Enthalpy and Gibbs Free Energy

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Contents

Enthalpy

  • The heat produced by a chemical reaction can be calculated from the First Law of Thermodynamics and the concept of enthalpy
First Law of Thermodynamics
  • First Law
    • The change in a system’s internal energy equals the heat added to the system from its surroundings minus the work done by the system on its surroundings.
    • That is, change in internal energy ΔU = heat added Q – work done W
      • ΔU = Q – W
  • Definitions
    • The internal energy of a system is the total kinetic and potential energies of its constituent particles.
    • Heat is the energy transferred from one body to another as the result of a difference in temperature.
    • Work is the energy transferred as the result of a force moving an object.
  • View First Law
Enthalpy
  • Enthalpy = EN-THOWL-pea
  • The enthalpy of a system equals its internal energy + the pressure of the system times its volume:
    • H = U + PV
  • PV is in units of energy:
    • P = force / length2 and V = length3. So PV = force x length = work.
  • Thus enthalpy is the internal energy of a system plus the work it does in the form of pressure times volume.
  • The standard enthalpy of formation of a compound is the change of enthalpy during the formation of one mole of the substance from its constituent elements under standard conditions:
    • ΔH = ΔU + PΔV
    • Standard Conditions:
      • Temperature of 293.15 K = 68 degrees Fahrenheit
      • Pressure of 101325 pascals = 1 atm = pressure at sea level
      • Substances are in their standard state: liquid, gas, solid
Heat produced by combustion of methane
Argument that the combustion of methane produces 890.345 kJ/mol of heat
  • Premise 1: If the only work done by a chemical reaction is a change of volume at constant pressure, the heat added to the reaction (Q) equals the change in enthalpy (ΔH).
    • The proof of Q=ΔH principle is below.
  • Premise 2: Change in enthalpy (ΔH) = -890.345 kJ/mol
    • Reactant Side
      • Standard Enthalpy of Formation for CH4 =  -74.848 kJ/mol
      • Standard Enthalpy of Formation for O2 = 0 kJ/mol
      • Total (-74.848 + 2 (0)) = -74.848 kJ/mol
    • Product Side
      • Standard Enthalpy of Formation for CO2 = -393.513 kJ/mol
      • Standard Enthalpy of Formation for H2O =  -285.84 kJ/mol
      • Total (-393.513 + 2 (-285.84)) = -965.193 kJ/mol
    • Change in Enthalpy = -965.193 – (-74.848) = -890.345 kJ/mol
  • Premise 3: The only work done by the combustion of methane is a change of volume at constant pressure
    • Experimental conditions
  • Therefore, the heat added to the reaction is -890.345 kJ/mol, meaning the reaction produced 890.345 kJ/mol of heat.
Proof of the Q=ΔH Principle
  • Principle
    • If the only work done by a chemical reaction is a change of volume at constant pressure, the heat added to the reaction (Q) equals the change in enthalpy (ΔH).
  • Proof 
    • #1 ΔU = Q − W
      • First Law of Thermodynamics
      • Change in internal energy = heat added − work done
    • #2 W = PΔV
      • Assumption that the only work done is a change of volume at constant pressure
    • #3 Therefore, ΔU = Q − PΔV
      • From #1 and #2
    • #4 Q = ΔU + PΔV
      • Rearranging #3 
    • #5 ΔH = ΔU + PΔV
      • From the definition of enthalpy (H = U + PV) for a system at constant pressure
    • Therefore, Q = ΔH
      • Frome #4 and #5
      • That is, the heat transferred to the system = change in enthalpy

Gibbs Free Energy

  • In the 1870s Josiah Willard Gibbs developed the ingenious notion of Gibbs free energy, combing the internal energy of the First Law of Thermodynamics with the entropy of the Second.
  • The change in Gibbs free energy of a chemical reaction equals the change in enthalpy minus the temperature of the reaction times the change in entropy.
    • ΔG = ΔH -T ΔS
  • A chemical process at constant temperature and pressure is
    • exergonic and spontaneous if ΔG < 0
      • e.g. combustion of methane
    • endergonic and non-spontaneous if ΔG > 0
      • e.g. photosynthesis
    • in chemical equilibrium if ΔG = 0
      • e.g. carbonation
  • Definitions
    • A spontaneous process is one that, once started, requires no external energy.
    • A non-spontaneous process, by contrast, requires constant external energy to keep it going.
    • A chemical reaction is exoergic (exergonic) if it releases energy.
    • A chemical reaction is endoergic (endergonic) if it absorbs energy.
    • A chemical reaction is in chemical equilibrium if the forward and reverse reactions proceed at the same rate, so that the concentrations of reactants and products remain the same.
  • The change ΔG in the Gibbs free energy of a chemical reaction equals the Gibbs free energy of formation of the products minus the Gibbs free energy of formation of the reactants
    • ΔG = Gf of products− Gf of reactants
  • The Gibbs free energy of formation of a compound is the change of Gibbs free energy in the formation of the compound from its elements.