Calculate The Delta G Using The Following Information 2h2s 3o2

Introduction

The Gibbs free energy change (ΔG) is a key thermodynamic parameter that indicates whether a reaction is spontaneous or non-spontaneous at constant temperature and pressure. For the reaction 2H₂S + 3O₂ → 2H₂O + 2SO₂, we can calculate ΔG using standard Gibbs free energies of formation.

This calculation assumes standard conditions (25°C and 1 atm pressure) and uses standard Gibbs free energies of formation for each compound. The result will tell us whether the reaction is thermodynamically favorable (ΔG < 0) or unfavorable (ΔG > 0).

Gibbs Free Energy Formula

The standard Gibbs free energy change for a reaction is calculated using the following formula:

Where:

• ΔG° is the standard Gibbs free energy change for the reaction
• ΔG°_f are the standard Gibbs free energies of formation for each compound
• Σ indicates summation over all products and reactants

For the reaction 2H₂S + 3O₂ → 2H₂O + 2SO₂, we need the standard Gibbs free energies of formation for H₂S, O₂, H₂O, and SO₂.

Calculation Steps

1. Identify the balanced chemical equation: 2H₂S + 3O₂ → 2H₂O + 2SO₂
2. Look up the standard Gibbs free energies of formation for each compound:
   • H₂S: -20.1 kJ/mol
   • O₂: 0 kJ/mol (element in standard state)
   • H₂O: -237.2 kJ/mol
   • SO₂: -296.8 kJ/mol
3. Calculate the sum of Gibbs free energies for the products:
   • 2H₂O: 2 × (-237.2) = -474.4 kJ
   • 2SO₂: 2 × (-296.8) = -593.6 kJ
   • Total products: -474.4 + (-593.6) = -1068.0 kJ
4. Calculate the sum of Gibbs free energies for the reactants:
   • 2H₂S: 2 × (-20.1) = -40.2 kJ
   • 3O₂: 3 × 0 = 0 kJ
   • Total reactants: -40.2 + 0 = -40.2 kJ
5. Calculate ΔG° using the formula: ΔG° = ΣΔG°_f(products) - ΣΔG°_f(reactants)
6. ΔG° = -1068.0 kJ - (-40.2 kJ) = -1027.8 kJ

Worked Example

Let's calculate ΔG° for the reaction 2H₂S + 3O₂ → 2H₂O + 2SO₂ using the standard Gibbs free energies of formation:

1. Products:
   • 2H₂O: 2 × (-237.2) = -474.4 kJ
   • 2SO₂: 2 × (-296.8) = -593.6 kJ
   • Total: -474.4 + (-593.6) = -1068.0 kJ
2. Reactants:
   • 2H₂S: 2 × (-20.1) = -40.2 kJ
   • 3O₂: 3 × 0 = 0 kJ
   • Total: -40.2 + 0 = -40.2 kJ
3. ΔG° = -1068.0 kJ - (-40.2 kJ) = -1027.8 kJ

The calculation shows ΔG° = -1027.8 kJ, indicating the reaction is spontaneous under standard conditions.

Interpreting Results

The Gibbs free energy change (ΔG) provides important information about the spontaneity of a reaction:

• If ΔG is negative (ΔG < 0), the reaction is spontaneous and will proceed as written
• If ΔG is positive (ΔG > 0), the reaction is non-spontaneous as written
• If ΔG is zero (ΔG = 0), the system is at equilibrium

For our reaction, ΔG° = -1027.8 kJ, which is negative, indicating the reaction is spontaneous under standard conditions.