Properties of the Equilibrium Constant

AP Chemistry· 12 min read

1. Rule 1: Reversing a Chemical Reaction★★☆☆☆⏱ 8 min

When you reverse a balanced chemical reaction, the products of the original reaction become the reactants of the reversed reaction, and vice versa. This flips the numerator and denominator of the original K expression entirely.

K_{\text{reversed}} = \frac{1}{K_{\text{original}}} = K_{\text{original}}^{-1}

📐 Worked Example

The equilibrium constant for the reaction N₂(g) + 3 H₂(g) ⇌ 2 NH₃(g) is K = 4.2 × 10⁸ at 25°C. Calculate K for the reverse reaction: 2 NH₃(g) ⇌ N₂(g) + 3 H₂(g).

1
Identify that the target reaction is the exact reverse of the given reference reaction.
2
$K_{\text{reverse}} = \frac{1}{K_{\text{forward}}} = \frac{1}{4.2 \times 10^8}$
3
$K_{\text{reverse}} = 2.4 \times 10^{-9}$

✓ Quick check

Test your understanding of the reverse K rule

What is K for the reverse of a reaction with K=0.032?
Reveal answer
31.25 —
You simply take 1 divided by the original K value to get the reversed K.

2. Rule 2: Scaling a Reaction by a Constant Factor★★★☆☆⏱ 10 min

If you multiply every stoichiometric coefficient in a balanced reaction by a constant factor n, each concentration term in the K expression is raised to the power of n. This means the new K value is the original K raised to the power of n.

K_{\text{scaled}} = (K_{\text{original}})^n

📐 Worked Example

Given the reference reaction H₂(g) + I₂(g) ⇌ 2 HI(g) has K = 54.3 at 400°C, calculate K for the reaction ½ H₂(g) + ½ I₂(g) ⇌ HI(g).

1
Identify the scaling factor n: every coefficient in the target reaction is ½ of the reference reaction, so n = 0.5.
2
$K_{\text{new}} = (K_{\text{original}})^{0.5} = \sqrt{54.3}$
3
$K_{\text{new}} = 7.37$

Exam tip:

AP exam questions often ask for K for a reaction with fractional coefficients, do not forget to take the root instead of dividing the original K by n.

3. Rule 3: Combining Multiple Sequential Reactions★★★☆☆⏱ 10 min

When you add two or more individual chemical reactions to get an overall net reaction, you multiply their respective equilibrium constants together to get the K value for the net reaction.

K_{\text{net}} = K_1 \times K_2 \times K_3 \times ...

📐 Worked Example

Given Reaction 1: 2 C(s) + O₂(g) ⇌ 2 CO(g) K₁ = 1.2 × 10¹⁶; Reaction 2: 2 CO(g) + O₂(g) ⇌ 2 CO₂(g) K₂ = 2.3 × 10⁹⁰. Calculate K for the net reaction C(s) + O₂(g) ⇌ CO₂(g).

1
Add Reaction 1 and Reaction 2 first: 2 C(s) + 2 O₂(g) ⇌ 2 CO₂(g). The K for this sum is K₁ × K₂.
2
$K_{\text{sum}} = (1.2 \times 10^{16}) \times (2.3 \times 10^{90}) = 2.76 \times 10^{106}$
3
Divide all coefficients of the summed reaction by 2 to get the target net reaction, so raise K_sum to the power of ½.
4
$K_{\text{net}} = \sqrt{2.76 \times 10^{106}} = 1.7 \times 10^{53}$

4. Relationship Between Kc and Kp★★★★☆⏱ 12 min

For reactions containing gaseous species, you can convert between Kc (concentration-based) and Kp (pressure-based) using the ideal gas law, which relates partial pressure to molar concentration.

K_p = K_c (RT)^{\Delta n}

📘 Definition

\Delta n

Δn

Total moles of gaseous products minus total moles of gaseous reactants in the balanced reaction. Solids and liquids are not counted.

📐 Worked Example

For the reaction 2 SO₃(g) ⇌ 2 SO₂(g) + O₂(g), Kc = 4.2 × 10⁻³ at 700 K. Calculate Kp for this reaction.

1
Calculate Δn: total moles of gas products = 2 + 1 = 3; total moles of gas reactants = 2. Δn = 3 - 2 = 1.
2
Substitute values into the Kp equation: R = 0.0821 L·atm/(mol·K), T = 700 K, Δn = 1.
3
$K_p = (4.2 \times 10^{-3}) \times (0.0821 \times 700)^1$
4
$K_p = 0.24$

5. Common Pitfalls

Wrong move:

Adding K values together when summing reactions

Why:

Students confuse K rules with enthalpy rules (which do add directly)

Correct move:

Multiply individual K values when combining reactions, only add ΔH values.

Wrong move:

Dividing K by the scaling factor n instead of raising K to the power of n

Why:

Treating K as a linear value instead of an exponential ratio

Correct move:

If you multiply reaction coefficients by n, raise the original K to the nth power.

Wrong move:

Counting moles of solid or liquid species when calculating Δn

Why:

Forgetting that pure solids and liquids do not appear in K expressions at all

Correct move:

Only count moles of gaseous reactants and products to calculate Δn for Kp/Kc conversion.

Wrong move:

Using temperature in Celsius instead of Kelvin for the Kp/Kc equation

Why:

Missing that the ideal gas law requires absolute temperature units

Correct move:

Always convert Celsius temperature to Kelvin before substituting into the RT term.

6. Quick Reference Cheatsheet

Operation on Reaction	Corresponding Operation on K
Reverse full reaction	Take reciprocal: K_new = 1/K_old
Multiply all coefficients by n	Raise K to power n: K_new = K_old^n
Add two reactions together	Multiply K values: K_net = K1 * K2
Convert Kc to Kp	Kp = Kc(RT)^Δn

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2025 · Paper 1 Multiple Choice
K value manipulation for reversed reaction
2024 · Paper 2 Free Response
Combine K values for 3 sequential reactions
2023 · Paper 2
Relate Kp and Kc for heterogeneous equilibrium

What's Next

Mastering these properties of K is a critical prerequisite for solving all equilibrium calculation problems on the AP Chemistry exam, including ICE table setups, reaction quotient comparisons, and Le Chatelier's principle predictions. You will use these manipulation rules repeatedly across Unit 7, especially when calculating equilibrium constants for reactions that are not given directly in exam prompts. These skills together make up ~10-15% of your total AP Chemistry exam score, so ensure you can apply all K manipulation rules without error before moving forward.

→Reaction Quotient Q and Comparing Q vs K