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# Aqueous Environmental Geochemistry by aR8wG9

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```									                                Fall 2007

Aqueous Environmental
Geochemistry

Brooklyn College
The City University of New York
Natural Systems
Open and Close Natural Systems

•   Natural systems can be large or small
•   Different phases
•   In relative sense
•   Reaction rates vs. Flux rates
Gibbs Phase Rule
• F=C–P+2
What do C and P mean?

• Example:
H2O (ice) = H2O (liquid) = H2O (vapor)

• F = C’-R – P + 2:
What are C’ and R? Give one example.
Ehthalpy (H)
•   Heat content at constant pressure
•   Heat of formation from elements
•   ΔHf0 for (most stable form) element is zero
•   ΔHr0 : Heat exchange
ΔHr0 : H>0, endothermic
ΔHr0 H<0, exothermic
• How T & P change affect the equilibrium of
a reaction?
Entropy (S)
• Degree of randomness or disorder
T   Cp
ST  S 0            dT
0    T
• Cp: heat capacity. Energy needed to raise the
temperature of 1 mole by 1 K
• At 0 K, most substances S=0
• S increases as temperature increases
Gibbs Free Energy (G)
• At equilibrium condition:
ΔGr0 = - RT ln Keq
R: gas constant, 1.9872 cal/mol K
T: 25 ºC, or 298.15 K
• Can be transformed into:
ΔGr0 = -0.59248 ln Keq
= -1.3642 log Keq
Direction of Reaction

ΔGr = ΔGr0 + RT ln Q
• Q: reaction quotient
• Sign of ΔGr indicate the direction of reaction
Chemical Potential (µ)
• Similar to Gibbs Free Energy
• µi = µi0 + RT ln(αi)
- Chemical potential is for individual component

- αi is activity, which is different than concentration!

• At equilibrium, is the same for the same
component in different phases!
Solutions
• In solutions
(αi) = λi · Ni
-λ   is the rational activity coefficient
- for ideal solutions, λ ≈ 1 for major components (Raoult’s Law);
- for ideal solutions, λ ≠ 1 for minor components or dilute solutions
(Henry’s Law)
- See Fig. 1.3 for differences
Solid Solutions (binary mixing)
• Only equations to remember:
ln λA = α0 NB2
ln λB = α0 NA2

 Can be treated as exchange reaction:

KAX   AmA    BNB 
Kex                    
KEX   BmB    ANA 
Keq Dependence on T
•   Empirical constants
•   Determined in experiments
•   Table 1.1 (P39-45)
•   Equation:

F
log Keq  A  BT   D log T  ET 
C
T
2
 GT 1/ 2

T2
• Calculate ΔGr0 , ΔHr0 ΔCpr0 ΔSr0
• ΔHr0 controls the dependence.

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