What s free about Gibbs free energy?
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1 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 = w max
2 Example: What is the maximum work that can be performed by the combustion of 25.0 g of methanol (CH 3 OH)? Step 1: Write a balanced equation.
3 Step 2: Calculate DG rxn Step 3: Calculate the DG for the mass used in the reaction.
4 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.
5 You should be able to write a balanced equation for the combustion of an organic compound or a metal. Organic compounds: C n H m + O 2 C x H Y O n + O 2 Metals: Metal + O 2 CO 2 + H 2 O CO 2 + H 2 O Metal oxide Not bal. Not bal.
6 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
7 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
8 Effect of Temperature of Spontaneity DH DS DG Spontaneity - + always - Spon. all T + - always + Non-spon. all T at low T spon. at low T at high T spon. at high T
9 Example: Predict whether the following reaction will be spontaneous at low temperature, high temperature, at all temperatures or always nonspontaneous. 2 PbS(s) + 3 O 2 (g) 2 PbO (s) + 2 SO 2 (g) DH = neg. DS = neg
10 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 nonspontaneous. CaO (s) + 3 C (graphite) CaC 2 (s) + CO (g) DH f o (CaO) = kj/mol DH f o (CaC 2 ) = kj/mol DH f o (CO) = kj/mol
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12 For a system in which the reactants and/or products are not present in their standard states, the values of DG and DG o are related: DG = DG o + RT lnq where DG = Gibbs free energy change DG o = standard Gibbs free energy change R = J/mol. K T = temp. in Kelvin Q = reaction quotient
13 Free Energy and Equilibrium Constants For a system at equilibrium, DG = 0 Q = K and the standard free energy change (DG o ) for the reaction is directly related to the equilibrium constant for the reaction DG o = -RT ln K
14 Free Energy and Equilibrium Constants This equation can be used to calculate DG o 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 DG o for the reaction is known: o K = e-dg /RT
15 Free Energy and Equilibrium Constants Example: Find DG o for the following reaction at 25 o C if K p = 7.00 x N 2 (g) + 3 H 2 (g) 2 NH 3 (g)
16 Free Energy and Equilibrium Constants Example: Calculate the equilibrium constant at 25 o C for the dissolution of barium fluoride if DG o for this process is kj per mole of barium fluoride.
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