AP Chemistry 7.4 Calculating the Equilibrium Constant Study Notes - New Syllabus Effective fall 2024
AP Chemistry 7.4 Calculating the Equilibrium Constant Study Notes- New syllabus
AP Chemistry 7.4 Calculating the Equilibrium Constant Study Notes – AP Chemistry – per latest AP Chemistry Syllabus.
LEARNING OBJECTIVE
Calculate Kp or Kc based on experimental observations of concentrations or pressures at equilibrium.
Key Concepts:
- Determining Equilibrium Constants from Experimental Data
Determining Equilibrium Constants from Experimental Data
The equilibrium constant (\( \mathrm{K_c} \) or \( \mathrm{K_p} \)) expresses the ratio of the concentrations or partial pressures of products and reactants at equilibrium. It can be determined experimentally by measuring the equilibrium concentrations (for \( \mathrm{K_c} \)) or equilibrium partial pressures (for \( \mathrm{K_p} \)) of all species involved in the reaction.
Key Idea:
- Equilibrium constants are numerical values that depend only on the temperature and the specific chemical reaction.
- The value of \( \mathrm{K_c} \) or \( \mathrm{K_p} \) can be calculated using experimentally measured equilibrium quantities substituted into the appropriate equilibrium expression.
- (a) The change in the concentrations of reactants and products is depicted as the 2SO2(g) + O2(g) ⇌ 2SO3(g) reaction approaches equilibrium.
- (b) The change in concentrations of reactants and products is depicted as the reaction 2SO3(g) ⇌ 2SO2(g) + O2(g) approaches equilibrium.
- (c) The graph shows the change in the value of the reaction quotient as the reaction approaches equilibrium.
Law of Mass Action:
For a general reversible reaction:
\( \mathrm{aA + bB ⇄ cC + dD} \)
The equilibrium constant in terms of concentration is:
\( \mathrm{K_c = \dfrac{[C]^c [D]^d}{[A]^a [B]^b}} \)
and in terms of partial pressures:
\( \mathrm{K_p = \dfrac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b}} \)
Steps to Determine \( \mathrm{K_c} \) or \( \mathrm{K_p} \):
- Write the balanced chemical equation.
- Set up the correct equilibrium expression for \( \mathrm{K_c} \) or \( \mathrm{K_p} \).
- Substitute the measured equilibrium concentrations or pressures into the expression.
- Calculate the numerical value of \( \mathrm{K} \).
Summary Table:
| Type | Expression | Measured Quantities | Units (if any) |
|---|---|---|---|
| \( \mathrm{K_c} \) | \( \mathrm{\dfrac{[Products]^p}{[Reactants]^r}} \) | Molar concentrations (M) | Depends on Δn |
| \( \mathrm{K_p} \) | \( \mathrm{\dfrac{(P_{products})^p}{(P_{reactants})^r}} \) | Partial pressures (atm) | Depends on Δn |
Important Notes:
- The magnitude of \( \mathrm{K} \) gives information about reaction extent:
- \( \mathrm{K \gg 1} \): Products favored at equilibrium.
- \( \mathrm{K \ll 1} \): Reactants favored at equilibrium.
- \( \mathrm{K} \) is temperature-dependent — it remains constant at a fixed temperature.
- Changes in concentration or pressure do not alter \( \mathrm{K} \); they affect \( \mathrm{Q} \), not the equilibrium constant.
Example :
\( \mathrm{H_2(g) + I_2(g) ⇄ 2HI(g)} \)
At equilibrium, \( \mathrm{[H_2] = 0.200\ M} \), \( \mathrm{[I_2] = 0.200\ M} \), and \( \mathrm{[HI] = 1.80\ M} \). Calculate \( \mathrm{K_c} \).
▶️ Answer / Explanation
Step 1: Write the equilibrium constant expression:
\( \mathrm{K_c = \dfrac{[HI]^2}{[H_2][I_2]}} \)
Step 2: Substitute equilibrium concentrations:
\( \mathrm{K_c = \dfrac{(1.80)^2}{(0.200)(0.200)}} \)
Step 3: Calculate:
\( \mathrm{K_c = \dfrac{3.24}{0.0400} = 81.0} \)
Final Answer: \( \mathrm{K_c = 81.0} \) (at the given temperature)
Example :
\( \mathrm{N_2O_4(g) ⇄ 2NO_2(g)} \)
At equilibrium, \( \mathrm{P_{N_2O_4} = 0.50\ atm} \) and \( \mathrm{P_{NO_2} = 1.00\ atm} \). Calculate \( \mathrm{K_p} \).
▶️ Answer / Explanation
Step 1: Write the equilibrium constant expression in terms of partial pressures:
\( \mathrm{K_p = \dfrac{(P_{NO_2})^2}{P_{N_2O_4}}} \)
Step 2: Substitute values:
\( \mathrm{K_p = \dfrac{(1.00)^2}{0.50}} \)
Step 3: Calculate:
\( \mathrm{K_p = 2.0} \)
Final Answer: \( \mathrm{K_p = 2.0} \) (at the given temperature)