Analytical Chemistry 7ed 2014 by Gary D. Christian, Purnendu K. Dasgupta, Kevin A. Schug

1. Chapter 6
General Concepts of
Chemical Equilibrium

2. Introduction Chemical Equilibrium
Ø The state where the concentrations
of all reactants and products
remain constant with time.
Ø Equilibrium is not static, but is a
highly dynamic situation.

3. Chemical Reactions: The rate Concept
Ø A + B C + D ( forward)
Ø C + D A + B (reverse)
Ø Initially there is only A and B so only
the forward reaction is possible
Ø As C and D build up, the reverse
reaction speeds up while the forward
reaction slows down.
Ø Eventually the rates are equal

4. ReactionRate
Time
Forward Reaction
Reverse reaction
Equilibrium
Dynamic?
Rate forwards = Rate reverse

5. The equilibrium constant
Law of Mass Action
Ø For any reaction
Ø aA + bB cC + dD
Ø [C]c[D]d
[A]a[B]b
Ø K is called the equilibrium constant.
Ø is how a reversible reaction is
identified
K =

6. v Comments on Law of mass action
v K is constant regardless of the amounts
of materials mixed initially
v Equilibrium concentrations will not
always be the same but K is the same
v Each set of equilibrium concentrations
in an equilibrium system is called
equilibrium position
v There is only one K value for a given
system but infinite number of
equilibrium positions
v The law of mass action applies to
solution and gaseous equilibria

7. Changing the chemical equation of an
equilibrium system: Reciprocal rule
Ø If we write the reaction in reverse.
Ø cC + dD aA + bB
Ø Then the new equilibrium constant is
Ø K reversible=
forwardK
1
[D][C]
[B][A]
dc
ba
= Reciprocal rule

8. Multiplying the equation by a coefficient:
Coefficient Rule
Ø If we multiply the equation by a
constant
Ø naA + nbB ncC + ndD
Ø Then the equilibrium constant is
Ø K =
[C]nc[D]nd
=
([C] c[D]d)n
=
Kn [A]na[B]nb ([A]a[B]b)n

9. Rules of Multiple Equlibria
Ø Reaction 3 = Reaction 1 + Reaction 2
A2 B A + AB K1 = 2.2
AB A + B; K2 = 4.0
A2B 2A + B
K3=2.2 X4.0 = 8.8
][
][][
2
2
BA
BA
K3 = K1XK2
K3 = = K1XK2
Ø K (Reaction 3) =K (reaction 1) X K (reaction 2)
][
]][[
2
1
BA
ABA
K =
][
]][[
2
AB
BA
K =

10. Notes on Equilibrium Expressions
v The Equilibrium Expression for a reaction is
the reciprocal of that for the reaction written
in reverse.
v When the equation for a reaction is
multiplied by n, the equilib expression
changes as follows:
v (Equilib Expression) final = (Equilib Expression initial)n
v Usually K is written without units

11. Calculation of K
Ø N2 + 3H2 2NH3
Ø Initial At Equilibrium
Ø [N2]0 =1.000 M [N2] = 0.921M
Ø [H2]0 =1.000 M [H2] = 0.763M
Ø [NH3]0 =0 M [NH3] = 0.157M
= 9.47X10-33
22
2
3
]][[
][
HN
NH
K =

12. Ø N2 + 3H2 2NH3
Ø Initial At Equilibrium
Ø [N2]0 = 0 M [N2] = 0.399 M
Ø [H2]0 = 0 M [H2] = 1.197 M
Ø [NH3]0 = 1.000 M [NH3] = 0.157M
Ø K is the same no matter what the
amount of starting materials
Calculation of K

13. Homogeneous Equilibria
Ø All reactants and products are in
one phase, gases for example
Ø K can be used in terms of either
concentration or pressure.

14. Heterogeneous Equilibria
Ø If the reaction involves pure solids or pure
liquids as well as gases, the concentration
of the solid or the liquid doesn t change.
Ø As long as they are not used up they are
left out of the equilibrium expression.
Ø Thus, there is no term for L or S in K
expression.
Ø However, the presence of L or S is a must
for equilibrium to occur.

15. Example: Equilibrium expression for
heterogeneous equilibria
Ø H2(g) + I2(s) 2HI(g)
Ø
Ø But the concentration of I2 does
not change.
Ø
]][[
][
'
22
2
IH
HI
K =
][
][
]['
2
2
2
H
HI
IK = K=

16. Ø The magnitude of K helps prediction of the
feasibility (extent or direction but not the speed)
of the reaction
Ø K> 1; the reaction system consists mostly
products (equilibrium mostly lies to the right)
Ø Systems with very large K go mostly to
completion
Ø Systems with very small values of K do not
occur to any significant extent
Ø There is no relation between the value of K and
the time to reach equilibrium (the rate of reaction)
Ø Time to reach equilibrium depends on Ea for
reactants and products
Applications of the equilibrium Constant

17. The Reaction Quotient, Q
(Quantitative prediction of direction of reaction)
Ø Q Tells how the direction of a reaction will
go to reach equilibrium
Ø Q s are calculated the same as K s, but
for a system not at equilibrium
Ø [Products]coefficient
[Reactants] coefficient
aA(g) + bB(g) cC(g) + dD(g)
Q =
b
B
a
A
d
D
c
C
PXP
PXP
Q
)()(
)()(
=
Ø Compare value of Q to that of K

