Equilibrium Constants and Expressions

⚖️ Equilibrium Constants and Expressions

Part 1 of 7 — What Is Chemical Equilibrium?

Topics in This Part

🔑 Key Concept: Mastering this material will strengthen your foundation for both the AP Chemistry exam and more advanced chemistry topics.

What You'll Master in Part 1

• Understanding the core concepts covered in Part 1
• Applying these ideas to solve practice problems
• Building toward AP exam readiness for this topic

⚖️ Dynamic Equilibrium Revisited

At dynamic equilibrium:

$\text{Rate}_{\text{forward}} = \text{Rate}_{\text{reverse}}$

Key Features

⚠️ Common Misconception: Equilibrium does NOT mean the concentrations of reactants and products are equal. It means they are constant.

For example, in the Haber process:

$\text{N}_2(g) + 3\,\text{H}_2(g) \rightleftharpoons 2\,\text{NH}_3(g)$

At equilibrium, $[\text{NH}_3]$ might be much larger or much smaller than $[\text{N}_2]$ — it depends on conditions. But all concentrations stop changing.

Concept Check — Equilibrium Basics 🎯

⚖️ The Equilibrium Constant

The equilibrium constant $K$ quantifies the ratio of product concentrations to reactant concentrations at equilibrium.

For the general reaction:

$a\text{A} + b\text{B} \rightleftharpoons c\text{C} + d\text{D}$

The equilibrium constant expression is:

$\boxed{K_c = \frac{[\text{C}]^c[\text{D}]^d}{[\text{A}]^a[\text{B}]^b}}$

What $K$ Tells Us

Critical Facts About $K$

🔑 Key Concept: $K$ depends only on temperature — not on initial concentrations, pressure, or catalysts.

• $K$ is unitless (in the thermodynamic definition using activities)
• A larger $K$ means more products at equilibrium

Fill in the Blanks — Equilibrium Fundamentals 🔽

Quick Practice 🧮

Answer the following about equilibrium constants:

1) If $K = 4.2 \times 10^8$, are products or reactants favored? (Enter "products" or "reactants")

2) If $K = 6.3 \times 10^{-11}$, are products or reactants favored? (Enter "products" or "reactants")

3) Does adding a catalyst change the value of $K$? (Enter "yes" or "no")

Exit Check — What Is Equilibrium? ✅

✍️ Writing Equilibrium Expressions

Part 2 of 7 — Writing $K$ Expressions

Topics in This Part

🔑 Key Concept: Mastering this material will strengthen your foundation for both the AP Chemistry exam and more advanced chemistry topics.

What You'll Master in Part 2

• Understanding the core concepts covered in Part 2
• Applying these ideas to solve practice problems
• Building toward AP exam readiness for this topic

✍️ Rules for Writing $K_c$ Expressions

For the reaction:

$a\text{A}(aq) + b\text{B}(g) \rightleftharpoons c\text{C}(aq) + d\text{D}(g)$

$K_c = \frac{[\text{C}]^c[\text{D}]^d}{[\text{A}]^a[\text{B}]^b}$

What Goes In and What Stays Out

Example 1

$\text{CaCO}_3(s) \rightleftharpoons \text{CaO}(s) + \text{CO}_2(g)$

$K_c = [\text{CO}_2]$

Both $\text{CaCO}_3$ and $\text{CaO}$ are pure solids — they are omitted from the expression.

Example 2

$\text{2 H}_2\text{O}(l) \rightleftharpoons \text{2 H}_2(g) + \text{O}_2(g)$

$K_c = [\text{H}_2]^2[\text{O}_2]$

Water as a pure liquid is omitted.

Which Expression Is Correct? 🎯

📌 Homogeneous vs. Heterogeneous Equilibria

Homogeneous Equilibrium

All species are in the same phase:

$\text{N}_2\text{O}_4(g) \rightleftharpoons 2\,\text{NO}_2(g)$

$K_c = \frac{[\text{NO}_2]^2}{[\text{N}_2\text{O}_4]}$

Heterogeneous Equilibrium

Species are in different phases — exclude pure solids and pure liquids:

$\text{C}(s) + \text{CO}_2(g) \rightleftharpoons 2\,\text{CO}(g)$

$K_c = \frac{[\text{CO}]^2}{[\text{CO}_2]}$

The solid carbon is omitted.

💡 AP Tip: The AP exam loves to test whether you know to exclude pure solids and liquids. If you see $(s)$ or $(l)$, leave it out of $K$.

