🎯⭐ INTERACTIVE LESSON

Equilibrium Constants and Expressions

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Equilibrium Constants and Expressions - Complete Interactive Lesson

Part 1: What Is Equilibrium?

⚖️ Equilibrium Constants and Expressions

Part 1 of 7 — What Is Chemical Equilibrium?

Before we can write equilibrium expressions or calculate $K$ values, we need a solid understanding of what equilibrium actually means at the molecular level and how to recognize it experimentally.

⚖️ Dynamic Equilibrium Revisited

At dynamic equilibrium:

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

Key Features

Feature	What It Means
Dynamic	Both forward and reverse reactions are still occurring
No net change	Concentrations of all species remain constant over time
Closed system	No matter enters or leaves the system
Temperature-dependent	The equilibrium position depends on temperature

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:

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")

Exit Check — What Is Equilibrium? ✅

Part 2: Writing K Expressions

✍️ Writing Equilibrium Expressions

Part 2 of 7 — Writing $K$ Expressions

Now that we understand what $K$ represents, let's master the rules for writing equilibrium constant expressions from balanced equations.

✍️ Rules for Writing $K_c$ Expressions

For the reaction:

$a A (a q$

Part 3: Kc vs Kp

🔄 $K_c$ vs $K_p$

Part 3 of 7 — Concentration vs. Pressure Equilibrium Constants

For gas-phase equilibria, we can express $K$ in terms of molar concentrations () or partial pressures (). This part covers both forms and how to convert between them.

Part 4: Magnitude of K

📏 Magnitude of K

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

The numerical value of $K$ carries enormous meaning. In this part, we'll learn to interpret $K$ values and understand how they connect to the extent of a reaction.

📌 Interpreting the Magnitude of $K$

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

$K$ Value

Part 5: Manipulating K

🔧 Manipulating Equilibrium Constants

Part 5 of 7 — Manipulating $K$

On the AP exam, you'll need to predict how $K$ changes when you reverse a reaction, multiply coefficients, or add reactions together. These are essential algebraic rules for working with equilibrium expressions.

📏 Three Key Manipulation Rules

Rule 1: Reversing a Reaction

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

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

Part 6: Reaction Quotient Q

🔍 The Reaction Quotient $Q$

Part 6 of 7 — Reaction Quotient $Q$

The reaction quotient $Q$ has the same form as $K$ but uses current concentrations instead of equilibrium concentrations. Comparing $Q$ to $K$ lets us predict which direction a reaction will shift to reach equilibrium.

Part 7: AP Review

🎯 AP Review — Equilibrium Constants & Expressions

Part 7 of 7 — Putting It All Together

This final section covers AP-style problems that combine multiple concepts: writing expressions, calculating $K$ , using $Q$ , converting between $K_c$ and $K_p$ , and manipulating equilibrium constants.

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

Value of $K$	Meaning
$K \gg 1$	Products are strongly favored at equilibrium
$K \approx 1$	Comparable amounts of reactants and products
$K \ll 1$	Reactants are strongly favored at equilibrium

Critical Facts About $K$

$K$ 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

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

a A (a q) + b B (g) ⇌ c C (a q) + d D (g)

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

What Goes In and What Stays Out

Species	Include in $K$ ?	Why
Gases $(g)$	✅ Yes	Concentration varies
Aqueous $(aq)$	✅ Yes	Concentration varies
Pure solids $(s)$	❌ No	Activity = 1 (constant density)
Pure liquids $(l)$	❌ No	Activity = 1 (constant density)

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

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

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

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

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

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 ✅

💨 $K_p$ — The Pressure-Based Constant

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

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

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

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:

$R = 0.08206\;\text{L·atm·mol}^{-1}\text{·K}^{-1}$
= temperature in

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:

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

They are equal!

