Gibbs Free Energy What’s “free” about Gibbs free energy? The change in free energy for a process equals the maximum work that can be done by the system on the surroundings in a spontaneous process occurring at constant temperature and pressure. DG = wmax

Gibbs Free Energy Example: What is the maximum work that can be performed by the combustion of 25.0 g of methanol (CH3OH)? Step 1: Write a balanced equation.

Gibbs Free Energy Step 2: Calculate DGrxn Step 3: Calculate the DG for the mass used in the reaction.

Gibbs Free Energy On your exam, you must be able to write a balanced equation for a simple combustion reaction (including predicting the products). You will then be expected to calculate the maximum work that can be performed using a given number of grams or moles of a reactant.

Gibbs Free Energy You should be able to write a balanced equation for the combustion of an organic compound or a metal. Organic compounds: Metals: Not bal. Not bal.

Gibbs Free Energy You can use the signs (positive or negative) of DH and DS to predict whether a reaction (or process) will be: Spontaneous at all temperatures Spontaneous only at high temperatures Spontaneous only at low temperatures Non-spontaneous at all temperatures

Gibbs Free Energy The sign of DG (and therefore the spontaneity of the reaction) will depend on the sign of DH and DS relative magnitude of the enthalpy and the entropy terms. In some cases, the temperature will impact the spontaneity of a reaction. DG = DH – TDS DG = DH + (- TDS) Enthalpy term Entropy term

Effect of Temperature of Spontaneity Gibbs Free Energy Effect of Temperature of Spontaneity

Gibbs Free Energy Example: Predict whether the following reaction will be spontaneous at low temperature, high temperature, at all temperatures or always non-spontaneous. 2 PbS(s) + 3 O2 (g)  2 PbO (s) + 2 SO2 (g) DH = neg. DS = neg

Gibbs Free Energy Example: Given the standard heats of formation below, predict whether the following reaction will be spontaneous at low temperature, high temperature, at all temperatures or always non-spontaneous. CaO (s) + 3 C (graphite)  CaC2 (s) + CO (g) DHfo (CaO) = - 635.1 kJ/mol DHfo (CaC2) = - 59.9 kJ/mol DHfo (CO) = - 110.5 kJ/mol

Gibbs Free Energy

Gibbs Free Energy For a system in which the reactants and/or products are not present in their standard states, the values of DG and DGo are related: DG = DGo + RT lnQ where DG = Gibbs free energy change DGo = standard Gibbs free energy change R = 8.314 J/mol.K T = temp. in Kelvin Q = reaction quotient

Free Energy and Equilibrium Constants For a system at equilibrium, DG = 0 Q = K and the standard free energy change (DGo) for the reaction is directly related to the equilibrium constant for the reaction DGo = -RT ln K

Free Energy and Equilibrium Constants This equation can be used to calculate DGo for a reaction when the equilibrium constant or the equilibrium concentrations are known. The equation can also be rearranged and used to find the value of the equilibrium constant if DGo for the reaction is known: K = e-DG /RT o

Free Energy and Equilibrium Constants Example: Find DGo for the following reaction at 25oC if Kp = 7.00 x 105. N2 (g) + 3 H2 (g) 2 NH3 (g)

Free Energy and Equilibrium Constants Example: Calculate the equilibrium constant at 25oC for the dissolution of barium fluoride if DGo for this process is +32.9 kJ per mole of barium fluoride.

Free Energy and Equilibrium Constants

Free Energy and Equilibrium Constants Once you find the value for the equilibrium constant, you can use the equilibrium constant to : Calculate the equilibrium concentrations of the products and/or reactants. How would you calculate the concentrations of barium ions and fluoride ions present in a saturated solution of barium fluoride?

Free Energy and Equilibrium Constants