Calculate Delta S Rxn for The Following Reaction

What is ΔS Rxn?

ΔS Rxn (change in entropy of reaction) measures the disorder or randomness of a system during a chemical reaction. Entropy is a fundamental thermodynamic property that helps predict whether a reaction will occur spontaneously.

In chemical reactions, entropy typically increases when:

• Gases are produced from solids or liquids
• Molecules dissociate into smaller parts
• Solutes dissolve in solvents
• Molecules become more disordered in solution

Entropy decreases when reactions form more ordered structures, such as when gases combine to form liquids or solids.

How to Calculate ΔS Rxn

The change in entropy for a reaction is calculated using the standard entropy values (S°) of the reactants and products:

Where:

• ΔS° rxn = standard change in entropy for the reaction (J/mol·K)
• ΣS°(products) = sum of standard molar entropies of all products
• ΣS°(reactants) = sum of standard molar entropies of all reactants

Standard entropy values are typically found in thermodynamic tables or databases. The units for entropy are joules per mole per kelvin (J/mol·K).

Interpreting the Results

The sign of ΔS° rxn indicates the direction of entropy change:

• Positive ΔS° rxn: The reaction increases entropy (more disordered products)
• Negative ΔS° rxn: The reaction decreases entropy (more ordered products)
• Zero ΔS° rxn: The entropy remains unchanged

When combined with the change in enthalpy (ΔH° rxn), ΔS° rxn helps determine the spontaneity of a reaction at constant temperature and pressure using the Gibbs free energy equation:

A negative ΔG° rxn indicates a spontaneous reaction under standard conditions.

Worked Example

Let's calculate ΔS° rxn for the following reaction:

Using standard entropy values:

• H₂(g): 130.7 J/mol·K
• O₂(g): 205.1 J/mol·K
• H₂O(l): 69.9 J/mol·K

Calculation:

The negative value indicates the reaction decreases entropy, forming more ordered liquid water from gaseous reactants.