# Enthalpy and Gibbs Free Energy

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#### 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
###### 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=ΔHPrinciple
• 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.