18. What Q tells us?
Ø If Q<K
Ø Not enough products
Ø Equilibrium shifts to right; forward
reaction is predominant
Ø If Q>K
Ø Too many products
Ø Equilibrium shifts to left; reverse
reaction is predominant
Ø If Q=K system is at equilibrium; there
is no further change

19. Le Chatelier s Principle
Ø if a change is imposed on a system
at equilibrium, the position of the
equilibrium will shift in a direction
that tends to reduce that change.
Ø If a stress is applied to a system at
equilibrium, the position of the
equilibrium will shift to reduce the
stress.
Ø There are 3 Types of stress

20. External conditions that cause a
disturbance to a chemical equilibrium
Ø Adding or removing reactants or
products
Ø Changing the volume (or pressure)
of the system
Ø Changing the temperature

21. The effect of a change in concentration of
reactants and/or products
Ø Adding product makes Q>K
Ø Removing reactant makes Q>K
Ø Adding reactant makes Q<K
Ø Removing product makes Q<K
Ø knowing the effect on Q, will tell you
the direction of the shift
Ø Adding or removing liquids or solids
does not affect the equilibrium
Ø The system will shift away from the added component

22. Ø The pressure changes as a result of:
Ø Adding or removing gaseous reactant or
product
Ø Changing the volume of the container
Ø By reducing the volume of the container,
the system will move in the direction that
reduces its volume.
The effect of a Change in Pressure

23. Changes in volume

24. Changes in Temperature
Ø Affects the rates of both the
forward and reverse reactions.
Ø changes the equilibrium constant.
Ø The direction of the shift depends
on whether it is exo- or
endothermic

25. Exothermic
Ø DH<0
Ø Releases heat
Ø heat is a product
Ø Raising temperature shifts the
reaction direction toward reactants
(to the left)

26. Endothermic
Ø DH>0
Ø Heat is added to the system
Ø Heat as a reactant
Ø Raising temperature shifts the
direction of reaction toward
products (to the right)

27. Example
Ø Consider:
A + B C + D
At 25 oC, K is 0.30. Calculate the equilibrium
concentrations of all species if 0.20 mol of A
is reacted with 0.5 mol of B and dissolved in
1.00 L flask
A + B C + D
Initial(mol) 0.2 0.5 0 0
[ ] (mol/L) 0.2 0.5 0 0
Change(mol/L-1) -x -x +x +x
Equilib 0.2-x 0.5-x +x +x

28. 3.0
)1(
)(
)5.0)(20.0(
))((
2
2
=
−
=
−−
=
x
x
xx
xx
K
3.0
)1(
)(
)5.0)(20.0(
))((
2
2
=
−
=
−−
=
x
x
xx
xx
K
0.70 x
2
+ 0.21 X - 0.030 = 0
a
acbb
x
2
42
−±−
−=
X = 0.11 M

29. Example
Ø Consider:
A + B C + D
At 25 oC, K is 2.0x1016. Calculate the equilibrium
concentrations of all species if 0.20 mol of A is
reacted with 0.5 mol of B and dissolved in 1.00
L flask
• Since K is very large, the reaction of A with B will be virtually
complete to the right
• Thus, only traces of A will be left at equilibrium.
• Let x represent the equilibrium concentration of A.

31. Example
Assume 0.10 mol of A is reacted with 0.20 mol of B in a
volume of 1000 mL; K = 1.0 X 10
10
. What are the equilibrium
concentrations of A, B, and C

32. Dissociation Equilibria
Calculate the equilibrium concentrations of A and B in
a 0.10 M solution of a weak electrolyte AB with an
equilibrium constant of 3.0 X 10-6.

33. The Common Ion Effect-Shifting the Equilibrium
Calculate the equilibrium concentrations of A and B in
a 0.10 M solution of a weak electrolyte AB with an
equilibrium constant of 3.0 X 10-6 and 0.20 molar B

34. Systematic approach to equilibrium calcualations
This approach involves writing expressions for mass
balance of species and one for charge balance of
Species
Mass Balance

35. Example

36. Charge balance equations
principle of electroneutrality
• All solutions arc electrically neutral that is,
there is no solution containing a
detectable excess of positive or negative
charge
• The sum of the positive charges equals
the sum or negative charges
• A single charge balance equation lor a
given set of equilibria.

37. Example
The total charge concentrations from all sources is always
equal to the net equilibrium concentration of the species
multiplied by its charge

38. Example
Write a charge balance expression for a solution
containing KCI, AI2(SO4)3 and KNO3. Neglect the
dissociation of water.

39. Example
Write the charge balance equation for a solution of
[Ag(NH3)2]Cl

40. Example
Calculate the equilibrium concentrations of A and B
In a 0.10 M solution of a weak electrolyte AB with an
equilibrium constant of 3.0 X 10-6. Use the mass
charge balance approach

43. Example
Calculate the equilibrium concentrations of A and B
In a 0.10 M solution of a weak electrolyte AB with an
equilibrium constant of 3.0 X 10-6. Use the mass
charge balance approach. Assume the charge A is
+ I, the charge on B is - I, and that the extra B (0.20M)
comes from MB; MB is completely dissociated.