Gibbs Free EnergyGibbs free energy is a measure of chemical energyAll chemical systems tend naturally toward statesof minimum Gibbs free energyG = H - TSWhere:G = Gibbs Free EnergyH = Enthalpy (heat content)T = Temperature in KelvinsS = Entropy (can think of as randomness)• Products and reactants are in equilibrium when their Gibbsfree energies are equal• A chemical reaction will proceed in the direction of lower Gibbs free energy (i.e., ΔGr < 0)…so the reaction won’t proceed if the reaction produces an increase in Gibbs free energyGibbs Free Energyformation ofenergy free =ΔofGGibbs Free EnergyΔG°r = ΣnG°f (products) - ΣnG°f (reactants) ΔG°r > 0, backwards reaction with deficient energyΔG°r < 0, forwards reaction with excess energy ΔG°r = 0, reaction is in equilibriumΔG°r is a measure of the driving forceThermodynamicsFor a phase we can determine V, T, P, etc., but not G or HWe can only determine changes in G or H as we change some otherparameters of the systemExample: measure ΔH for a reaction by calorimetry - the heatgiven off or absorbed as a reaction proceedsArbitrary reference state and assign an equally arbitrary value of Hto it:Choose 298.15 K/25°C and 0.1 MPa/1 atm/1 bar (lab conditions) ...and assign H = 0 for pure elements (in their natural state - gas,liquid, solid) at that referenceThermodynamicsIn our calorimeter we can then determine ΔH for the reaction: Si (metal) + O2 (gas) = SiO2 ΔH = -910,648 J/mol= molar enthalpy of formation of quartz (at 25°C, 1 atm)It serves quite well for a standard value of H for the phaseEntropy has a more universal reference state:entropy of every substance = 0 at 0K, so we use that(and adjust for temperature)Then we can use G = H - TS to determine G forquartz = -856,288 J/molThermodynamicsKRTGoRln−=ΔK=equilibrium constant at standard TT in kelvin 298.18KR=gas constant=1.987 cal/moloKGoRlog364.1−=Δ364.110oRGKΔ−=Example: What is the ΔGoR of calcite dissociation?Use data in appendix B for ΔGofΔGoR = [(-132.3)+(-126.17)] - [(-269.9)] = +11.43 kcal(+) means that the reaction goes from right to left so K must be smallWhat is the value of K?364.110oRGKΔ−=K = 10(-11.43/1.364) = 10-8.3798 = 4.171 x 10-9CaCO3 Ca2+ + CO32-What if T ≠ 25oC?Use the Van’t Hoff Equation−Δ−=15.298113025.2loglogTRHKKoRoTToRHΔEnthalpy of reactionR=1.987 cal/mol°T in KelvinKRTGoRln−=ΔΔG°r = ΔH°r-TΔS°randlnKT - lnKT° = (-ΔH°r/R)(1/T-1/T°)We can derive:Example: What is KT of calcite dissociation at T=38°C?−Δ−=15.298113025.2loglogTRHKKoRoTToRHΔ= [(-129.74)+(-161.8)] - [(-288.46)] = -3.081091085.80532.915.29813111)987.1(3025.208.3)1071.4log(log−−=−=−−−=xKxKTTWhen T increases, K decreases(KT° = 4.171 x 10-9)ThermodynamicsSummary thus far:– G is a measure of relative chemical stability for a phase– We can determine G for any phase by measuring H and S forthe reaction creating the phase from the elements– We can then determine G at any T and P mathematically• Most accurate if know how V and S vary with P and T– dV/dP is the coefficient of isothermal compressibility– dS/dT is the heat capacity (Cp)If we know G for various phases, we can determine which ismost stable• Why is melt more stable than solids at high T?• Is diamond or graphite stable at 150 km depth?• What will be the effect of increased P on