Reactivity 1.2.4 – Hess’s Law using enthalpy of formation and combustion data

Hess’s Law is a key tool in thermochemistry that allows us to calculate the enthalpy change of a reaction using enthalpy data from related reactions. When direct measurement is not feasible, we use known values of either:

• Standard enthalpies of formation (\( \Delta H_f^\circ \))
• Standard enthalpies of combustion (\( \Delta H_c^\circ \))

What Is \( \Delta H_f^\circ \)?

The standard enthalpy of formation, denoted \( \Delta H_f^\circ \), is the enthalpy change when 1 mole of a compound is formed from its constituent elements, all in their standard states under standard conditions (298 K and 100 kPa).

For any element in its standard state, \( \Delta H_f^\circ = 0 \).

Applying Hess’s Law with \( \Delta H_f^\circ \)

Hess’s Law states that the total enthalpy change for a chemical reaction is independent of the path taken.

In a Hess cycle that uses \( \Delta H_f^\circ \) values:

• The base of the cycle consists of the elements in their standard states.
• Arrows in the diagram point upward — from the elements to the reactants and the products.
• This method builds the enthalpy change by imagining that all reactants are broken down into their elements and then reassembled into products.

What Is \( \Delta H_c^\circ \)?

The standard enthalpy of combustion, symbolized as \( \Delta H_c^\circ \), is the energy released when 1 mole of a substance undergoes complete combustion in excess oxygen under standard conditions (298 K and 100 kPa), with all reactants and products in their standard states.

Combustion values are always exothermic, so \( \Delta H_c^\circ \) values are negative.

Applying Hess’s Law with \( \Delta H_c^\circ \)

Hess’s Law allows us to calculate the enthalpy change of a reaction indirectly by comparing the combustion enthalpies of the substances involved.

In a Hess cycle based on \( \Delta H_c^\circ \):

• The common combustion products — usually \( \text{CO}_2(g) \) and \( \text{H}_2\text{O}(l) \) — are placed at the bottom of the cycle.
• All arrows point downwards from the reactants and products to the combustion products.
• This method constructs a Hess cycle where both reactants and products are burned completely in oxygen to form common products (typically CO₂ and H₂O).
• Because all combustion paths lead to the same final products, the relative energy differences can be used to deduce \( \Delta H^\circ \).

Important Notes:

• Always use balanced chemical equations with correct stoichiometry.
• Only use data for substances in their standard states — gas, liquid, solid, or aqueous, as specified.
• Values of \( \Delta H_f^\circ \) and \( \Delta H_c^\circ \) are provided in the IB Chemistry data booklet.
• Keep units consistent (usually kJ/mol).

Calculating Enthalpy Changes Using Enthalpy of Formation or Combustion Data

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

To determine the enthalpy change of a reaction using formation data, apply the equation:

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

This method considers the hypothetical cycle in which all reactants are broken into their elements and reassembled into products.

Steps:

1. Write a balanced chemical equation.
2. Look up the \( \Delta H_f^\circ \) values of all reactants and products.
3. Multiply each value by the number of moles in the equation.
4. Use the equation: total of products minus total of reactants.

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

To calculate the enthalpy change of a reaction using combustion data, use:

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

In this method, all substances are hypothetically combusted in oxygen, and their combustion enthalpies are compared via Hess’s Law.

Steps:

1. Write and balance the chemical equation for the reaction.
2. Locate the \( \Delta H_c^\circ \) values (standard enthalpies of combustion) for all relevant substances.
3. Multiply each \( \Delta H_c^\circ \) value by the number of moles present in the balanced equation.
4. Apply the Hess’s Law equation: total combustion enthalpy of reactants minus products:

   Key Tips for Calculation:

• Use balanced chemical equations with correct stoichiometric coefficients.
• Always check that data corresponds to the correct physical states.
• Ensure all enthalpy values are in kJ/mol as given in the IB Data Booklet.
• Understand which formula to apply: use products − reactants for \( \Delta H_f^\circ \), and reactants − products for \( \Delta H_c^\circ \).