Calculating Enthalpy of a Reaction using Standard Enthalpy of Formations

Key Concepts

• Enthalpy of Reaction (ΔH): Represents the heat change during a reaction.
• Standard Enthalpy of Formation (ΔH⁰_f): The heat change when one mole of a compound is formed from its constituent elements in their standard states.
• Standard States: Most stable form of an element or compound at 25°C (298 K) and 1 atmosphere pressure.
• Symbols:
  • ΔH: Enthalpy change.
  • ΔH⁰_f: Standard enthalpy of formation.

Determining ΔH Using Standard Enthalpy of Formations

1. Understanding Standard Enthalpy of Formation:
   • Occurs when 1 mole of a substance is formed from its elements in their standard states.
   • Example: Formation of water from hydrogen and oxygen.
     • Reaction: ½ H₂(g) + ½ O₂(g) → H₂O(l)
     • Enthalpy change: ΔH⁰_f = -285.8 kJ/mol.
2. **Using Standard Molar Heats of Formation: Typical Values: Iron:
   • Positive or negative values.
   • Given in kJ/mol.
   • Standard enthalpy for a pure element in its standard state is zero.
   • Need appendix or table for these values during problems.

Steps to Calculate ΔH of a Reaction

1. Write the balanced chemical equation.
2. Identify ΔH⁰_f values for all reactants and products.
3. Apply the equation:
   • ΔH_rxn = Σ ΔH⁰_f(products) - Σ ΔH⁰_f(reactants).
   • Ensure correct values for phases (solid, liquid, gas).
4. Practice Problem:
   • Given Reaction: C₃H₈ (g) + 5 O₂ (g) → 3 CO₂ (g) + 4 H₂O (l)
   • Find ΔH⁰_f for each species:
     • CO₂(g): -393.5 kJ/mol
     • H₂O(l): -285.8 kJ/mol
     • C₃H₈(g): -103.9 kJ/mol
     • O₂(g): 0 kJ/mol (element)
   • Apply the formula:
     • ΔH_rxn = [(3 × -393.5) + (4 × -285.8)] - [(1 × -103.9) + (5 × 0)]
     • ΔH_rxn = [-1180.5 + -1143.2] - [-103.9 + 0]
     • ΔH_rxn = -2323.7 + 103.9 = -2219.8 kJ/mol.

Example Problems

1. Problem: Determine which reaction represents standard enthalpy of formation for NO₂(g):
   • A: N₂(g) + O₂(g) → 2 NO₂(g)
   • B: ½ N₂(g) + O₂(g) → NO₂(g)
   • Correct answer: B (produces 1 mole of compound from elements in standard states).
2. Another problem: Calculate ΔH for the reaction of butane combustion:
   • Given Reaction: 2 C₄H₁₀(g) + 13 O₂(g) → 8 CO₂(g) + 10 H₂O(l)
   • Find ΔH⁰_f for each species:
     • CO₂(g): -393.5 kJ/mol
     • H₂O(l): -285.8 kJ/mol
     • C₄H₁₀(g): -124.7 kJ/mol
     • O₂(g): 0 kJ/mol (element)
   • Apply the formula:
     • ΔH_rxn = [(8 × -393.5) + (10 × -285.8)] - [(2 × -124.7) + (13 × 0)]
     • ΔH_rxn = [-3148 + -2858] - [-249.4 + 0]
     • ΔH_rxn = -6006 + 249.4 = -5756.6 kJ/mol.

Final Notes

• Always ensure you are using the correct sign and phase of matter.
• Products come first in the equation; it’s products minus reactants, not the other way around.
• Reference tables are crucial for accurate ΔH⁰_f values.
• Use coefficients from balanced equations as multipliers in calculations.