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Week 2 Hydrogeochemistry
Acid/Base reactions
Reactions of H+ with chemical species
Normality = eq/L and eq wt. = GMW/ion charge
30 mg/L solution of H2S
H2S = H+ + HSEq. Wt. = 33/1 = 33 mg/meq
H2S = 2H+ + S-2
Eq. Wt. = 32/2 = 16 mg/meq
normality: 30/33 = 0.91 meq/L
normality: 30/16 = 1.875 meq/L
Chemical Species
Elements + Periodic table
Properties of elements are a function of atomic number
Atomic number increases from left to right in the periodic table
In 18 columns, all elements in the same column has the same valence number.
Valence: number of hydrogen atoms that will bond with one atom of the element in question
Atomic number: number of protons in the nucleus
Atomic weight: combination of proton + neutron in nucleus
Atomic weight can vary, but atomic number is fixed for an element.
Electronegravity
Property of an element that attempts to acquire rather than lose electrons
Linus Pauling (twice noble prize winner)
Difference in electronegravity between two atomes Xa and Xb
|Xa – Xb| = 0.208 [Dab – (Daa Dbb)1/2]1/2
Daa Dbb – geometric mean
Dab
-- bond energy of AB
Daa
-- bond energy of AA
Dbb
-- bond energy of BB
Oxidation state
Quantify changes in an element during oxidation/reduction reactions
Simple atomic substances oxidation state = net charge of valence of the atom
Cl-1 = -1, Fe+2 = 2
(1)
(2)
(3)
(4)
oxidation state of all elements in allotropic (pure substance) form = 0
oxidation state of oxygen = -2 in all compounds except peroxides
oxidation state of hydrogen = +1 except in hydrides
all oxidation states are selected so as to make the algebraic sum of the oxidation state = to the
net charge of the molecular
CH40 (methane)
Carbon = -4 because rule 3 states that H = +1
CO20
Carbon = +4 because rule 2
H-COOH (formic acid)
Carbon = +2
2
HPO4-2
P = +5
Atoms will bond with the atoms to form stable or quasi-stable polyatomic structures (molecular)
--attain lowest state of energy
Three atomic bond
Ionic bond -- simple electrostate attraction between electron positive (e.g., alkalis earths + metals)
electronegative elements
--mutual coulombic attractions result in a stable crystal
octef rule is satisfied
covalent bond -- for atoms with the same electron affinities
sharing of electrons in the ansence of coulombic attraction
no permanent charge transform
electrons distribute themselves evenly around nuclei's to form a molecular orbital
unique to the molecule
Coordinate - covalent bonds -- electrons that one shares in the "inner shell" orbitals
Chemical Thermodynamics
System & region or object selected for the study and it's bounded by surrounding
System can be further divided into physically and chemically homogeneous phases
Close system vs open system
close system can exchange heat and work (not matter)
Extensive properties -- additive properties (ex, mass, moles)
Intensive properties -- nonadditive properties (ex, temperature, pressure)
Extensive: volume, entropy, moles, enthalpy, free energy
Zero (0) law of thermodynamics
Systems in thermal equilibrium have same temperature
1st law
the change in internal energy "E" is = to the sum of heat transformed and work done in the system
dE = dq + dw
where q is heat transformed and w is work done in the system
close system at constant volume
w = force x change in volume
if we assume that there is no change with time, w = 0
so dE = dq, if for finite changes, E = q
exothermic reaction: heat evolve
ondothermic reaction: heat is absorbed
chemical reactions do not run at constant volume, but we can maintain constant pressure
heat evolved not = internal energy
so we must define a function called "enthalpy", H = E + P V
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dH = dE + P dV + V dP
2nd law
(V dP = 0, if P is constant)
(closed system in contact with surrounding)
the entropy of an isolated system increases in the course of spontaneous changes
the total entropy
dS = sum of entropy changes in the system dSin and the entropy transferred to the system from
surroundings dSsurr
dS = dSin + dSsurr
Two states
Microscopic -- quantify the position velocity of every atom in the system
Macroscopic -- eg, defined by V, T, P
Entropy -- is the number of microscopic states associated with a particular macroscopic state
Deck of cards has two macroscopic states: ordered and disordered.