Example Calculation

For $\text{N}_2\text{O}_4(g) \rightleftharpoons 2\,\text{NO}_2(g)$ at 25°C,

$\Delta n = 2 - 1 = 1$

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

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

$K_c$ 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 $K_p$ ✅

Reaction	$K$	Interpretation
$2\,\text{H}_2(g) + \text{O}_2(g) \rightleftharpoons 2\,\text{H}_2\text{O}(g)$ at 500 K	$\sim 10^{80}$	Essentially irreversible — goes to completion
$\text{N}_2\text{O}_4(g) \rightleftharpoons 2\,\text{NO}_2(g)$ at 25°C
$\text{H}_2(g) + \text{I}_2(g) \rightleftharpoons 2\,\text{HI}(g)$ at 425°C

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.

Example

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

At equilibrium: $[\text{N}_2] = 0.50\;\text{M}$ , $[\text{H}_2] = 0.30\;\text{M}$ ,

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

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

Steps

Write the balanced equation
Write the $K_c$ expression (products over reactants, with exponents)
Substitute equilibrium concentrations
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 $K$ ✅

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:

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

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:

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

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.

Example

Given: $\text{A}(g) + \text{B}(g) \rightleftharpoons \text{C}(g)$ , $K = 8.0$

Find $K$ for: $3\,\text{C}(g) \rightleftharpoons 3\,\text{A}(g) + 3\,\text{B}(g)$

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

Operation	Effect on $K$
Reverse reaction	$K^{\prime} = 1/K$
Multiply coefficients by $n$

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 ? (Use scientific notation like 8.0e9)

Exit Check — Manipulating $K$ ✅

📖 What Is $Q$ ?

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

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

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

Comparing $Q$ to $K$

Comparison	Meaning	Shift Direction
$Q < K$	Too many reactants, not enough products	Shifts right (toward products)
$Q = K$	System is at equilibrium	No shift
$Q > K$

Intuition

Think of it this way:

$Q < K$ : The system needs to make more products to reach equilibrium → forward reaction
$Q > K$ : The system has too many products → reverse reaction
$Q = K$ : Already 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

At a certain moment: $[\text{CO}] = 0.20\;\text{M}$ , $[\text{H}_2\text{O}] = 0.30\;\text{M}$ , ,

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 CO₂ and H₂.

AP Test 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: $[\text{H}_2] = 0.10\;\text{M}$ , $[\text{I}_2] = 0.20\;\text{M}$ ,

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 $Q$ ✅

🔄 Key Concepts Review

The Big Picture

Concept	Formula / Rule
$K_c$ expression	$\frac{[\text{products}]^{\text{coeff}}}{[\text{reactants}]^{\text{coeff}}}$
Exclude from $K$	Pure solids $(s)$ and pure liquids $(l)$
$K_p$ expression	Same form but with partial pressures
$K_p$ ↔ $K_c$	$K_p = K_c(RT)^{\Delta n}$
Reverse reaction	$K_{\text{rev}} = 1/K$
Multiply by $n$	$K_{\text{new}} = K^n$
Add reactions	$K_{\text{overall}} = K_1 \times K_2$
$Q < K$	Shift right (forward)
$Q > K$	Shift left (reverse)
$Q = K$	At equilibrium

Common AP Mistakes to Avoid ⚠️

Forgetting to exclude solids/liquids from the $K$ expression
Confusing coefficients as multipliers instead of exponents
Using Celsius instead of Kelvin in $K_p = K_c(RT)^{\Delta n}$

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: $[\text{SO}_2] = 0.10\;\text{M}$ , $[\text{O}_2] = 0.20\;\text{M}$ ,

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 ✅

\Delta n

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

K_c = 4.61 \times 10^{-3}

[\text{NH}_3] = 0.20\;\text{M}

(0.50)(0.30)3(0.20)2

K^{''} = (0.125)^{3} = 1.95 \times 1 0^{- 3}

K_{\text{overall}}

[\text{CO}_2] = 0.40\;\text{M}

[\text{H}_2] = 0.50\;\text{M}

(0.20)(0.30)(0.40)(0.50)=

[\text{HI}] = 0.40\;\text{M}

Counting all moles for $\Delta n$ instead of only gaseous moles

Thinking $K$ tells us about rate — it only describes the equilibrium position

[\text{SO}_3] = 0.60\;\text{M}

$K > 10^3$	Reaction goes nearly to completion	Products dominate
$1 < K < 10^3$	Products slightly favored	More products than reactants
$K \approx 1$	Neither side strongly favored	Comparable amounts
$10^{-3} < K < 1$	Reactants slightly favored	More reactants than products
$K < 10^{-3}$	Reaction barely proceeds	Reactants dominate

