1. Ch. 13: Fundamental Equilibrium Concepts
Dr. Namphol Sinkaset
Chem 201: General Chemistry II

2. I. Chapter Outline Introduction Chemical Equilibria
Equilibrium Constants
Le Châtelier’s Principle
Equilibrium Calculations

3. I. Introduction

4. II. Chemical Equilibria
Equilibrium will be the focus for the next several chapters.
Most reactions are reversible, meaning they can proceed in both forward and reverse directions.
This means that as products build up, they will react and reform reactants.
At equilibrium, the forward and backward reaction rates are equal.

5. II. Example Equilibrium

6. II. Equilibrium Concentrations
Equilibrium does not mean that concentrations are all equal!!
However, we can quantify concentrations at equilibrium.

7. III. The Reaction Quotient
The reaction quotient is a number that expresses the extent of a reaction at any given point in time.
For the reaction mA + nB  xC + yD:
What is the value of Qc when pure reactants are mixed (at time zero)?

8. III. Units in Equilibrium Expressions
Square brackets mean molarity concentration, e.g. [NaOH] = 1.00 M.
But, in equilibrium expressions, we use activity, which is a substance’s effective concentration under specific conditions.
Activity has no units, and for dilute solutions, activity is similar to molarity.
Activities of pure solids and liquids = 1.

9. III. Sample Problem
Write Qc expressions for the following equilibrium reactions.
N2(g) + 3H2(g)  2NH3(g)
4NH3(g) + 5O2(g)  4NO(g) + 6H2O(g)

10. III. Value of Qc Over Time
What happens to the value of Qc as a reaction proceeds and eventually reaches equilibrium?

11. III. The Equilibrium Constant
When calculated at equilibrium, Qc becomes Kc, the equilibrium constant.
This is the mathematical statement of the law of mass action: when a reaction reaches equilibrium at a given T, the reaction quotient for the reaction always has the same value.

12. III. Equilibrium [ ]’s vs. Kc
For any reaction, the final equilibrium [ ]’s will depend on the initial [ ]’s of reactants or products.
However, no matter how you set up the reaction, the value of the equilibrium constant will be the same if the temperature is the same.

13. III. Equilibrium [ ]’s vs. Kc

14. III. Physical Meaning of Kc
Kc is a measure of the yield of the reaction at equilibrium, i.e. how far the reaction goes to completion.
Large values of Kc mean that the equilibrium favors products. Why?*
Small values of Kc mean that the equilibrium favors reactants. Why?*

15. III. Sample Problem
Write the equilibrium constant expression for the following reaction. What does it mean if its listed Kc states “approaches infinity”?
C3H8(g) + 5O2(g)  3CO2(g) 4H2O(g)

16. III. Using Qc With Kc
The value of Qc relative to Kc tells you whether the reaction will form more products or more reactants to reach equilibrium.
Qc < Kc means reaction forms products.
Qc > Kc means reaction form reactants.
Qc = Kc means reaction is at equilibrium.

17. III. Sample Problem
Consider the reaction N2O4(g)  2NO2(g) with Kc = 5.85 x If a reaction mixture contains [NO2] = M and [N2O4] = M, which way will the reaction proceed?

18. III. Homogeneous Equilibria
As can be guessed, these systems have all reactants and products in a single solution.
These can be liquid-based solutions or gas-phase solutions.
In either case, we can calculate Qc or Kc as shown on the next slide.

19. III. Homogeneous Equilibria

20. III. K in Terms of Pressure
Up to this point, we’ve been using concentration (activity) exclusively in the equilibrium expressions.
Partial pressures are proportional to concentration via PV = nRT.
Thus, for gas reactions, partial pressures can be used in place of concentrations.

21. III. Two Different K’s
For the reaction 2SO3(g)  2SO2(g) + O2(g), we can write two equilibrium expressions.

22. III. Relationship Between Concentration and Pressure
To be able to convert between Kc and Kp, we need a relationship between concentration and pressure.

23. III. Converting Between Kc and Kp

24. III. Converting Between Kc and Kp
The Δn is the change in the number of moles of gas when going from reactants to products.
When does Kp equal Kc?*

25. III. Sample Problem
Methanol can be synthesized via the reaction CO(g) + 2H2(g)  CH3OH(g). If Kp of this reaction equals 3.8 x 10-2 at 200 °C, what’s the value of Kc?

26. III. Heterogeneous Equilibria
If an equilibrium contains pure solids or pure liquids, they are not included in the equilibrium constant expression because their activities are equal to 1.

27. III. Rules for Manipulating K
If the equation is reversed, the equilibrium constant is inverted.

28. III. Rules for Manipulating K
If the equation is multiplied by a factor, the equilibrium constant is raised to the same factor.

29. III. Rules for Manipulating K
When chemical equations are added, their equilibrium constants are multiplied together to get the overall equilibrium constant.

30. III. Sample Problem
Predict the equilibrium constant for the first reaction given the equilibrium constants for the second and third reactions.
CO2(g) + 3H2(g)  CH3OH(g) + H2O(g) K1 = ?
CO(g) + H2O(g)  CO2(g) + H2(g) K2 = 1.0 x 105
CO(g) + 2H2(g)  CH3OH(g) K3 = 1.4 x 107

31. IV. Predicting Qualitative Changes to Equilibrium
If a system is at equilibrium, what happens when it is disturbed?
Le Châtelier’s Principle allow us to make qualitative predictions about changes in chemical equilibria:
When a chemical system at equilibrium is disturbed, it returns to equilibrium by counteracting the disturbance.