Microscopic leads many possible states
Ordered microscopic state = ordered macroscopic state
As the number of microscopic state increases, the entropy of the system also increases
Increases of entropy measures the response of systems moving from low probability situation to
high probability situation
Spontaneous change
Reversible + irreversible
Reversible change that occurs spontaneously and is easily reversed by small changes in the
opposing force
Irreversible changes: reactions will not reverse itself if small changes in the opposing occur
Entropy is transformed to a closed system from surrounding
dSsurr = dq/T
where q is change in heat
Entropy changes inside the system
For reversible processes, dSin = 0
For irreversible processes, dSin >= 0
So dSsys = dSin + dSsurr >= 0+ dq/T >= dq/T
Reversible processes (equilibrium)
dS = dq/T
>>
dq=T dS
from 1st law, dE = dq + dW = T dS + dW
if the work is defined by expansion, dW = -P dV
dE = T dS - P dV
so
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dH = dE + P dV +V dP = T dS + V dP
Free energy is energy available for work
A=E-TS
dA = dE - T dS - S dT = T dS - T dS + V dP - S dT = -T dS - S dT
expresses free energy in terms of changes in volume
(usually not used because change in volume is hard to measure)
Gibbs
G =H -T S
dG = dH - S dT - T dS = T dS + V dP -S dT - T dS = V dP - S dT
for constant temperature and pressure, dP = dT = 0 and dG=0
Irreversible processes:
dS > dq/T
>>
dE < T dS - P dV
dH < T dS + V dP
dG < V dP - S dT
constant entropy + volume, dE < 0
constant entropy + pressure, dH < 0
constant pressure + temperature, dG < 0
T dS > dq
Conditions of equilibrium
Reversible
Spontaneous (irreversible)
dG = 0
dG < 0
Processes @ constant temperature and pressure
G=H-TS
DG = dH - S dT - T dS = dH - T dS
For finite change, G = H - T S
3rd law
entropy of a perfect substance (i.e., crystal and glass is not crysatl) = 0 at one absolute temperature
= 0 and @ constant pressure: dH = T dS + V dP = T dS
dS = dH/T
heat capacity: Cp = dH/dT
amount of heat required to raise one mole of material on degree C
process at constant T & P
dH = Cp dT
 dS =  Cp dT/T
S = T1T2 Cp dT /T
Open system
Internal energy we can define heat, work and matter exchange
dE = T dS - P dV +  i dni
heat work partial molar free energy term = f (matter)
i = G / ni = rate in change of free energy divided by change in number of moles
chemical potential
dG = V dP - S dT +  i dni
work heat partial molar free energy term
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at constant T & P,
dG =  i dni
comparison
for closed system,
dG = 0
for open system with exchange heat and work, dG =  i dni
chemical potential - quantifies the capacity of a system to work other than pressure - volume work
e.g., a cup of water
>
adding gas
>
water moles don't change
so water is not part of reaction, but chemical potential of water change
convenient way to determine variation in  of one component if  and  # of moles of other
components are known.
