Gibbs Free EnergyPowerPoint PresentationSlide 3ThermodynamicsSlide 5Slide 6Slide 7Slide 8Slide 9Slide 10Gibbs Free EnergyGibbs free energy is a measure of chemical energyAll chemical systems tend naturally toward states of 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., Gr < 0)…so the reaction won’t proceed if the reaction produces an increase in Gibbs free energyGibbs Free Energyformation ofenergy free =ΔofGGibbs Free EnergyG°r = nG°f (products) - nG°f (reactants) G°r > 0, backwards reaction with deficient energyG°r < 0, forwards reaction with excess energy G°r = 0, reaction is in equilibriumG°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 other parameters of the systemExample: measure H for a reaction by calorimetry - the heat given off or absorbed as a reaction proceedsArbitrary reference state and assign an equally arbitrary value of H to 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 H for the reaction: Si (metal) + O2 (gas) = SiO2 H = -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 for quartz = -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 GoR of calcite dissociation?Use data in appendix B for GofGoR = [(-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−=ΔG°r = H°r-TS°randlnKT - lnKT° = (-H°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 for the 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 is most 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