Equilibrium Constants and Expressions

What $K$ Tells Us

Critical Facts About $K$

What Goes In and What Stays Out

Example 1

Example 2

📌 Homogeneous vs. Heterogeneous Equilibria

Homogeneous Equilibrium

Heterogeneous Equilibrium

AP Tip 💡

💨 $K_p$ — The Pressure-Based Constant

Example

🔄 Converting Between $K_c$ and $K_p$

Finding $\Delta n$

When $\Delta n = 0$

Example Calculation

Real-World Examples

AP Key Point 💡

🔢 Calculating $K$ from Equilibrium Concentrations

Example

Steps

Rule 2: Multiplying Coefficients by $n$

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

📏 Combining Multiple Rules

Example

Summary Table

📖 What Is $Q$ ?

Comparing $Q$ to $K$

Intuition

🧪 Worked Example: Using $Q$

Problem

AP Test Strategy 💡

🔄 Key Concepts Review

The Big Picture

Common AP Mistakes to Avoid ⚠️

Equilibrium Constants and Expressions

Equilibrium Constants and Expressions - Complete Interactive Lesson

Part 1: What Is Equilibrium?

⚖️ Equilibrium Constants and Expressions

⚖️ Dynamic Equilibrium Revisited

Key Features

Common Misconception

⚖️ The Equilibrium Constant

Part 2: Writing K Expressions

✍️ Writing Equilibrium Expressions

✍️ Rules for Writing KcK_cKc​ Expressions

Part 3: Kc vs Kp

🔄 KcK_cKc​ vs KpK_pKp​

Part 4: Magnitude of K

📏 Magnitude of K

📌 Interpreting the Magnitude of KKK

Part 5: Manipulating K

🔧 Manipulating Equilibrium Constants

📏 Three Key Manipulation Rules

Rule 1: Reversing a Reaction

Part 6: Reaction Quotient Q

🔍 The Reaction Quotient QQQ

Part 7: AP Review

🎯 AP Review — Equilibrium Constants & Expressions

What KKK Tells Us

Critical Facts About KKK

What Goes In and What Stays Out

Example 1

Example 2

📌 Homogeneous vs. Heterogeneous Equilibria

Homogeneous Equilibrium

Heterogeneous Equilibrium

AP Tip 💡

💨 KpK_pKp​ — The Pressure-Based Constant

Example

🔄 Converting Between KcK_cKc​ and KpK_pKp​

Finding Δn\Delta nΔn

When Δn=0\Delta n = 0Δn=0

Example Calculation

Real-World Examples

AP Key Point 💡

🔢 Calculating KKK from Equilibrium Concentrations

Example

Steps

Rule 2: Multiplying Coefficients by nnn

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

📏 Combining Multiple Rules

Example

Summary Table

📖 What Is QQQ?

Comparing QQQ to KKK

Intuition

🧪 Worked Example: Using QQQ

Problem

AP Test Strategy 💡

🔄 Key Concepts Review

The Big Picture

Common AP Mistakes to Avoid ⚠️

✍️ Rules for Writing $K_c$ Expressions

🔄 $K_c$ vs $K_p$

📌 Interpreting the Magnitude of $K$

🔍 The Reaction Quotient $Q$

What $K$ Tells Us

Critical Facts About $K$

💨 $K_p$ — The Pressure-Based Constant

🔄 Converting Between $K_c$ and $K_p$

Finding $\Delta n$

When $\Delta n = 0$

🔢 Calculating $K$ from Equilibrium Concentrations

Rule 2: Multiplying Coefficients by $n$

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

📖 What Is $Q$ ?

Comparing $Q$ to $K$

🧪 Worked Example: Using $Q$