Thermodynamics

• “the branch of science that deals with energy levels and the transfer of energy between systems and between different states of matter”

What is Energy???• “It is important to realize that in physics today, we have no

knowledge of what energy is. We do not have a picture that energy comes in little blobs of a definite amount. It is not that way.” –Richard Feynman

• HOWEVER Feynman goes on to elaborate that energy has meaning as a way to define, and quantify, changes which bring about reactions – between systems, energy levels, or states of matter.

• “How seriously must we take the physical existence of this energy? No more and no less than any other bookkeeping practices.” –Richard Feynman

Thermodynamics• Thermodynamics answers the following question:

• For any reaction - defined by a set of reactants and products set in exactly defined conditions (temperature, pressure, concentration, etc.) will that reaction go forward spontaneously or not??

• For ANY geochemical reaction, if thermo says NO, rest assured the reaction will not proceed.

• Thermo says NOTHING about the speed a reaction occurs!!

Equilibrium

• Anything at equilibrium is theoretically undergoing forward and reverse reactions:

• A + B ↔ C– A + B C AND C A +B

• Equilibrium has 2 criteria:– Reaction does not appreciably change in time– Perturbation of that equilibrium will result in a

return to the equilibrium

log Keq

• CaCO3(calcite) = Ca2+ + CO32- -8.48

• CO2(g) + H2O = H2CO30 -1.47

• H2CO30 = H+ + HCO3

- -6.35

• H+ + CO32- = HCO3

- +10.33

CaCO3(calcite) + CO2(g) + H2O = Ca2+ + 2 HCO3- -5.97

Equations can be ‘added’ together, equilibrium constants also get ‘added’ together!

Convenient way to rewrite reactions (to look at more appropriate reactions or to use things you’ve more directly measured….)

Assessing equilibrium

Q reaction quotient, aka Ion Activity Product (IAP) is calculated from knowing activity of all components of a reaction

K aka Keq, we get from thermodynamic data – it is one number defined AT EQUILIBRIUM

Equilibrium for any reaction is when Q = K

i

ni

n

reactants

productsK

][

][

i

ni

n

reactants

productsQ

][

][

Where do K’s come from?

• Measure directly – experimental determination of conditions at equilibrium

• Use thermodynamic data – K is directly related to free energy of reaction – GR

Hydroxylapatite

• Ca5(PO4)3(OH) = OH- + 3 PO43- + 5 Ca2+

• Log K = -59.0351 at 25ºC

Aqueous Complexes• Combinations of ions to form dimers, trimers,

etc., are complexes• Why do we care??

1. Complexation of an ion also occurring in a mineral increases solubility

2. Some elements occur as complexes more commonly than as free ions

3. Adsorption of elements greatly determined by the complex it resides in

4. Toxicity/ bioavailability of elements depends on the complexation

How do we know about all those species??

• Based on complexation how any ion interacts with another ion to form a molecule, or complex (many of these are still in solution)

• Yet we do not measure how much CaNO3

+, CaF+, or CaPO4- there is in a

particular water sample• We measure Ca2+ But is that Ca2+ really

how the Ca exists in a water??

Defining Complexes

• Use equilibrium expressions:

• cC + lHL CL + lH+

• Where B is just like Keq!

lc

nc

i HLC

HCL

][][

][][

Equilibrium• Equilibrium Constant, K (or Keq) describes conditions AT equilibrium (where GR=0)

GR-G0R = RTlnK

G0R = -RTlnK

G0R= G0

R products – G0R reactants

GR= GR products – GR reactants

i

ni

n

reactants

productsK

][

][

G0

• Energy at STANDARD STATE

• = 25°C, 1 bar Pressure, 1 molal concentration for each

Speciation• Any element exists in a solution, solid, or

gas as 1 to n ions, molecules, or solids

• Example: Ca2+ can exist in solution as: Ca++ CaCl+ CaNO3

+

Ca(H3SiO4)2 CaF+ CaOH+

Ca(O-phth) CaH2SiO4 CaPO4-

CaB(OH)4+ CaH3SiO4

+ CaSO4

CaCH3COO+ CaHCO3+ CaHPO4

0

CaCO30

• Plus more species gases and minerals!!

Mass Action & Mass Balance

• mCa2+=mCa2++MCaCl+ + mCaCl20 + CaCL3- +

CaHCO3+ + CaCO3

0 + CaF+ + CaSO40 +

CaHSO4+ + CaOH+ +…

• Final equation to solve the problem sees the mass action for each complex substituted into the mass balance equation

lc

nc

i HLC

HCL

][][

][][

nxLmCamCa 22

Mineral dissolution/precipitation

• To determine whether or not a water is saturated with hydroxyapatite, we could write a dissolution reaction such as:

Ca5(PO4)3(OH) = OH- + 3 PO43- + 5 Ca2+

• We could then determine the equilibrium constant:

• If K = -59.04, can determine how much Ca2+ and PO43-

might dissolve at any pH and T

1

135 34

2

titehydroxyapa

OHPOCa

a

aaaK

Activity

• Sometimes called ‘effective concentration’, which is misleading and reflects a poor understanding of the property…

• Think of more of the effect the rest of a solution has on how easily two ions come together..

Activity

• For solids or liquid solutions:ai=Xii

• For gases:

ai=Pii = fi

• For aqueous solutions:

ai=mii

Xi=mole fraction of component iPi = partial pressure of component imi = molal concentration of component i

Activity Coefficients

• Where do they come from??• The standard state for dissolved ions is

actually an infinitely dilute solution…• Activity of phases - gases, minerals, and bulk

liquids (H2O) are usually pretty close to 1 in waters

• Dissolved molecules/ ions have activity coefficients that change with concentration (ions are curved lines relating concentration and activity coefficients, molecules usually more linear relation)

Application to ions in solution

• Ions in solutions are obviously nonideal mixtures!

ai = imi

• The activity coefficient, i, is found via some empirical foundations

• Dependent on the other ions in water…

Dissolved species i

• First must define the ionic strength (I) of the solution the ion is in:

Where mi is the molar concentration of species i and zi is the charge of species I

2

izmI

ii

Activity Coefficients

• Debye-Huckel approximation (valid for I:

• Where A and B are constants (depending on T), z is charge, I is ionic strength, and å is a measure of the effective diameter of the ion

2

1

2

12

1

log

BIa

IAzo

Different ways to calculate i

• Limiting law

• Debye-Huckel

• Davies

• TJ, SIT models

• Pitzer, HKW models

Neutral species

• Setchnow equation:

• Logn=ksI

For activity coefficient (see table 4-2 for selected coefficients)

Mass Action & Mass Balance

• mCa2+=mCa2++MCaCl+ + mCaCl20 + CaCL3- +

CaHCO3+ + CaCO3

0 + CaF+ + CaSO40 + CaHSO4

+ + CaOH+ +…

• Final equation to solve the problem sees the mass action for each complex substituted into the mass balance equation

• Equations for each ion – iterative solution…

lc

nc

i HLC

HCL

][][

][][

nxLmCamCa 22

Speciation Models

• PHREEQC, or WebPHREEQ, is a USGS program that solves, simultaneously (iteratively really), all of the mass action and mass balance equations for a water’s chemical composition