Reactivity 1.2.3 – Standard Enthalpy Changes of Combustion and Formation

What Are Standard Enthalpy Changes?

Standard enthalpy changes represent the heat energy change that occurs during a chemical process under specific, defined conditions. These are:

• Pressure: 100 kPa (1 atmosphere)
• Temperature: 298 K (25 °C)
• Concentration: 1 mol dm⁻³ for all solutions
• All substances must be in their standard states (most stable physical form at 298 K and 100 kPa)

The standard enthalpy change is represented with the symbol \( \Delta H^\circ \), where the superscript \( \circ \) indicates standard conditions.

1. Standard Enthalpy Change of Combustion (\( \Delta H_c^\circ \))

This is defined as the enthalpy change when one mole of a substance undergoes complete combustion in excess oxygen under standard conditions.

\( \Delta H_c^\circ = \text{Enthalpy change when 1 mol of substance is completely burned in O}_2 \)

Key Features:

• The products of combustion are typically CO₂(g) and H₂O(l).
• Combustion reactions are always exothermic, so the enthalpy values are negative.
• The enthalpy change depends on the amount of substance combusted (always 1 mol for standard definition).

Example:

\( \text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(l), \quad \Delta H_c^\circ = -890 \, \text{kJ/mol} \)

Here, -890 kJ of heat is released when 1 mole of methane undergoes complete combustion.

2. Standard Enthalpy Change of Formation (\( \Delta H_f^\circ \))

This is defined as the enthalpy change when 1 mole of a compound is formed from its elements in their standard states under standard conditions.

\( \Delta H_f^\circ = \text{Enthalpy change for forming 1 mol of compound from its elements in standard states} \)

Key Features:

• The equation must produce exactly 1 mole of the compound as the product.
• All reactants must be elements in their standard states.
• The sign of \( \Delta H_f^\circ \) may be positive (endothermic) or negative (exothermic), depending on the compound formed.

Example:

\( \text{C}(s) + 2\text{H}_2(g) \rightarrow \text{CH}_4(g), \quad \Delta H_f^\circ = -75 \, \text{kJ/mol} \)

This means that 75 kJ of energy is released when 1 mole of methane is formed from carbon and hydrogen in their standard states.

3. Importance in Thermodynamic Calculations

Both \( \Delta H_c^\circ \) and \( \Delta H_f^\circ \) values are widely used to determine enthalpy changes of other reactions using Hess’s Law. Since many reactions cannot be measured directly, these standard enthalpies allow indirect calculation of:

• Reaction enthalpies
• Formation and combustion of substances
• Energy comparisons between different chemical pathways

Calculating Enthalpy Changes Using \( \Delta H_f^\circ \) and \( \Delta H_c^\circ \)

1. Calculating Reaction Enthalpy Using Standard Enthalpies of Formation (\( \Delta H_f^\circ \))

To calculate the standard enthalpy change of a reaction using formation data, use the following equation:

\( \Delta H_{\text{reaction}}^\circ = \sum \Delta H_f^\circ(\text{products}) – \sum \Delta H_f^\circ(\text{reactants}) \)

Steps:

1. Write the balanced chemical equation.
2. Ensure all substances are in their standard states.
3. Obtain \( \Delta H_f^\circ \) values for each compound.
4. Multiply each \( \Delta H_f^\circ \) value by the number of moles in the equation.
5. Apply the formula to calculate \( \Delta H_{\text{reaction}}^\circ \).

2. Calculating Reaction Enthalpy Using Standard Enthalpies of Combustion (\( \Delta H_c^\circ \))

When using combustion data, you must construct a Hess cycle. The following formula applies:

\( \Delta H_{\text{reaction}}^\circ = \sum \Delta H_c^\circ(\text{reactants}) – \sum \Delta H_c^\circ(\text{products}) \)

Why the formula is reversed: Combustion always leads to common products (CO₂ and H₂O), so we’re calculating the difference in energy released by burning the reactants vs. the products.

Steps:

1. Write a balanced equation for the reaction.
2. List the combustion enthalpies of each substance.
3. Multiply each \( \Delta H_c^\circ \) by the number of moles involved.
4. Apply the formula carefully (reactants minus products).

Key Tips and Common Pitfalls:

• Always double-check that the chemical equation is balanced before starting calculations.
• Be sure to use correct physical states (e.g., \( \text{H}_2\text{O}(l) \) vs. \( \text{H}_2\text{O}(g) \)) as values differ.
• Use data from the IB data booklet and verify the sign (enthalpies of combustion are always negative).
• Clearly distinguish between when you are using formation data (products – reactants) vs. combustion data (reactants – products).