Transcript Mixing in water

Mixing in water
• Solutions dominated by water (1 L=55.51 moles
H2O)
• aA=kHXA where KH is Henry’s Law coefficient –
where is this valid? Low concentration of A
1.0
aH2O
Raoult’s Law – higher
concentration ranges (higher XA):
aA
Activity
mA=mA0+RTlnGAXA
where GA is Rauolt’s law activity
coefficient
Ideal mixing
0.0
0.0
H2O
Mol fraction A
1.0
A
Activity
• Activity, a, is the term which relates Gibbs
Free Energy to chemical potential:
mi-G0i = RT ln ai
• Why is there now a correction term you might
ask…
– Has to do with how things mix together
– Relates an ideal solution to a non-ideal solution
Activity II
• For solids or liquid solutions:
ai=Xigi
• For gases:
ai=Pigi = fi
Xi=mole fraction of component i
Pi = partial pressure of component i
mi = molal concentration of component i
• For aqueous solutions:
ai=migi
Activity Coefficients
• Where do they come from??
• We think of ‘ideal’ as the standard state, but
for dissolved ions, that is actually an infinitely
dilute solution
• Gases, minerals, and bulk liquids (H2O) are
usually pretty close to 1 in waters
• Dissolved molecules/ ions are 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!
• Use activities (ai) to apply thermodynamics
and law of mass action
ai = gimi
• The activity coefficient, gi, is found via
some empirical foundations
Dissolved species gi
• First must define the ionic strength (I) of the
solution the ion is in:
I   mi z i
2
i
Where mi is the molar concentration of species i
and zi is the charge of species I
Activity Coefficients
• Debye-Huckel approximation (valid for I:
 log g 
2
Az I
1
2
1
2
I  aBI
• Where A and B are constants (depending
on T, see table 10.3 in your book), and a is
a measure of the effective diameter of the
ion (table 10.4)
Different ways to calculate gi
•
•
•
•
Limiting law
Debye-Huckel
Davies
TJ, SIT
models
• Pitzer, HKW
models
Neutral species
• Setchnow equation:
• Logan=ksI
For activity coefficient (see table 4-2 for
selected coefficients)
Law of Mass Action
• Getting ‘out’ of the standard state:
P
P
dP
0 dG  RT 0 P
P
P
GP – G0 = RT(ln P – ln P0)
GP – G0 = RT ln P
• Accounting for free energy of ions ≠ 1:
m=m0 + RT ln P
• Bear in mind the difference between the standard
state G0 and m0 vs. the molar property G and m (not
at standard state  25 C, 1 bar, a mole)
Equilibrium Constant
•
For a reaction of ideal gases, P becomes:
 PCc PDd 
for
aA
+
bB

cC
+
dD
  RT ln Q
RT ln 
 P a Pb 
 A B
•
•
Restate the equation as:
DGR – DG0R = RT ln Q
AT equilibrium, DGR=0, therefore:
DG0R = -RT ln Keq
where Keq is the equilibrium constant
Assessing equilibrium
[ products]
n
K
i
[reactants]
n
i
[ products]
Q
[reactants]
n
i
n
i
If DGR – DG0R = RT ln Q, and at equilibrium DG0R = 0, then:
Q=K
Q  reaction quotient, aka Ion Activity Product (IAP) is the
product of all products over product of all reactants at any
condition
K  aka Keq, same calculation, but AT equilibrium
Solubility Product Constant
• For mineral dissolution, the K is Ksp, the
solubility product constant
• Use it for a quick look at how soluble a
mineral is, often presented as pK (table 10.1)
DG0R = RT ln Ksp
• Higher values  more soluble
CaCO3(calcite)  Ca2+ + CO32Fe3(PO4)2*8H2O  3 Fe2+ + 2 PO43- + 8 H2O
Ion Activity Product
• For reaction aA + bB  cC + dD:

C  D 
IAP 
a
b
A B 
c
d
Q
DGR  RT ln
K eq
• For simple mineral dissolution, this is only the
product of the products  activity of a solid
phase is equal to one
CaCO3  Ca2+ + CO32IAP = [Ca2+][CO32-]
c
d

C  D 
IAP 
1
Saturation Index
•
•
•
•
When DGR=0, then ln Q/Keq=0, therefore Q=Keq.
For minerals dissolving in water:
Saturation Index (SI) = log Q/K or IAP/Keq
When SI=0, mineral is at equilibrium, when SI<0
(i.e. negative), mineral is undersaturated
Q
DG   RT ln
K eq
o
R
Q
DG  2.303RT log
K eq
0
R
Calculating Keq
DG0R = -RT ln Keq DGR0   niGi0 ( products)   niGi0 (reactants )
i
i
0
• Look up G i for each component in data tables
(such as Appendix F3-F5 in your book)
• Examples:
• CaCO3(calcite) + 2 H+  Ca2+ + H2CO3(aq)
• CaCO3(aragonite) + 2 H+  Ca2+ + H2CO3(aq)
• H2CO3(aq)  H2O + CO2(aq)
• NaAlSiO4(nepheline) + SiO2(quartz)  NaAlSi3O8(albite)