Unit 7 Part 2

 

 Why This Equation Matters (The Exam-Winning Formula)

In AP Chemistry, equilibrium is one of the highest-tested topics, and within that, the relationship between Kc and Kpshows up constantly — often subtly embedded in FRQs, MCQs, or data tables.

Students are frequently confident with Kc — the equilibrium constant based on concentration (mol/L) — but Kp, which involves partial pressures, is often misunderstood.

The bridge between them?
A deceptively simple formula:

🧠 Kp = Kc(RT)^Δn

This equation doesn’t just relate pressure and concentration — it reveals the mathematical connection between gas behavior and chemical equilibrium.

Let’s master it.

---

🔍 The Terms Unlocked

Symbol	Meaning	Units
Kp	Equilibrium constant using pressure	atm (implied)
Kc	Equilibrium constant using concentration	mol/L
R	Ideal gas constant	0.0821 L·atm/mol·K (or 8.314 J/mol·K)
T	Temperature in Kelvin	K
Δn	Change in moles of gas (products − reactants)	unitless

---

📌 Δn — The Most Misused Term in the Entire Equation

Let’s be crystal clear:

Δn = (moles of gaseous products) − (moles of gaseous reactants)

• Only gases count.

• Ignore solids and liquids completely.

• A wrong Δn = a wrong exponent = a wrong answer.

📍 Example:

N₂(g) + 3H₂(g) ⇌ 2NH₃(g)
→ Δn = 2 − (1 + 3) = –2

Even the sign matters. It affects whether the exponent increases or decreases the value of Kp relative to Kc.

---

🧠 Understanding R and Its Units — The Hidden Danger

This is where most AP students lose points without even realizing it.

There are two R values you’ll encounter:

• 0.0821 L·atm/mol·K
  → Use when pressure is in atm and volume is in liters

• 8.314 J/mol·K
  → Use when working in joules or kilopascals (kPa)

🔥 RULE:

Your units must match.
If you're using atm in the Kp value, you must use R = 0.0821.

The exam will try to trap you by mixing units. Don’t fall for it.

---

🧩 Where Students Go Wrong – Common Traps

1. ❌ Forgetting to count only gases in Δn

2. ❌ Using the wrong R value

3. ❌ Plugging in Celsius instead of Kelvin

4. ❌ Forgetting that exponents affect magnitude dramatically

5. ❌ Using Kc when the problem gives Kp (and vice versa)

---

⚙️ Step-by-Step: How to Apply Kp = Kc(RT)^Δn

1. Identify the reaction. Write the balanced chemical equation.

2. Determine Δn from the gaseous species.

3. Choose the correct R based on units given or required.

4. Convert T to Kelvin if needed (K = °C + 273).

5. Plug values into the equation.

6. Box your answer and label units clearly.

---

🧠 Strategic Tip for AP Free Response Questions

💡 On FRQs, always do the following:

• Write the formula before plugging in → earns rubric points.

• Show units (especially for R and T).

• Box final answer — AP scorers love this.

• If asked to justify equilibrium direction, compare Kp vs. Qp using partial pressure data.

---

📘 Practice Example

Given:

• Kc = 0.0400 at 500 K

• Reaction:
  2SO₂(g) + O₂(g) ⇌ 2SO₃(g)

• Δn = (2) − (2 + 1) = –1

• R = 0.0821

• T = 500 K

Calculate Kp:

Kp = Kc × (RT)^Δn
Kp = 0.0400 × (0.0821 × 500)^–1
Kp = 0.0400 / (41.05) ≈ 9.75 × 10⁻⁴

📦 Final boxed answer with units and steps shown.
This is how you get full credit.