Fill in the Blanks — Building $K$ Expressions 🔽

Write the Exponents 🧮

For the reaction: $\text{2 NO}(g) + \text{O}_2(g) \rightleftharpoons \text{2 NO}_2(g)$

$K_c = \frac{[\text{NO}_2]^{\boxed{?}}}{[\text{NO}]^{\boxed{?}}[\text{O}_2]^{\boxed{?}}}$

Enter the three exponents (integers):

Exit Check — Writing $K$ Expressions ✅

🔄 $K_c$ vs $K_p$

Part 3 of 7 — Concentration vs. Pressure Equilibrium Constants

Topics in This Part

🔑 Key Concept: Mastering this material will strengthen your foundation for both the AP Chemistry exam and more advanced chemistry topics.

What You'll Master in Part 3

• Understanding the core concepts covered in Part 3
• Applying these ideas to solve practice problems
• Building toward AP exam readiness for this topic

💨 $K_p$ — The Pressure-Based Constant

For gas-phase reactions, we can use partial pressures instead of molar concentrations.

For: $a\text{A}(g) + b\text{B}(g) \rightleftharpoons c\text{C}(g) + d\text{D}(g)$

$\boxed{K_p = \frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b}}$

where $P_X$ is the partial pressure of species X in atm (for AP Chemistry).

Example

$\text{N}_2(g) + 3\,\text{H}_2(g) \rightleftharpoons 2\,\text{NH}_3(g)$

$K_p = \frac{(P_{\text{NH}_3})^2}{(P_{\text{N}_2})(P_{\text{H}_2})^3}$

The same rules apply: products over reactants, coefficients as exponents.

🔄 Converting Between $K_c$ and $K_p$

The relationship between $K_p$ and $K_c$ is:

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

where:

• $R = 0.08206\;\text{L}\cdot\text{atm}\cdot\text{mol}^{-1}\text{}\cdot\text{K}^{-1}$
• $T$ = temperature in Kelvin
• $\Delta n$ = (moles of gaseous products) − (moles of gaseous reactants)

Finding $\Delta n$

For $\text{N}_2(g) + 3\,\text{H}_2(g) \rightleftharpoons 2\,\text{NH}_3(g)$:

$\Delta n = 2 - (1 + 3) = 2 - 4 = -2$

When $\Delta n = 0$

If the total moles of gas are the same on both sides:

$K_p = K_c(RT)^0 = K_c$

🔑 Key Concept: When $\Delta n = 0$, $K_p = K_c$ — they are equal!

Problem: For $\text{N}_2\text{O}_4(g) \rightleftharpoons 2\,\text{NO}_2(g)$ at 25°C, $K_c = 4.61 \times 10^{-3}$. Calculate $K_p$.

Solution:

$\Delta n = 2 - 1 = 1$

$K_p = K_c(RT)^{\Delta n} = (4.61 \times 10^{-3})(0.08206 \times 298)^1$

$K_p = (4.61 \times 10^{-3})(24.45) = 0.113$

$K_c$ vs $K_p$ — Concept Check 🎯

Fill in the Blanks — $K_c$ and $K_p$ 🔽

Calculate $\Delta n$ 🧮

Find $\Delta n$ for each reaction (enter an integer, use a negative sign if needed):

1) $\text{2 SO}_2(g) + \text{O}_2(g) \rightleftharpoons \text{2 SO}_3(g)$

2) $\text{PCl}_5(g) \rightleftharpoons \text{PCl}_3(g) + \text{Cl}_2(g)$

3) $\text{CO}(g) + 2\,\text{H}_2(g) \rightleftharpoons \text{CH}_3\text{OH}(g)$

Exit Check — $K_c$ vs $K_p$ ✅

📏 Magnitude of K

Part 4 of 7 — What the Size of $K$ Tells Us

Topics in This Part

🔑 Key Concept: Mastering this material will strengthen your foundation for both the AP Chemistry exam and more advanced chemistry topics.

What You'll Master in Part 4

• Understanding the core concepts covered in Part 4
• Applying these ideas to solve practice problems
• Building toward AP exam readiness for this topic

📌 Interpreting the Magnitude of $K$

The equilibrium constant tells us the extent to which a reaction proceeds:

Real-World Examples

💡 Key Point: A very large $K$ does not mean the reaction is fast. $K$ tells us about equilibrium position (thermodynamics), not rate (kinetics).

Interpreting $K$ Values 🎯

🔢 Calculating $K$ from Equilibrium Concentrations

If we know the equilibrium concentrations, we can calculate $K$ by direct substitution.

Problem: For $\text{N}_2(g) + 3\,\text{H}_2(g) \rightleftharpoons 2\,\text{NH}_3(g)$, calculate $K_c$ given equilibrium concentrations: $[\text{N}_2] = 0.50\;\text{M}$, $[\text{H}_2] = 0.30\;\text{M}$, $[\text{NH}_3] = 0.20\;\text{M}$.