Gibb-Duken equation
Variation in dG for a component system is strictly a function of the number of moles in the phase
dG = i dni
G = i ni
Several pure phase mixed together
G = i ni + 2 n2 + …… + i ni
dG =  i dni +  ni di
G =  i ni
For open system, we have
dG = V dp - S dT +  i ni =  i dni +  ni di
at constant T & P
dG =  ni di
at equilibrium
dG = 0 =  ni di
Gibbs-Duken equation
Chemical potential & ideal gasses
dG = V dP - S dT
and
 dG = nRT  dP / P
G - G0 = nRT ln (P/P0)
G = n i
dG = V dP at constant temperature and V = nRT/P
(G - G0)/n= RT ln (P/P0)
i - i0 = RT ln (P/P0)
i == i0 + RT ln (P/P0) = i0 + RT ln P +RT ln P0
ln P0 = ln 1 = 0 and i0 = chemical potential of pure gas at P0 ( 1 atmosphere)
i == i0 + RT ln P
>>
di == RT dln P
0 = n1 RT d ln P1 + n2 RT d ln P2
0 = n1 d1 + n2 d2
Ideal solution
P = Xi P 0
Where X is mole fraction and P0 is vapor pressure of a pure substance
i == i0 (gas) + RT ln (Xi P0)
i == i0 (gas)+ RT ln P0 + RT ln Xi = i0 (liquid) + RT ln Xi
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Non-ideal solution
ai = I Xi
Where a is activity of I and  is activity coefficient of I
i == i0 (gas)+ RT ln ai
i == i0 (liquid) + RT ln Xi + RT ln i
same as ideal solution potential molar free energy excess
positive deviation of  from Raoult's law, i.e.,  > 1.0
negative deviation of  from Raoult's law, i.e.,  < 1.0
ideal solution,  = 1.0
in a dilute solution
component 1 = solvent
component 2 = solvent
Xi = 1.0
Xi = 0.0
Gas in "real solution" (non-ideal) behaves by Henry's law
P=KX
K is Henry's law constant
Thermochemistry
at constant T & P
at equilibrium
dG =  i dni
dG = 0 =  i dni
spontaneous reaction:
dG < 0
&
 i dni < 0
Generic reaction
VA A + V B B = V C C + V D D
Where V is stochiometric coefficient and A, B, C, and D are chemical species
Variable that quantifies the extent of a reaction called 
di = Vi dI
>>
dG =  i Vi di
G = dG/d =  i Vi
free energy of the reaction
at equilibrium, G = 0 =  i Vi
spontaneous reaction, G <  i Vi
i == i0 + RT ln ai -- multiply by  Vi
 Vi i =  Vi i0 + RT Vi ln ai
dG/d =  i Vi = G0 + RT ln  aVi
VA A + V B B = V C C + V D D
G = G0 + RT ln ([C]VC [D]VD)/([A]VA [B]VD)
 aVi = 0 = ([C]VC [D]VD)/([A]VA [B]VD)
Free energy of formation - G0
i0 = Gf0
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pure elements: Gf0 == 0
relative change in free energy of formation of compounds could be + or - (lots of compound is -)
 G0 = (Vi Gf0)products - (Vi Gf0)reactions
G = G0 + RT ln Q
at equilibrium, G = 0 and substitute Q for K where K is equilibrium constant
G0 = -RT ln Q
Q/K (thermodynamic constant) = 1.0
Q/K < 1.0
Q/K > 1.0
at equilibrium
reaction proceed
no reaction
For thermodynamic equilibrium
K = ([C]VC [D]VD)/([A]VA [B]VD) = Q (if now at equilibrium)
This relationship is called the law of mass action or mass law equation
Solubility
CaCO3 (solid) = Ca+2 + CO3
Ksb - solubility product
Gas exchange
[CO2](solution) =  CO2 (gas)
henry's law constant
KH =  CO2 (gas) / (CO2)(solution)
Acid-base
HA = H+ + AAcidity constant
Kiq = [H+] [A-] / [HA]
Complexation
Hg+2 + 3 Cl- = Hg Cl3Stability constant
Kb = [Hg Cl3-]/[ Hg+2] [Cl-]3
Rules
(1) {i} = i [i]
where is activity coefficient and [i] is moles concentration of i
 equals 1.0 for every dilute solution (dilute reference state)
(2) for solvent
{i} = i Xi
where X is moles fraction
Raoults law is obeyed for dilute solution
 = 1.0 and X =1.0
(3) pure solids
{i} = 1.0 and liquid
(4) for a mixture of liquid
Temperature effect
G0 = -RT ln K = H0 - T S0
{i} = Xi
{i} = 1.0
{i} = 1
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ln K1 = -H0/RT1 - T1 S0/RT1
ln K2 = -H0/RT2 - T2 S0/RT2
ln (K2/K1) = - H/R (1/T2 - 1/T1)
van't Haff equation
 H0 = (Vi Hf0)products - (Vi Hf0)reactions
where H is entropy of formation and V is stoichiometric coefficient
define
G0 = -RT ln K at 25 degree C and 1 atm
Ionic strength effects
The behavior of electrolytes
In dilute solution
[i] = 0  = 1.0
reference state at infinite dilution
infinite concentrations of i or other species increase  not = 1.0
electrostatic repulsive / attractive forces + separation of charge