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Geology 2142 Thermodynamics of Mineral Reactions Energy and Reactions • Under any conditions of pressure and temperature, the stable mineral assemblage is the one with the lowest GIBBS FREE ENERGY – If this condition is not satisfied, then the assemblage is said to be metastable • Reaction will proceed toward equilibrium if the activation energy for the reaction can be achieved Energy and Reactions • All chemical reactions proceed in the direction that will minimize the energy of the system – Reactions will only occur however, if the Activation Energy is overcome Stability and Activation Energy Types of Reaction - Examples • Solid – solid reactions – Andalusite = sillimanite • This is a phase transition – Grossular + quartz = anorthite + 2 wollastonite Types of Reaction - Examples • Dehydration Reactions – Muscovite + quartz = Kspar + sillimanite + vapour – Kaolinite + 2 quartz = pyrophyllite + vapour Types of Reaction - Examples • Decarbonation reactions – Calcite + quartz = wollastonite + CO2 – Dolomite + 2 quartz = diopside + 2 CO2 Types of Reaction - Examples • Carbonation reactions – Forsterite + 2 CO2 = 2 Magnesite + quartz • Hydration reactions – Enstatite + 2 H2O = 2 brucite + 2 quartz Equilibrium • Reactions involve changes in minerals or in mineral composition –A+B=C+D – A mineral assemblage is at equilibrium if the amount of A+B reacting to form C+ D is exactly the same as the amount of C + D that is reacting to form A + B • There is no net gain on either side of the reaction Equilibrium • This is called stable equilibrium • If reaction stops before this is reached it is called metastable equilibrium – Role of kinetics • Rates of reaction – Controlled by P, T availability of volatiles etc Equilibrium assemblages • Called a PARAGENESIS – As conditions change a new paragenesis may form • E.g. the progression across isograds • Most reactions involve a vapour of some sort – If we ignore the fluid, reactions are isochemical Isochemical? • Isochemical reactions – Not net gain or loss of any element • Except water or CO2 • Non-isochemical metamorphism is called metasomatism – Important in skarns – Also important in the earth’s mantle Thermodynamic Definitions • Thermodynamics is the study of energy in chemical reactions – Variables involved • Pressure • Volume • Temperature • Internal energy – From a knowledge these we can calculate all other variables First Law • Defines the internal energy (E) of a system. If the system is closed (isochemical) E is constant unless heat flows or work is done – Expressed in units of energy per mole • Usually joule (or kilojoules) per mole Second Law • Defines ENTROPY (S) – as a variable that expresses the degree of disorder of a system – Simple structure and simple composition = low S – Complex structure or composition = high S • Expressed in units of energy per mole per degree – Joules per mole per Kelvin Third Law • Entropy varies with temperature. Entropy approaches zero (but does not reach it) when temperature approaches zero Kelvin – Why can entropy not be zero at zero Kelvin? Important Definitions • Molar Volume – The volume occupied by one mole of a substance • Expressed in units of cubic cm per mole Molar Volume of Quartz • Molar volume of quartz – Atomic weight = 60.0843 grams • So 6.022*1023 SiO2 molecules = this weight – Unit cell = 112.985 Angstroms • Each unit cell has three SiO2 molecules – V=6.022*1023*112.986/3 • = 2.268 *1025 cubic Angstroms • =22.68 cm3 – About the size of a golf ball Enthalpy • Minerals with large volume are less stable at high P than at low P (and vice versa) – Enthalpy (H) reflects this idea • Includes the internal energy so that – H = E + PV • Expressed in energy per mole – Joules or kilojoules per mole Gibbs Free Energy • Minerals of high entropy (S) are more stable at high T than at low (and vice versa). Gibbs free energy (G) relfects this by adding an entropy (S) term to enthalpy (H) – G= H - TS = E + PV – TS • Remember H = E + PV • Also expressed in energy per mole Clausius – Clapeyron Equation • Relates volume and entropy of a reaction to its slope on a P – T diagram – dP/dT = DS/DV Pressure A Slope = dP/dT B Temperature Gibbs Phase Rule • Relates the number of phases that can exist to the number of chemical components – P + f = c+ 2 (or F=c-p+2) – P = number of phases – C =number of components – F = degrees of freedom • More on this in another lecture Gibbs Free Energy of a Reaction • The mineral or assemblage with the lowest G is more stable than others of the same composition • G is a numerical value that describes a minerals stability – There is no absolute value, G is always relative • Usually referenced to the elements that form the mineral Gibbs Free Energy of Formation DGof reference value for the reaction of elements to form a mineral – Example reaction of Ca, C and O to give calcite • Ca + C + 3 O = CaCO3 • G can be used to calculate the Gibbs free energy of a reaction DGrxn (difference between products and reaction) – Determines if reaction will occur Gibbs Free Energy of Formation DGof elements (calcite) = Gcalcite –GCa – Gc – 3GO • Reaction of calcite to give aragonitE DG = Garagonite – Gcalcite – The G values for these two minerals are rarely equal. • If Garagonite is less than Gcalcite then DG for the reaction calcite = aragonite is negative and aragonite is stable • Aragonite forms as reaction goes to the right Gibbs Free Energy of Formation • If Gcalcite is less than Garagonite then DG for the reaction calcite to aragonite is positive and calcite is stable – This means that the reaction proceeds to the left • The two minerals can only coexist when DG is zero – will be represented by a line on a phase diagram Effects of P&T on DG • Gibbs free energy varies with pressure – G = E + PV – TS (remember H = E + PV) • We can write an equation for the Gibbs Free Energy of a reaction DGrxn = DErxn +PDVrxn –TDSrxn – The difference terms are calculated as DErxn = S DEf (products) = S DEf (reactants) • Same idea for V and S Consequences DGrxn = DErxn +PDVrxn –TDSrxn • If V is large and P high the mineral is unstable – So minerals with low V (high density) are most stable at high P • At high T, high entropy minerals are most stable since high S and high T give low G Equilibrium at P and T 0 = DErxn +PDVrxn –TDSrxn • The above reaction is at equilibrium • G=0 • This relationship holds for a specific set of P and T values – These define a line on a P – T plot • Define reaction curves Equilibrium at P and T • Slope of reaction curve = dP/dT = DSrxn/DVrxn • Clausius – Clayperon equation • Solid – solid reactions = straight lines • Reactions involving fluids or melts are curves as volume and entropy vary with pressure