32. IV. Three Ways to Disturb an Equilibrium
We look at three ways that disturb a system at equilibrium:
Adding/removing a reactant or product.
Changing the volume/pressure in gaseous reactions.
Changing the temperature.

33. IV. Adding Reactant/Product
If we add or remove a reactant or product, we’re changing the [ ]’s.
The equilibrium will shift in a direction that will partially consume a reactant or product that is added, or partially replace a reactant or product that has been removed.

34. IV. Adding Product

35. IV. Adding Reactant/Product

36. IV. Changing Volume/Pressure
Via PV = nRT, pressure and volume are inversely related.
For example, decreasing volume of a container increases the pressure of all gases in the container.
Reducing container volume of a gaseous reaction mixture shifts the equilibrium in the direction that will, if possible, decrease the # of moles of gas.

37. IV. Changing Pressure

38. IV. Changing Temperature
To determine the effect of changing the temperature, we need to know the heat of reaction, ΔHrxn.
Once we know if a reaction is exo or endo, we can write “heat” as a product or reactant.
We then apply Le Châtelier’s Principle in the same manner as when we considered the add product/reactant case.

39. IV. Changing T Changes K!
In previous disturbances, K didn’t change. What did?
However, changes in T change K which leads to shifts in the equilibrium.

40. IV. Visual Example

41. IV. Sample Problem
For the reaction N2(g) + 3H2(g)  2NH3(g), ΔHrxn = kJ/mole. Which way will the equilibrium shift when each of the following occurs?
NH3 is removed via reaction w/ HCl.
The reaction vessel is opened.
The reaction vessel is cooled by 25 °C.
Some Ar gas is added to the reaction vessel.
A catalyst is added.

42. V. Equilibrium Problems
2 main categories of equilibrium problems:
Finding Kc or Kp from known equilibrium concentrations or partial pressures
Finding one or more equilibrium [ ]’s or partial pressures w/ a known Kc or Kp

43. V. Finding Kc or Kp
To find equilibrium constants, we must be given information as to what [ ]’s to use in the equilibrium expression.
Often, we will need to set up a table to organize the information.

44. V. Sample Problem
An equilibrium was established for the reaction CO(g) + H2O(g)  CO2(g) + H2(g). At equilibrium, the following [ ]’s were found: [CO] = M, [H2O] = M, [CO2] = M, [H2] = M. What’s the value of Kc?

45. V. Sample Problem
In the reaction 2CO(g) + O2(g)  2CO2(g), it was found the concentration of O2 dropped by mole/L. When the reaction reached equilibrium, how had the [CO] and [CO2] changed?

46. V. Sample Problem
A student placed mole PCl3(g) and mole Cl2(g) into a 1.00 L container at 250 °C. After the reaction PCl3(g) + Cl2(g)  PCl5(g) came to equilibrium, mole PCl3 was found. What’s the value of Kc for this reaction?

47. V. Key Points Only use equilibrium [ ]’s in the Kc/Kp expression.
Initial [ ]’s should be in molarity if using Kc.
Changes in [ ]’s always occur in agreement with stoichiometry in the balanced equation.
When entering the “Change” row, make sure all reactants change in one direction and all products change in the opposite direction.

48. V. Finding Equil. [ ]’s
This second type of problem is more challenging than the first.
Key is interpreting information given and organizing it into a concentration table!

49. V. Sample Problem
At 25 °C, Kc = 4.10 for the reaction CH3COOH(l) + CH3CH2OH(l)  CH3C(O)OCH2CH3(l) + H2O(l). At equilibrium, it was found that [CH3COOH] = M, [H2O] = M, [CH3C(O)OCH2CH3] = M. What’s the equilibrium [ ] of CH3CH2OH?

50. V. Sample Problem
The reaction CO(g) + H2O(g)  CO2(g) + H2(g) has a Kc of 4.06 at 500 °C. If mole CO and mole H2O are placed in a 1.00 L reaction vessel at this temperature, what are the equilibrium concentrations of reactants and products?

51. V. Sample Problem
A reaction mixture at 25 °C initially contains PI2 = atm, PCl2 = atm, and PICl = atm. If the reaction I2(g) + Cl2(g)  2ICl(g) has a Kp of 81.9 at 25 °C, find the equilibrium partial pressures of each species.

52. V. Sample Problem
At a certain temperature, Kc = 4.50 for the reaction N2O4(g)  2NO2(g). If mole N2O4 is placed in a 2.00 L flask at this temperature, what will be the equilibrium [ ]’s of both gases?

53. V. Simplifications
When Kc or Kp is very small or very big, we can treat x as being insignificant.
As such, we discard x in any addition/subtraction operation. Why?*
We must verify our assumption by comparing the value we obtain for x to the number it was discarded from.
Assumption is valid if value of x is less than 5% of the number it would have been subtracted from.

54. V. Sample Problem
In air at 25 °C and 1 atm, [N2] = M and [O2] = M. The reaction between molecular nitrogen and molecular oxygen to form nitrogen monoxide has Kc = 4.8 x at 25 °C. What is the natural [NO] in the atmosphere?

55. V. Sample Problem
What are the concentrations of all dissolved species at equilibrium of a 0.15 M HClO solution given that its Kc in water is 2.9 × 10-8?