1. Models
“Models are attempts to describe reality, that doesn’t mean they necessarily have anything to do with reality”
Models describe some aspect(s) of a system governed by phenomena the model attempts to describe
How does Geochemistry differ from Chemistry??

2. Variables
In any model, looking at a process involves something that can change, a variable:
Extensive variable: depends on the amount present (mass, volume)
Intensive Variable: property is not additive, divisible (temperature)
Models describing energy transfer fall under the study called thermodynamics

3. Variables
For models, variables are key, and how some process changes a variable is the key to these models
ex. As we heat a pool of water how does the amount of mineral dissolved change, as our car burns gas, how does it’s position change
Describing these changes is done through differential calculus:

4. Review of calculus principles
Process (function) y driving changes in x: y=y(x), the derivative of this is dy/dx (or y’(x)), is the slope of y with x
By definition, if y changes an infinitesimally small amount, x will essentially not change: dy/dk=
This derivative describes how the function y(x) changes in response to a variable

5. Partial differentials
Most models are a little more complex, reflecting the fact that functions (processes) are often controlled by more than 1 variable
How fast Fe2+ oxidizes to Fe3+ is a process that is affected by temperature, pH, how much O2 is around, and how much Fe2+ is present at any one time
what does this function look like, how do we figure it out???

6. Total differential, dy, describing changes in y affected by changes in all variables (more than one, none held constant)

7. ‘Pictures’ of variable changes
2 variables that affect a process: 2-axis x-y plot
3 variables that affect a process: 3 axis ternary plot (when only 2 variables are independent; know 2, automatically have #3)
Miscibility Gap
microcline
orthoclase
sanidine
anorthoclase
monalbite
high albite
low albite
intermediate albite
Orthoclase
KAlSi3O8
Albite
NaAlSi3O8
% NaAlSi3O8
Temperature (ºC)
300
900
700
500
1100 10 90 70 50 30

9. Properties derived from outer e-
Ionization potential  energy required to remove the least tightly bound electron
Electron affinity  energy given up as an electron is added to an element
Electronegativity  quantifies the tendency of an element to attract a shared electron when bonded to another element.

10. In general, first ionization potential, electron affinity, and electronegativities increase from left to right across the periodic table, and to a lesser degree from bottom to top.

11. Ionic vs. Covalent
Elements on the right and top of the periodic table draw electrons strongly
Bonds between atoms from opposite ends more ionic, diatomics are 100% covalent
Bond strength  Covalent>Ionic>metallic
Affects hardness, melting T, solubility
Bond type affects geometry of how ions are arranged
More ionic vs. covalent = higher symmetry
Go over this on a periodic table – this is electronegativity argument essentially
Test them a little – SiO2, CaO, AsS (realgar), ZnS (sphalerite) more or less ionic – properties?
More ionic  less strength  melts lower, more soluble
Realgar much softer than Sphalerite

12. Atomic Radius
A function partly of shielding, size is critical in thinking about substitution of ions, diffusion, and in coordination numbers

13. Units review
Mole = x1023 ‘units’ make up 1 mole, 1 mole of H+= x1023 H+ ions, 10 mol FeOOH = x1024 moles Fe, x1024 moles O, x1024 moles OH. A mole of something is related to it’s mass by the gram formula weight  Molecular weight of S = g, so grams S has x1023 S atoms.
Molarity = moles / liter solution
Molality = moles / kg solvent
ppm = 1 part in 1,000,00 (106) parts by mass or volume
Conversion of these units is a critical skill!!

14. Let’s practice! 10 mg/l K+ = ____ mM K 16 mg/l Fe = ____ mM Fe
10 mg/l PO43- = _____ mM P
50 mm H2S = _____ mg/l H2S
270 mg/l CaCO3 = _____ M Ca2+
FeS2 + 2H+  Fe2+ + H2S
75 mM H2S = ____ mg/l FeS2
GFW of Na2S*9H2O = _____ g/mol
how do I make a 100ml solution of 5 mM Na2S??

15. Scientific Notation 4.517E-06 = 4.517x10-6 = 0.000004517
Another way to represent this: take the log = M k d c m n p
1E+6
1000 1
0.1
0.01
1E-3
1E-6
1E-9
1E-12

16. Significant Figures Precision vs. Accuracy
Significant figures – number of digits believed to be precise  LAST digit is always assumed to be an estimate
Using numbers from 2 sources of differing precision  must use lowest # of digits
Mass = g, volume= ml = g/l

17. Logarithm review 103 = 1000 ln = 2.303 log x
pH = -log [H+]  M H+ is what pH?
Antilogarithms: 10x or ex (anti-natural log)
pH = -log [H+]  how much H+ for pH 2?

18. Logarithmic transforms
Log xy = log x + log y
Log x/y = log x – log y
Log xy = y log x
Log x1/y = (1/y) log x
ln transforms are the same

19. Line Fitting
Line fitting is key to investigating experimental data and calibrating instruments for analysis
Common assessment of how well a line ‘fits’ is the R2 value – 1 is perfect, 0 is no correlation