A Level Chemistry - How to Solve: Equilibrium Constants (Kc, Kp, Partial Pressure Calculations) – Complete Guide

How to Solve: Equilibrium Constants (Kc, Kp, Partial Pressure Calculations) – Complete Guide

Introduction

"Mastering equilibrium constants lets you predict how far a reaction goes—whether it’s the Haber process making fertiliser or your lungs exchanging oxygen. On A-Level exams, this topic is worth 10-15% of your marks in chemistry papers. Get it right, and you’re one step closer to an A."

WHAT YOU NEED TO KNOW FIRST

Before diving in, ensure you understand:
1. Dynamic equilibrium – Forward and reverse reactions occur at the same rate; concentrations remain constant.
2. Mole ratios – Coefficients in balanced equations tell you the ratio of reactants to products.
3. Ideal gas law basics – For Kp, you’ll need to relate pressure to moles (PV = nRT).

KEY TERMS & FORMULAS

1. Equilibrium Constant (Kc)

Formula: [ K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b} ] - [A], [B] = Concentrations of reactants (mol/dm³) - [C], [D] = Concentrations of products (mol/dm³) - a, b, c, d = Coefficients from the balanced equation - MEMORISE THIS: Only gases and aqueous solutions appear in Kc. Solids and pure liquids are excluded.

2. Equilibrium Constant (Kp)

Formula: [ K_p = \frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b} ] - P_A, P_B = Partial pressures of reactants (atm or kPa) - P_C, P_D = Partial pressures of products (atm or kPa) - MEMORISE THIS: Only gases appear in Kp. Solids, liquids, and aqueous solutions are excluded.

3. Partial Pressure

Formula: [ P_A = \text{Mole fraction of A} \times \text{Total pressure} ] [ \text{Mole fraction of A} = \frac{\text{Moles of A}}{\text{Total moles of gas}} ] - Given on exam sheet: Usually provided, but memorise the concept.

4. Converting Between Kc and Kp

Formula: [ K_p = K_c (RT)^{\Delta n} ] - R = Gas constant (0.0821 dm³·atm·mol⁻¹·K⁻¹ or 8.314 J·mol⁻¹·K⁻¹) - T = Temperature (Kelvin) - Δn = Moles of gaseous products – moles of gaseous reactants - MEMORISE THIS: Only needed if the question asks for conversion.

STEP-BY-STEP METHOD

For Kc Problems:

1. Write the balanced equation.
2. Example: ( N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) )
3. Write the Kc expression.
4. ( K_c = \frac{[NH_3]^2}{[N_2][H_2]^3} )
5. List initial concentrations (if given).
6. If not given, assume initial concentrations are zero for products.
7. Set up an ICE table (Initial, Change, Equilibrium).
8. Example: | Species | Initial (M) | Change (M) | Equilibrium (M) | |---------|-------------|------------|------------------| | N₂ | 1.0 | -x | 1.0 - x | | H₂ | 3.0 | -3x | 3.0 - 3x | | NH₃ | 0 | +2x | 2x |
9. Substitute equilibrium concentrations into Kc.
10. ( K_c = \frac{(2x)^2}{(1.0 - x)(3.0 - 3x)^3} )
11. Solve for x.
12. Use algebra or approximations (if Kc is very small, assume x is negligible).
13. Find equilibrium concentrations.
14. Plug x back into the ICE table.
15. Check units.
16. Kc has no units (unless specified in the question).

For Kp Problems:

1. Write the balanced equation.
2. Example: ( 2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g) )
3. Write the Kp expression.
4. ( K_p = \frac{(P_{SO_3})^2}{(P_{SO_2})^2 (P_{O_2})} )
5. Find mole fractions at equilibrium.
6. Use an ICE table (in moles, not concentrations).
7. Calculate partial pressures.
8. ( P_A = \text{Mole fraction of A} \times \text{Total pressure} )
9. Substitute into Kp.
10. Solve for the unknown.
11. Check units.
12. Kp is usually in atm or kPa (depends on total pressure units).

WORKED EXAMPLES

Example 1 – Basic Kc Calculation

Question: For the reaction ( H_2(g) + I_2(g) \rightleftharpoons 2HI(g) ), at equilibrium, [H₂] = 0.20 M, [I₂] = 0.20 M, and [HI] = 0.80 M. Calculate Kc.

Solution:
1. Balanced equation: ( H_2 + I_2 \rightleftharpoons 2HI )
2. Kc expression: ( K_c = \frac{[HI]^2}{[H_2][I_2]} )
3. Substitute values: ( K_c = \frac{(0.80)^2}{(0.20)(0.20)} )
4. Calculate: ( K_c = \frac{0.64}{0.04} = 16 )

What we did and why: We used the equilibrium concentrations directly in the Kc expression. No ICE table was needed because all equilibrium concentrations were given.

Example 2 – Medium Kc with ICE Table

Question: For ( N_2O_4(g) \rightleftharpoons 2NO_2(g) ), initial [N₂O₄] = 0.50 M. At equilibrium, [NO₂] = 0.60 M. Calculate Kc.