Solution:

$K_c = \frac{[\text{NH}_3]^2}{[\text{N}_2][\text{H}_2]^3} = \frac{(0.20)^2}{(0.50)(0.30)^3}$

$K_c = \frac{0.040}{(0.50)(0.027)} = \frac{0.040}{0.0135} = 2.96$

Steps

1. Write the balanced equation
2. Write the $K_c$ expression (products over reactants, with exponents)
3. Substitute equilibrium concentrations
4. Calculate — no units on $K$

Fill in the Blanks — Magnitude of $K$ 🔽

Calculate $K_c$ 🧮

For $\text{A}(g) \rightleftharpoons 2\,\text{B}(g)$, the equilibrium concentrations are $[\text{A}] = 0.40\;\text{M}$ and $[\text{B}] = 0.80\;\text{M}$.

1) What is $K_c$? (Enter a number with one decimal place)

2) Are products or reactants favored? (Enter "products" or "reactants")

3) If the equation is reversed to $2\,\text{B}(g) \rightleftharpoons \text{A}(g)$, what is the new $K_c$? (Enter a number with two decimal places)

Exit Check — Magnitude of $K$ ✅

🔧 Manipulating Equilibrium Constants

Part 5 of 7 — Manipulating $K$

Topics in This Part

🔑 Key Concept: Mastering this material will strengthen your foundation for both the AP Chemistry exam and more advanced chemistry topics.

What You'll Master in Part 5

• Understanding the core concepts covered in Part 5
• Applying these ideas to solve practice problems
• Building toward AP exam readiness for this topic

📏 Three Key Manipulation Rules

Rule 1: Reversing a Reaction

If you reverse a reaction, the new $K$ is the reciprocal:

$\boxed{K_{\text{reverse}} = \frac{1}{K_{\text{forward}}}}$

Example: If $\text{A} \rightleftharpoons \text{B}$, $K = 100$

Then $\text{B} \rightleftharpoons \text{A}$, $K^{\prime} = \frac{1}{100} = 0.01$

Rule 2: Multiplying Coefficients by $n$

If you multiply all coefficients by a factor $n$, the new $K$ is raised to that power:

$\boxed{K_{\text{new}} = K^n}$

Example: If $\text{A} \rightleftharpoons 2\,\text{B}$, $K = 4.0$

Then $2\,\text{A} \rightleftharpoons 4\,\text{B}$, $K^{\prime} = 4.0^2 = 16$

And $\frac{1}{2}\text{A} \rightleftharpoons \text{B}$, $K^{\prime} = 4.0^{1/2} = 2.0$

Rule 3: Adding Reactions (Hess's Law for $K$)

If you add two reactions, the $K$ values are multiplied:

$\boxed{K_{\text{overall}} = K_1 \times K_2}$

Example:

• Reaction 1: $\text{A} \rightleftharpoons \text{B}$, $K_1 = 10$
• Reaction 2: $\text{B} \rightleftharpoons \text{C}$, $K_2 = 5$
• Overall: $\text{A} \rightleftharpoons \text{C}$, $K_{\text{overall}} = 10 \times 5 = 50$

Apply the Rules 🎯

📏 Combining Multiple Rules

AP problems often require you to apply more than one rule at a time.

Problem: Given $\text{A}(g) + \text{B}(g) \rightleftharpoons \text{C}(g)$, $K = 8.0$. Find $K$ for: $3\,\text{C}(g) \rightleftharpoons 3\,\text{A}(g) + 3\,\text{B}(g)$.

Solution:

Step 1: Reverse the original reaction:

$\text{C}(g) \rightleftharpoons \text{A}(g) + \text{B}(g)$, $K^{\prime} = \frac{1}{8.0} = 0.125$

Step 2: Multiply all coefficients by 3:

$3\,\text{C}(g) \rightleftharpoons 3\,\text{A}(g) + 3\,\text{B}(g)$, $K^{\prime\prime} = (0.125)^3 = 1.95 \times 10^{-3}$

Summary Table

Fill in the Blanks — Manipulating $K$ 🔽

Calculate the New $K$ 🧮

Given: $\text{2 NO}(g) + \text{O}_2(g) \rightleftharpoons \text{2 NO}_2(g)$, $K = 4.0 \times 10^{6}$

1) What is $K$ for the reverse reaction? (Use scientific notation like 2.5e-7)

2) What is $K$ for $\text{NO}(g) + \frac{1}{2}\text{O}_2(g) \rightleftharpoons \text{NO}_2(g)$? (Round to the nearest integer)

3) If $K_1 = 4.0 \times 10^6$ and $K_2 = 2.0 \times 10^3$, and you add the two reactions, what is $K_{\text{overall}}$? (Use scientific notation like 8.0e9)

Exit Check — Manipulating $K$ ✅

🔍 The Reaction Quotient $Q$

Part 6 of 7 — Reaction Quotient $Q$

Practice Makes Perfect

This workshop features multi-step problems that mirror the AP Chemistry exam format. Each problem requires you to combine concepts from previous parts and show your work clearly.

