Week 2 Hydrogeochemistry
Example
Angie’s fish tank suffers from the effect of ammonium (NH
4
+ ) from the degradation of urea. In order to determine whether levels in the tank are toxic to her friends, she studies the following reactions.
CO
2, aq
= CO
2, gas
and CO
2, aq
= [H
2
CO
3
]
H
2
CO
3
= H + + HCO
3
and finally: NH
3
+ H + = NH
4
+
If there is 10 -4.5
model/L HCO
3
and 10 -4 NH3, how much NH
4
+ is in solution?
Debye-Huckel theory
Activity {i} = γ i
[i]
For nonideal solution
 i
=
 i
0 + RT ln {i} =
 i
0 + RT ln γ i
[i]
 i
=
 i
0 + RT ln γ i
+ RT ln [i]
Partial molar free energy
RT ln γ
Where Z
Debye-Huckel i
= Z i i
F i
ψ
is charge; F i
is Fanday’s constant; ψ is electrostatic potential
Ψ = -2.303 (RT/F) A Z i
I 1/2
Where I is ionic strength; A is constant; F is dielectric constant at T
A = 1.82 x 10 6 ((εT) -3/2 )
Where ε is dielectric constant; ε = 80 (water at 25 0 C and A = 0.495
RT ln γ
RT ln γ ln γ i log γ i i
= Z i
F
= -2.303 (RT/F) A Z
= -2.303 A Z i
= -A Z i
2 i
ψ
I 2 i
2 I 2 i
I 1/2 (Z i
F i
)
Only good for I less or equal to 5 mM
Extended Debye Huckel log γ i
= -A Z i
2 I 2 / (1 + β a I 1/2 )
Where β = 50.3 [ (εT) -1/2 ]
ε = 80 at 25 0 C and β = 0.326
1

a is adjustable parameter; depends on side of the ion for many electrolytes, β x a = 1.0
Gauter Faure: β x a = 1.0 >> Log γ i
= -A Z i
2 I 2 / (1 + I 1/2 )
Example
I – ionic strength; imply a quantity of all species in the solution
I = ½ ∑ Z i
2 [i]
Find I of 0.1 mM CaCl
2
solution
I calculated from conductivity
I = 1.6 x 10 5 x conductivity (μ mho cm -1 ); strictly empirical
I calculated from total dissolved solids (TDS)
I = 2.5 x 10 -5 x TDS (mg/l)
Davis equation log γ i
= -A Z i
2 / [ (I 1/2 /(1+I 1/2 )) - 0.2 I], for I less or equal 0.5 M
Notice {i} are not equal [i] because of electrolytes
K = {C} 1/c {D} 1/D / {A} 1/A {B} 1/B = [γC] 1/c [γD] 1/D / [γA] 1/A [γB] 1/B
K = [γ] 1/c [γ] 1/D / [γ] 1/A [γ] 1/B x [C] 1/c [D] 1/D / [A] 1/A [B] 1/B
K c
– concentration equilibrium constant
K c
= K x [γ] 1/A [γ] 1/B / [γ] 1/c [γ] 1/D
2