Geology 2142 by gjjur4356

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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

								
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