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Chemical Equilibrium
& Activity
Equilibrium Constant
Most chemical systems are governed by equilibria
such that if:
a A + b B c C + d D, then
a b
c d
a b
c d
A B
C D
K
x x
ax x x a a
a a K a b
c d
[][ ]
[ ][ ]
Indilutesolutions, 1 ,ifweassume 1 ,
where [X], istheactivitycoefficient ( )( )
( )( )
Equilibrium constants may be written for dissociations, associations, reactions,Equilibrium constants may be written for dissociations, associations, reactions, or distributions.
©Gary Christian, Analytical Chemistry, 6th Ed. (Wiley)
Equilibrium Constant
- If K is very large, that the equilibrium lies far to the right
(or towards products). If K is small, the reaction lies
towards reactants.
- Knowledge of reaction stoichiometry and the equilibrium
constant allows us to make some predictions about the
system.
a b
c d
A B
C D
K
[ ][ ]
[ ][ ]
a A + b B c C + d D
Important items to regarding K
expressions
1. All solute concentrations should be in mol/L (M).
2. All gas concentrations should be in atmospheres.
3. By convention, all K’s are calculated relative to 1 M
solutions or 1 atm gas, so the resulting constants are
dimensionless.
4. Concentrations of pure solids, pure liquids and
solvents are omitted from the equilibrium constant
expression.
Equilibrium constant expressions are
thermodynamic relations.
Equilibrium and Thermodynamics
• Gibbs free energy:
• If K >1 G
o
<0 Spontaneous
• If K<1 G
o
NOT Spontaneous
G RT
o
o
K e
G -RT K
/
ln
− ∆
Reaction Quotient (Q)
The equilibrium constant expression with non-
equilibrium concentrations plugged in.
• If Q>K, the reaction must proceed to the left
• If Q<K, the reaction must proceed to the right
• If Q=K the reaction is at equilibrium
Using equilibria to characterize
systems
Solubility: solubility product (Ksp)
Complexation: formation constants (Kn),
cumulative formation constants (n)
Acids and Bases: acid dissociation constant
(Ka), base hydrolysis constant (Kb)
Solubility
The solubility product (Ksp) describes the concentrations of
species present when ions are in equilibrium with
undissolved salt.
Example: CaCO 3 = Ca
2+
+ CO 3
2-
K= [Ca
2+
][CO 3
2-
]/[CaCO 3 ]= [Ca
2+
][CO 3
2-
] = Ksp = 6.0 x 10
What is the concentration of calcium in a saturated solution
of calcium carbonate?
Solubility - Separation by
precipitation
It is possible to quantitatively separate two or more species
based on their solubility.
Ability to do so is related to the magnitudes of the Ksp for each
ion.
Example:
Is it possible to precipitate 99% of 0.010M Ce3+^ by adding
oxalate (C 2 O 4 2-) without precipitate 0.010M Ca2+
CaC 2 O 4 Ksp = 1.3 x 10-
Ce 2 (C 2 O 4 ) 3 Ksp = 3.0 x 10-
Acids and Bases
- Definitions: Lewis – Electrons (acid: electron pair acceptor);
BrØnsted-Lowry (acid: proton donor)
- Conjugate Acid-Base Pairs: related by the gain or loss of one
proton (ex. Acetic acid & acetate ion).
- Neutralization Reactions: reactions of acid and base to form salts
and water
- Solvent Autoprotolysis or self-ionization: water is the most
common, in which it acts both an acid and a base:
H 2
O OH^
2 H 2 O H 3 O
14 3
[ ][ ] [ ][ ] 10
− −
Kw HO OH H OH
Autoprotolysis constant (equilibrium constants)
pH
H 2 O OH
P-function: pX = - log10[X]
pH = -log [H
]
pH > 7 is basic, pH<7 is acidic
pOH=-log[OH
]
pH + pOH = pKw = 14.00 at 25oC
Ex. Concentration of H
and OH
in pure water at 25
o
C
ANS: 1.0x10-7^ M
Activity Coefficient
- Related to the size of the hydrated species
- Calculate using the extended Debye-Hückel equation,
which relates activity coefficients to the ability of ions in
solution to interact with one another.
log
2
α μ
μ
z
r
z = charge of the ion
= effective diameter "hydrated" of the ion in nanometers
= ionic strength of the solution
Ionic Strength
i
i i
c z cz cz
2 2
22
2
11
Ex. What is the ionic strength of a 0.010 M Na 2 SO 4?
½{(0.0201)+(0.010*(-2)^2 )}=0.030 M
If add 0.020 M KBr?
½{(0.0201) + (0.0201) + (0.0201) + (0.010*4)}=0.050 M
where c is concentration and z is charge of each ion
The greater the ionic strength of a solution, the higher the charge in the
ionic atmosphere. Each ion-plus-atmosphere contains less net charge and
there is less attraction between any particular cation and anion.
Ionic Strength and Ionic Atmospheres
Hydrated Radius
radii and large charge
tend to more strongly
bind to solvent molecules
(Ion-dipole interactions).
- The result of this binding
is a larger hydrated
radius, causing
diminished interaction
with other ions.
Ionic Strength, Ion Charge, and Ion Size effect
decreased activity coefficient
increased departure of activity
coefficient from unity
(Multiply charged ions are
generally more likely to
interact with other ions than
singly charged.)
increased importance of
activity effects
305
1
- 51 log
2
α μ
μ
= −
z r
pH Revisited
• Concentration is replaced with activity
pH = -log aH+ = -log [H
]γH+
Examples :
- Calculate the pH of pure water using activity coefficients
correctly.
- Calculate the pH of water containing 0.10 M KCl at 25oC.
