Transcript Lecture 8
Equilibrium Constants
Lecture 8
• • • • • •
The Equilibrium Constant
Consider the reaction aA + bB = cC + dD The Free Energy change of reaction is:
∆G = cµ c At equilibrium: + dµ d
∆
– aµ a G
= å
– bµ b
n
i µ i
= 0
Expanding the right side
å n
i µ i o
+
RT
å n
i
ln
a i
= 0
or
å n
i µ i o
+
RT
ln Õ
a i
n
i
= 0
i We define the right term as the equilibrium constant:
K = ln Õ
i a i
n
i
• • • •
Free Energy and the Equilibrium Constant
Since: å n
i µ i o
+
RT
ln Õ
i a i
n
i
å n
i µ i o
= ∆
G r o
= 0 then ∆
G r o
-
RT
lnK = 0 and ∆
G r o
= -
RT
ln K Note of caution: our thermodynamic parameters are additive, but because of the exponential relation between the equilibrium constant and free energy, equilibrium constants are multiplicative.
• •
Manipulating Equilibrium Constants
Suppose we want to know the equilibrium constant for a reaction that can be written as the sum of two reactions, o e.g., we can sum
Fe
3 +
aq
+
e
-
Fe
2 +
aq
o o to yield
Fe
(
OH
) 2 +
aq Fe
(
OH
) 2 +
aq
+
e
+ +
H
+
H
+
Fe
3 +
aq Fe
+
H
2
O
2 +
aq
+
H
2
O
The equilibrium constant of the net reaction would be the product of the equilibrium constants of the individual reactions.
For this reason and because equilibrium constants can be very large or very small numbers, it is often convenient to work with logs of equilibrium constants: pK = - log K o (we can then sum the pK’s).
• • •
Apparent Equilibrium Constants and Distribution Coefficient
In practice, other kinds of equilibrium constants are used based on concentrations rather than activities.
K D
= Õ
X i
n
i
Õ
i i
K
app
= K
eq
K l = K
eq
Õ l
i
n
i
•
Other Forms
A ‘solubility constant’ is an equilibrium constant. For example: K =
aq a Na
+
aq a Cl
-
a NaCl s
o Since the activity of NaCl in halite = 1, then K
SP
=
a aq Na
+
a aq Cl
• Henry’s Law constants for describing solubility of gases in solution (e.g., CO 2 in water).
o Since
P i = h i X i h i
=
P i X i
• • • •
Law of Mass Action
Important to remember our equation K = Õ
a i
n
i i
describes the equilibrium condition. At non-equilibrium conditions it is called the reaction quotient, Q.
Written for the reaction H 2 CO 3 = HCO 3 + H + K =
a HCO
3 -
a H
+
a H
2
CO
3 We can see that addition of H + the left.
will drive the reaction to
“Changing the concentration of one species in a reaction in a system at equilibrium will cause a reaction in a direction that minimizes that change”
.
• • • •
Le Chatelier’s Principle
We can generalize this to pressure and temperature:
dG = VdP - SdT
An increase in pressure will drive a reaction in a direction such as to decrease volume An increase in temperature will drive a reaction in a direction such as to increase entropy.
“When perturbed, a system reacts to minimize the effects of perturbation.”
•
Temperature and Pressure Dependence
Since
∆G˚ = ∆H˚ - T∆S˚
and ∆G˚ = -RT ln K then ln K = ∆
H RT r o
+ ∆
S r o R
• Temperature and pressure dependencies found by taking derivatives of this equation with respect to T and P.
Oxidation and Reduction
Oxidation refers to processes in which atoms gain or loss electrons, e.g., Fe 2+ Fe 3+
• • • •
Valence and Redox
We define valence as the charge an atom acquires when it is dissolved in solution.
Conventions o Valence of all elements in pure form is 0.
o o o Sum of valences much equal actual charge of species Valence of hydrogen is +1 except in metal hydrides when it is -1 Valence of O is -2 except in peroxides when it is -1.
Elements generally function as either electron donors or acceptors.
o Metals in 0 valence state are electron donors (become positively charged) o Oxygen is the most common electron acceptor (hence the term oxidation) Redox o o A reduced state can be thought of as one is which the availability of electrons is high An oxidized state is one in which the availability of electrons is low.