate a reaction.
• The dissociation energy of a bond influences the stability of the molecule; stronger bonds require more energy to break.

Therefore, the value of 436.4 kJ/mol signifies the energy required for this specific bond dissociation.

Atomic Hydrogen

Atomic hydrogen is a single hydrogen atom in the gaseous state, denoted as (\(\mathrm{H}(g)\)). It is highly reactive and tends to form bonds with other atoms, converting back to its more stable diatomic form (\(\mathrm{H}_2\)).

• Atomic hydrogen is essential in various industrial processes, including welding and the Haber process for ammonia production.
• Its reactivity arises from its unpaired electron, which makes it eager to bond with other atoms to achieve stability.

In the enthalpy of formation exercise, understanding atomic hydrogen's nature helps explain why energy is involved in breaking down molecular hydrogen.

Molecular Hydrogen

Molecular hydrogen, represented as \(\mathrm{H}_2\), is the simplest known molecule and consists of two hydrogen atoms bonded together. It is the most abundant form of hydrogen due to its stability compared to atomic hydrogen.

• It naturally occurs in the atmosphere and is a critical component in numerous chemical reactions.
• The bond between the two hydrogen atoms in \(\mathrm{H}_2\) is strong, which explains why it requires significant energy to dissociate into atomic hydrogen.

Understanding this molecule's properties is crucial in determining the energy requirements in chemical processes like the one depicted in the exercise.