🔑 Why this matters: The AP Chemistry exam rewards students who can apply concepts to unfamiliar problems — structured practice is the best preparation.

What You'll Master in Part 6

• Working through complete multi-step problems from start to finish
• Building problem-solving strategies you can apply on the AP exam
• Identifying which concepts to apply and in what order

📖 What Is $Q$?

For: $a\text{A} + b\text{B} \rightleftharpoons c\text{C} + d\text{D}$

$\boxed{Q_c = \frac{[\text{C}]^c[\text{D}]^d}{[\text{A}]^a[\text{B}]^b}}$

This looks exactly like $K_c$ — but the concentrations plugged in are the current (non-equilibrium) values, not the equilibrium concentrations.

Comparing $Q$ to $K$

🔑 Key Intuition: $Q < K$ → system shifts right (needs more products). $Q > K$ → system shifts left (too many products). $Q = K$ → at equilibrium (no net change).

Predicting the Shift 🎯

🧪 Worked Example: Using $Q$

Problem: For $\text{CO}(g) + \text{H}_2\text{O}(g) \rightleftharpoons \text{CO}_2(g) + \text{H}_2(g)$, $K_c = 5.10$ at 700 K. Current concentrations: $[\text{CO}] = 0.20\;\text{M}$, $[\text{H}_2\text{O}] = 0.30\;\text{M}$, $[\text{CO}_2] = 0.40\;\text{M}$, $[\text{H}_2] = 0.50\;\text{M}$. Determine the direction of shift.

Solution:

Step 1: Calculate $Q$

$Q = \frac{[\text{CO}_2][\text{H}_2]}{[\text{CO}][\text{H}_2\text{O}]} = \frac{(0.40)(0.50)}{(0.20)(0.30)} = \frac{0.20}{0.060} = 3.33$

Step 2: Compare $Q$ to $K$

$Q = 3.33 < K = 5.10$

Step 3: Predict the shift

Since $Q < K$, the reaction shifts right (forward) to produce more $CO_{2}$ and $H_{2}$.

💡 AP Strategy: Always calculate $Q$ first, then compare to $K$. Don't try to guess the direction without doing the math!

Fill in the Blanks — The Reaction Quotient 🔽

Calculate and Compare 🧮

For $\text{H}_2(g) + \text{I}_2(g) \rightleftharpoons 2\,\text{HI}(g)$, $K_c = 50.0$ at 448°C.

Current concentrations: $[\text{H}_2] = 0.10\;\text{M}$, $[\text{I}_2] = 0.20\;\text{M}$, $[\text{HI}] = 0.40\;\text{M}$

1) Calculate $Q_c$ (enter a number with one decimal place)

2) Is $Q$ less than, equal to, or greater than $K$? (Enter "less", "equal", or "greater")

3) Will the reaction shift left, right, or not shift? (Enter "left", "right", or "none")

Exit Check — Reaction Quotient $Q$ ✅

🎯 AP Review — Equilibrium Constants & Expressions

Part 7 of 7 — Putting It All Together

Bringing It All Together

This comprehensive review connects every concept from Parts 1–6 with AP-style problems. The questions are designed to mirror what you'll see on the actual exam — multi-step, multi-concept, and requiring clear written explanations.

🔑 Why this matters: AP Chemistry exam questions rarely test one concept in isolation — success requires connecting ideas across topics.

What You'll Master in Part 7

• Solving AP-style questions that integrate multiple concepts from this unit
• Writing clear, concise explanations using proper chemistry terminology
• Identifying and avoiding common AP exam traps and mistakes

🔄 Key Concepts Review

The Big Picture

⚠️ Common AP Mistakes to Avoid:

1. Forgetting to exclude solids/liquids from the $K$ expression
2. Confusing coefficients as multipliers instead of exponents
3. Using Celsius instead of Kelvin in $K_p = K_c(RT)^{\Delta n}$
4. Counting all moles for $\Delta n$ instead of only gaseous moles
5. Thinking $K$ tells us about rate — it only describes the equilibrium position

AP-Style Questions 🎯

Final Concept Check 🔽

AP Calculation Practice 🧮

For $\text{2 SO}_2(g) + \text{O}_2(g) \rightleftharpoons \text{2 SO}_3(g)$

At equilibrium at 700 K: $[\text{SO}_2] = 0.10\;\text{M}$, $[\text{O}_2] = 0.20\;\text{M}$, $[\text{SO}_3] = 0.60\;\text{M}$

1) Calculate $K_c$ (enter an integer)

2) What is $\Delta n$ for this reaction? (enter an integer)

3) Is $K_p$ larger or smaller than $K_c$ for this reaction? (Enter "larger" or "smaller")

Final Exit Check — Equilibrium Constants & Expressions ✅