CE 520 Environmental Engineering Chemistry
Lecture 1
S.K. Ong
Equilibrium Constants
Let us use a general chemical reaction that is reversible (i.e., forward and reverse reaction may occur) as shown
below:
Assume that in a small container at time = 0 we add A and B together. If we were to plot the activities or
concentrations of the reactants (A and B) and the products (C and D) we will notice the following: activities or
concentrations of A and B will be reduced until they reach a steady value. At the same time, activities or
concentrations of C and D will increase until they reach a constant value. When A, B, C, and D activities reach
constant values, we say that the reactions is at equilibrium.
If we take the ratio of the activities or concentrations of the products to reactants, the ratio is called the equilibrium
constant or the mass law equation.
For our purposes, i.e., working with aqueous solutions, concentrations (expressed in terms of molarity) of reactants
and products are used in the equilibrium constant expression.
However, as solutions become more concentrated, the inter-ionic interactions of ions coupled with changes in
hydration with concentration, affect the interactiveness of the ions. Thus the activity of the ions or the effective
concentrations is decreased below the actual molar concentrations. In concentration terms, the equation may be
expressed as:
where { } means activity while [ ] means concentration.
In expressing the equilibrium constants, the following convention is usually followed:
1. Ions and molecules in _____________ - concentration or activity is expressed in _________________.
2. ____________ in a dilute solution – eg., water - the concentration or activity of the solvent is taken _________.
3. _______________________________ in equilibrium with the solution:
- concentration or activity of the solids is taken as ______________.
4.
________________________ - concentrations or activities of the liquids are expressed as mole fractions, i.e., 2
types of liquids A and B with moles of M A and MB moles each. The mole fraction of liquid A is :
5. _______________ - concentration or activity of a gas is expressed as _______________________________.
Equilibrium constants for various reactions:
1. ____________________________ - for weak acids and bases when they ionize in aqueous solutions eg.,
dibasic acid - H2CO3
H2CO3 <===> H+ + HCO3HCO3- <===> H+ + CO32the equilibrium constants or ionization constants (K1 and K2) are given by:
When water is ionized as given H2O <==> H+ + OH-,
we have :
or by convention H2O is the solvent, i.e., the activity is unity we have:
[ H  ][OH  ]  K w  10 14
where KW the equilibrium constant is the ionization constant or ____________________ of water.
2. _______________________: Solids present in water will dissolve slightly to form the following equilibria,
eg., AgCl
AgCl (s) <===> Ag
+
+ Cl
-
Ksp is called the solubility product constant
+
-
by convention [AgCl (s)] = 1, therefore Ksp = [Ag ] [Cl ]
.
3. _______________________________ - generally used for formation of complex compounds such as
Equilibrium relationships are written as _______________________ of the complex rather than as dissociation
reaction:
and K2, K3 and K4. These equilibrium constants are known as __________________________.
4. __________________________. If a gas is in equilibrium with the dissolved phase in water, eg., benzene (C6H6)
by convention, concentration or activity of gases should be expressed in atmosphere, therefore
where KH is the Henry's Law constant.
Activity
To relate the activity {i} of a compound to the analytical concentration [C i] of the compound, a proportionality
constant called the activity coefficient, i, is introduced. The relationship is:
{i} = i [Ci]
Note that single ion activity coefficients are constructs and are not measureable individually since it is not possible
to dissolve a cation only in water as there must be corresponding anion. But the use of single ion activity
coefficients greatly simplifies calculations. To calculate the activity coefficients of ions in aqueous solution, the
ionic strength, , of the solution is used:
 = ½ ∑ Ci (Zi)2
Ci = concentration (moles/liter)
Zi = charge of the species
Example: Seawater with the following composition
Species
Na+
Ca2+
Mg2+
K+
ClSO42HCO3-
Conc. (mg/l)
10,000
400
1,300
380
19,000
2,700
142
moles/l
0.43
0.01
0.056
0.0097
0.535
0.028
0.0023
Ionic Strengths of various waters
Types of water

Distilled Water
10-7 - 10-4
Drinking water
0.005 - 0.002
River
0.001 - 0.1
Seawater
0.6 - 2.0
Zi
1
2
2
1
1
2
1
0.5 ∑CiZi2
CiZi2
0.43
0.04
0.224
0.0097
0.535
0.112
0.0023
0.676
__________________________________
Water
TDS (mg/l)

Rain water
10
0.00025
Niagara River
165
0.0041
Well River, OH
440
0.011
Seawater
34,500
0.863
Rather than calculate the ionic strength from individual species, ionic strength can be estimated from total dissolved
solids (TDS) and specific conductance of the solution. Equations relating these two parameters are:
 = 2.5 x 10-5 TDS
 = 1.6 x 10-5 (specific conductance)
TDS in mg/l
Conductance in µmho/cm
Note: From the above two equations, we can estimate the TDS of the solution by measuring the specific
conductance, i.e.,
TDS = 0.64 x specific conductance
Equations to estimate activity coefficients:
________________________________________________________________________________
Name
Formula

________________________________________________________________________________
Debye-Huckel
log i = - A Zi2 √ 
Extended Debye-Huckel
log  i 
Guntelberg Approx.
Davies Approx.
< 10-2.3
 AZi 2 
<10-1
1 a i 
ai = effective radius of hydrated ion (in angstrom units, see attached table)
A = 1.82 x 106 /( T)3/2 ≈ 0.5
 = 50.3 /( T)1/2
≈ 0.33
where  = dielectric constant of the medium
log  i 
 12 Z i 2 
<10-1
1 



log  i   12 Z i 2 
 0.2  
 (1   )

< 0.5
beyond 0.5 no satisfactory
theory
___________________________________________________________________________________
For nonelectrolytes in aqueous solutions - for example, oxygen or organic compounds, there are no fundamental
equations available to predict the activity coefficients. Instead an empirical equation is used:
log i = ksi 
where ksi is defined as the salting out coefficient.
Example: for oxygen in river ( = 0.001) and sea water ( = 0.7), the activity coefficients are given by:
River :
log  = 0.132 x 0.001,
 = 1.0001
where ks = 0.132
Seawater
log  = 0.132 x 0.7,
 = 1.10
where ks = 0.132
For nonelectrolytes, the activity coefficients are greater than one. Water molecules have a tendency to associate
with the ions (a preference for ions rather than the nonionic compounds) such that the solubility of the nonionic
compounds will decrease with increasing salt concentration – a salting out effect. For gases such as oxygen, the
activity of the nonionic compound is controlled by the partial pressure of the compound in the atmosphere and is not
a function of the salt concentration in the solution. Therefore for the expression:
{i} =  [C]
 is greater than one.