1. Chemical Equilibria (Gaseous Systems)
Physical Chemistry
Presented by Gabriel Harewood, PhD.

2. Course Content Definition of Chemical Equilibria
Dynamic and Static Equilibrium
Equilibrium Constant, Kc, Kp
Le Chatelier’s Principle
Effect of temperature on K

3. Definition of Chemical Equilibrium
Chemical equilibrium applies to reactions that can occur in both directions.
The following reaction can happen both ways:
CH4(g) + H2O(g)  CO(g) + 3H2(g)
After some of the products are formed, the products begin to react to form the reactants – reversible reaction.

4. Definition of Chemical Equilibrium
At the beginning of the reaction, the rate of the forward reaction is higher than the rate of the reverse reaction.
Therefore, the net change is
more products.
When the net change of products
and reactants are zero – opposing processes occur at the same rate – the reaction has reached equilibrium.
For equilibrium to occur, the system must be a closed.

5. Static vs. Dynamic Equilibrium
Static Equilibrium:
occurs when the sum of the forces and torque acting on the particles in an object is zero – applies to stationary objects.
For example, a stick balancing on a fulcrum or a paperweight on a desk.

6. Static vs. Dynamic Equilibrium
occurs when two reversible processes (e.g., reactions) occur at the same rate – no net change.
You can show dynamic equilibrium in an equation by using special arrows:
At equilibrium, the concentrations of the reactants and products are constant.

7. Chemical Equilibrium & Equilibrium Constant
Consider the Haber Process:
N2 and H2 are combined in a high-pressure tank at high P and T, in the presence of a catalyst to produce ammonia, NH3.
Not all of the reactants are converted.
The reaction achieves an equilibrium where all three compounds are present.

8. Chemical Equilibrium & Equilibrium Constant
According to the Rate Law (see Unit 5: Chemical Kinetics):
Rate of forward rxn = kf [N2] [H2]3 and Rate of reverse rxn = kr [NH3]2
At equilibrium:
Rate of the forward process = Rate of the reverse process
Therefore: kf [N2] [H2]3 = kr [NH3]2
Rearranging this equation: kf / kr = [NH3] = Kc [N2] [H2]3
equilibrium constant

9. Equilibrium Constant Expression
For a reaction: aA + bB  cC + dD
The equilibrium-constant expression is
Kc = [C]c [D]d (Products)
[A]a [B]b (Reactants)
Also, for gaseous systems:
Kp = PCc PDd P – partial pressures PAa PBb
So for the Haber process: Kp = P(NH3)2
P(N2) P(H2)3
What are the units for Kc?

10. Equilibrium Constants
Example: Write the equilibrium expression for Kc for the following reaction:
Answer: Kc = [HI]2
[H2] [I2]
When Kc >> 1: equilibrium lies to the right; mostly products
When Kc << 1: equilibrium lies to the left; mostly reactants

11. Equilibrium Constants
The equilibrium constant for a reaction in one direction is the reciprocal of the one for the reverse reaction, e.g.,
Kp = P(NO2) = 6.46
P(N2O4)
Kp = P(N2O4) =
P(NO2)2
(at 100C)
(at 100C)

12. Example
A mixture of hydrogen and nitrogen in a reaction vessel are allowed to attain equilibrium at 472C. The equilibrium mixture was analysed and found to contain 7.38 atm H2, 2.46 atm N2 and NH3. Calculate the equilibrium constant, Kp, for:
Solution: Kp = P(NH3)2 = (0.166)2
P(N2) P(H2) (2.46) (7.38)3
Kp = 2.79 x 10-5

13. Note
The equation used to determine the equilibrium expression must be balanced!
Use the stoichiometric amounts in the equation to write the equilibrium expression.
Remember that the initial concentrations of a reaction are not equal to the equilibrium concentrations.

14. Relationship Between Kc and Kp
For gases, the pressure is proportional to concentration
PV = nRT  P = nRT/V = [ ]RT  [ ] = P/RT
Consider this system at equilibrium:

15. Relationship Between Kc and Kp
Recall: [ ] = P/RT

16. Relationship Between Kc and Kp
Therefore, the relationship between Kp and Kc is:

17. Le Châtelier’s Principle
In developing the production of ammonia, Haber experimented with various factors to try to improve the production of ammonia.
He calculated the equilibrium constant for the reaction under different conditions and noticed that:
As T increased, [NH3] decreased
As P increased, [NH3] increased

18. Le Châtelier’s Principle
These observations can be explained using Le Châtelier’s principle:
If a system at equilibrium is disturbed by a change in temperature, pressure, or the concentration of one of the components, the system will shift its equilibrium position in order to counteract the disturbance.
Le Châtelier’s principle can be used to make qualitative predictions about the response of a system to these changes.

19. Le Châtelier’s Principle
Change in Reactant or Product Concentrations
A system at equilibrium is in a dynamic state: system is in balance.
Therefore, if a system is at equilibrium and we add a reactant or product, the reaction will shift in order to reestablish equilibrium by consuming some of the added substance.

20. Le Châtelier’s Principle
Change in Pressure and Volume
If the volume of a gaseous system at equilibrium is decreased, (increasing its total pressure), Le Châtelier’s principle suggests that the equilibrium will shift to reduce the pressure.
Avogadro’s law applies:
Number of moles of gas on the left = 4 moles
Number of moles of gas on the right = 2 moles

21. Le Châtelier’s Principle
Will pressure or volume changes affect the following reaction?
Note:
concentration, pressure or volume changes do no change the equilibrium constant if temperature remains constant.

22. Le Châtelier’s Principle
Change in Temperature
When temperature is increased, it is as if we have added a reactant, or a product, to the system at equilibrium, The equilibrium shifts in the direction that consumes the excess reactant (or product), namely heat.
Endothermic rxn: Reactants + heat  products
Exothermic rxn: Reactants  products + heat
For an endothermic rxn,  T leads to  Kc
For an exothermic rxn,  T leads to  Kc.

23. Le Châtelier’s Principle
Effects of Catalysts
The addition of a catalyst to a reaction decreases the activation energy of a reaction.
A catalyst thereby increases the rates of both the forward and reverse reactions.
A catalyst increases the rate at which equilibrium is achieved but does not change the composition of the equilibrium mixture.

24. Le Châtelier’s Principle
Application to Haber Process:
-ve enthalpy means low T favoured

25. Summary Chemical Equilibria Static and dynamic equilibrium
Equilibrium expression and constants
Le Châtelier’s principle, effects of the following on equilibria:
Concentration changes
Volume or pressure changes
Temperature changes
Addition of a catalyst
Haber Process

26. Next Aqueous Equilibria / Acids and Bases
Solubility product and Common ion effect
Dissociation of acids and bases, Ka, Kb
Ionic Product, Kw
pH, pOH
Buffers
Back titration