Solution:
1. Balanced equation: ( N_2O_4 \rightleftharpoons 2NO_2 )
2. ICE table: | Species | Initial (M) | Change (M) | Equilibrium (M) | |---------|-------------|------------|------------------| | N₂O₄ | 0.50 | -x | 0.50 - x | | NO₂ | 0 | +2x | 2x |
3. Given [NO₂] at equilibrium = 0.60 M, so 2x = 0.60 → x = 0.30 M.
4. [N₂O₄] at equilibrium = 0.50 - 0.30 = 0.20 M.
5. Kc expression: ( K_c = \frac{[NO_2]^2}{[N_2O_4]} )
6. Substitute: ( K_c = \frac{(0.60)^2}{0.20} = \frac{0.36}{0.20} = 1.8 )

What we did and why: We used an ICE table to find the change in concentration. Since [NO₂] was given, we worked backward to find x and then [N₂O₄].

Example 3 – Exam-Style Kp Calculation

Question: For ( 2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g) ), at equilibrium, the mixture contains 0.40 mol SO₂, 0.20 mol O₂, and 0.60 mol SO₃ in a 2.0 dm³ vessel at 500 K. Total pressure = 1.5 atm. Calculate Kp.

Solution:
1. Balanced equation: ( 2SO_2 + O_2 \rightleftharpoons 2SO_3 )
2. Find mole fractions: - Total moles = 0.40 + 0.20 + 0.60 = 1.20 mol - Mole fraction SO₂ = 0.40 / 1.20 = 1/3 - Mole fraction O₂ = 0.20 / 1.20 = 1/6 - Mole fraction SO₃ = 0.60 / 1.20 = 1/2
3. Calculate partial pressures: - ( P_{SO_2} = (1/3) \times 1.5 = 0.50 ) atm - ( P_{O_2} = (1/6) \times 1.5 = 0.25 ) atm - ( P_{SO_3} = (1/2) \times 1.5 = 0.75 ) atm
4. Kp expression: ( K_p = \frac{(P_{SO_3})^2}{(P_{SO_2})^2 (P_{O_2})} )
5. Substitute: ( K_p = \frac{(0.75)^2}{(0.50)^2 (0.25)} = \frac{0.5625}{0.0625} = 9.0 )

What we did and why: We converted moles to mole fractions, then to partial pressures. Kp only uses gases, so we ignored any solids/liquids (none here).

COMMON MISTAKES

1. MISTAKE: Including solids/liquids in Kc or Kp.
2. WHY IT HAPPENS: Students forget the rule that only gases and aqueous solutions appear.

3. CORRECT APPROACH: Exclude solids and pure liquids from the expression.

4. MISTAKE: Forgetting to raise concentrations/pressures to the power of their coefficients.

5. WHY IT HAPPENS: Misreading the balanced equation.

6. CORRECT APPROACH: Always check coefficients and apply them as exponents.

7. MISTAKE: Using initial concentrations instead of equilibrium concentrations in Kc.

8. WHY IT HAPPENS: Skipping the ICE table when needed.

9. CORRECT APPROACH: Only use equilibrium values in Kc/Kp.

10. MISTAKE: Mixing up Kc and Kp units.

11. WHY IT HAPPENS: Not checking if the question specifies units.

12. CORRECT APPROACH: Kc is unitless (unless specified), Kp uses atm or kPa.

13. MISTAKE: Assuming Kc = Kp without conversion.

14. WHY IT HAPPENS: Forgetting that Kp = Kc(RT)^Δn.
15. CORRECT APPROACH: Only equate them if Δn = 0 (same moles of gas on both sides).

EXAM TRAPS

1. TRAP: Giving initial concentrations but asking for Kc.
2. HOW TO SPOT IT: The question provides starting values but no equilibrium data.

3. HOW TO AVOID IT: Always set up an ICE table to find equilibrium concentrations.

4. TRAP: Using pressure in Kc or concentration in Kp.

5. HOW TO SPOT IT: The question mixes units (e.g., gives pressure but asks for Kc).

6. HOW TO AVOID IT: Convert pressure to concentration (or vice versa) using PV = nRT if needed.

7. TRAP: Changing temperature and asking for Kc/Kp.

8. HOW TO SPOT IT: The question mentions heating/cooling the reaction.
9. HOW TO AVOID IT: Remember Kc/Kp only changes with temperature. If temperature changes, the value of K changes.

1-MINUTE RECAP

"Here’s the night-before cheat sheet:
1. Kc uses concentrations (mol/dm³), Kp uses partial pressures (atm/kPa).
2. Only gases and aqueous solutions go in the expression—solids and liquids are out.
3. ICE tables are your best friend. Use them to track changes in concentration or moles.
4. Partial pressure = mole fraction × total pressure. Mole fraction = moles of gas / total moles.
5. Check units! Kc is usually unitless, Kp uses pressure units.
6. If temperature changes, K changes. If not, K stays the same.
7. Common mistakes: Forgetting exponents, mixing up Kc and Kp, or including solids. Double-check every step. Now go ace that exam!"