A. The Concept of Chemical Equilibrium

1. Reversible Reactions and Equilibrium

Chemical reactions can proceed in both the forward and reverse directions. At equilibrium, the rates of the forward and reverse reactions are equal, and the concentrations of reactants and products remain constant over time.

• Reversible Reaction: A reaction that can proceed in both directions, from reactants to products and from products to reactants.

• Dynamic Equilibrium: The state in which the forward and reverse reactions occur at the same rate, so there is no net change in the concentrations of reactants and products.

Example 1: If one mole of H2 and one mole of I2 are placed in a container at 400°C, the following reaction occurs:

Example 2: If two moles of HI are placed in a container at 400°C, the reverse reaction occurs:

2. Concentration Changes Over Time

When a reaction mixture is set up, the concentrations of reactants and products change until equilibrium is reached. This can be represented graphically:

• At equilibrium, the concentrations of all species remain constant.

• The time at which equilibrium is reached can be identified on a concentration vs. time graph as the point where the curves level off.

Example 3: Plotting [HI] as a function of time when starting with 1 M H2 and 1 M I2.

Example 4: Plotting [H2] or [I2] as a function of time under similar conditions.

Example 5: Plotting both [HI] and [H2] or [I2] on the same graph to compare their changes over time.

3. Definition and Meaning of Equilibrium

• Equilibrium: The state in which the rate of the forward reaction equals the rate of the reverse reaction.

• The double arrow () indicates a reversible reaction and equilibrium.

• At equilibrium:

  • The reaction does not go to completion.

  • The concentrations of products and reactants are constant (but not necessarily equal).

  • The rates of the forward and reverse reactions are equal.

  • Equilibrium is dynamic: both reactions continue to occur.

B. The Equilibrium Constant

1. The General Expression for the Equilibrium Constant, Kc

The equilibrium constant () expresses the ratio of the concentrations of products to reactants at equilibrium, each raised to the power of their coefficients in the balanced equation.

• For a general reaction:

• The equilibrium constant expression is:

Example 7: Write the equilibrium constant expression for the reaction above.

2. Equilibrium Constants in Terms of Pressure, Kp

For reactions involving gases, equilibrium can also be expressed in terms of partial pressures ():

• For the reaction:

Relationship between and :

• Where is the change in moles of gas ( moles of gaseous products moles of gaseous reactants), is the gas constant, and is temperature in Kelvin.

3. Calculating Equilibrium Constants

Given equilibrium concentrations, can be calculated using the equilibrium constant expression.

• Example 9: For the reaction , if M and M at equilibrium, and M, then:

• Example 10: For at 700°C, if M and M, then:

4. Magnitude of K and Extent of Reaction

• If is much greater than 1, products are favored at equilibrium.

• If is much less than 1, reactants are favored at equilibrium.

• If is close to 1, significant amounts of both reactants and products are present at equilibrium.

Example 12: For at equilibrium with mol/L and mol/L, .

Example 13: For , calculate and interpret its value.

5. Writing Equilibrium Constant Expressions

• For :

C. Understanding and Working with Equilibrium Constants

1. Relating Chemical Equation Stoichiometry and Equilibrium Constants

• If a reaction is reversed, the new is the reciprocal of the original .

• If the coefficients in a balanced equation are multiplied by a factor , the new is the original raised to the th power.

D. Heterogeneous Equilibria

1. Homogeneous Equilibria

• All reactants and products are in the same phase (usually all gases or all aqueous solutions).

2. Heterogeneous Equilibria

• Reactants and/or products are in different phases (e.g., solids, liquids, gases).

• Concentrations of pure solids and liquids are not included in the equilibrium constant expression.

E. Calculating Equilibrium Constants

1. Using Initial and Equilibrium Concentrations

• Set up an ICE (Initial, Change, Equilibrium) table to organize data and solve for unknowns.

• Use stoichiometry to relate changes in concentrations.

Example 16: If 2.0 × 10−2 moles of A and 3.0 × 10−2 moles of B are placed in a 1 L container and the equilibrium concentration of C is 4.0 × 10−2 M, calculate for .

Example 17: For , if 3.00 moles of are placed in a 1 L container and at equilibrium is 0.11 M, find .

2. Calculating Equilibrium Concentrations

• Given and initial concentrations, set up an ICE table and solve for equilibrium concentrations using the equilibrium constant expression.

Example 24: For , if at 100°C and M, find , , and at equilibrium.

F. Applications of Equilibrium Constants

1. Direction of Reaction and K

• If , the reaction proceeds forward (to the right) to reach equilibrium.

• If , the reaction proceeds in reverse (to the left) to reach equilibrium.

• If , the system is at equilibrium.

Example 21: For at 100°C, . If M and M, is the reaction at equilibrium?

2. Calculating Q and Comparing to K

• The reaction quotient, , is calculated using the same expression as , but with initial or non-equilibrium concentrations.

• Compare to to predict the direction the reaction will proceed.

G. Le Chatelier's Principle

1. Effect of Changing Concentration

• If the concentration of a reactant or product is changed, the system will shift to counteract the change and restore equilibrium.

Example 25: For , if M, M, and M at equilibrium, what happens if more is added?

2. Effect of Volume or Pressure

• For gaseous equilibria, decreasing the volume (increasing pressure) shifts the equilibrium toward the side with fewer moles of gas.

• Increasing the volume (decreasing pressure) shifts the equilibrium toward the side with more moles of gas.

Example 27: For , what happens if the pressure is increased?

3. Effect of Temperature

• For endothermic reactions (), increasing temperature shifts equilibrium to the right (products).

• For exothermic reactions (), increasing temperature shifts equilibrium to the left (reactants).

Example 29: For , is the reaction endothermic or exothermic? How does temperature affect equilibrium?

Example 30: For , kJ/mol. If temperature increases, which direction does equilibrium shift?

Example 31: For , kJ/mol. If temperature increases, which direction does equilibrium shift?

4. Effect of the Addition of a Catalyst

• A catalyst increases the rate at which equilibrium is reached but does not affect the position of equilibrium or the value of .