🎯⭐ INTERACTIVE LESSON

Enthalpy and Calorimetry

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Enthalpy and Calorimetry - Complete Interactive Lesson

Part 1: Enthalpy & ΔH

🔥 Energy, Systems, and Surroundings

Part 1 of 7 — Foundations of Thermochemistry

Topics in This Part

Section
📌 System and Surroundings
Energy Transfer
Sign Conventions
📌 Endothermic vs. Exothermic Processes
Exothermic ( $q < 0$ )

🔑 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

📌 System and Surroundings

In thermochemistry, we divide the universe into two parts:

Term	Definition	Example
System	The part we are studying	The reacting chemicals in a beaker
Surroundings	Everything else	The beaker, the water, the air, the lab
Universe	System + Surroundings	Everything

Energy Transfer

Energy flows between the system and surroundings. The First Law of Thermodynamics states:

$\Delta E_{\text{universe}} = \Delta E_{\text{system}} + \Delta E_{\text{surroundings}} = 0$

📌 Endothermic vs. Exothermic Processes

Exothermic ( $q < 0$ )

The system releases heat to the surroundings.

The surroundings get warmer
$\Delta H < 0$ (negative)
Products have lower energy than reactants
Energy is a product of the reaction

Examples: combustion, neutralization, condensation, freezing

${CH}_{4} (g) + 2 O_{2} (g)$

📌 Energy Diagrams

Energy diagrams visually show the energy change during a reaction.

Exothermic Diagram

Reactants are at a higher energy level
Products are at a lower energy level
$\Delta H$ arrow points downward (negative)
The difference = energy released to surroundings

Endothermic Diagram

Reactants are at a lower energy level
Products are at a higher energy level
$\Delta H$ arrow points upward (positive)
The difference = energy absorbed from surroundings

Key Relationship

$Δ H_{forward} = - Δ$

Energy Fundamentals Quiz 🎯

Classify the Process 🧮

Type "exothermic" or "endothermic" for each process:

1) Water freezing into ice

2) Dissolving ammonium nitrate in water (the solution feels cold)

3) Burning natural gas on a stove

System and Energy Flow 🔽

Exit Quiz — Energy Fundamentals ✅

Part 2: Exothermic & Endothermic

🌡️ Enthalpy (ΔH) — The Heat of Reaction

Part 2 of 7 — State Functions and Standard Enthalpy

Topics in This Part

Section
📖 What Is Enthalpy?
At Constant Pressure
Key Signs
🌡️ Enthalpy Is a State Function
What This Means

🔑 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

📖 What Is Enthalpy?

Enthalpy ( $H$ ) is defined as:

$H = E + PV$

Part 3: Coffee Cup Calorimetry

☕ Calorimetry — Measuring Heat

Part 3 of 7 — q = mcΔT and the Coffee-Cup Calorimeter

Topics in This Part

Section
📌 The Heat Equation
Specific Heat Capacity
📌 The Coffee-Cup Calorimeter
How It Works
Key Assumptions

🔑 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

📌 The Heat Equation

$\boxed{q = mc\Delta T}$

Part 4: Bomb Calorimetry

💣 Bomb Calorimetry

Part 4 of 7 — Constant-Volume Calorimetry

Topics in This Part

Section
🏗️ Bomb Calorimeter Structure
Key Feature: Constant Volume
Relationship Between $\Delta H$ and $\Delta E$
📌 Heat Capacity of the Calorimeter
Important Distinction

🔑 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

🏗️ Bomb Calorimeter Structure

A bomb calorimeter consists of:

Part 5: Hess's Law

🔄 Hess's Law — Adding Enthalpy Changes

Part 5 of 7 — The Power of State Functions

Topics in This Part

Section
📏 Hess's Law
Rules for Manipulating Equations
🛠️ Problem-Solving Strategy
Step-by-Step Approach
Worked Example

🔑 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

📏 Hess's Law

Hess's Law: If a reaction can be expressed as the sum of two or more other reactions, the enthalpy change of the overall reaction is the sum of the enthalpy changes of the individual reactions.

$Δ H_{overall} = Δ H_{1} + Δ H_{2} + Δ_{}$

Part 6: Problem-Solving Workshop

🏗️ Standard Enthalpies of Formation

Part 6 of 7 — The Master Equation

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

🌡️ Standard Enthalpy of Formation ( $\Delta H°_f$ )

The enthalpy change when one mole of a compound is formed from its elements in their standard states.

Part 7: Synthesis & AP Review

🎯 Synthesis & AP Review — Enthalpy and Calorimetry

Part 7 of 7 — Bringing 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

📌 Complete Concept Map

Energy and Heat

Concept	Key Equation	Notes
Heat transfer	$q = mc\Delta T$

Energy is conserved — it is neither created nor destroyed, only transferred.

Direction of Energy Flow	$q_{\text{system}}$	Temperature of Surroundings
Energy flows into system	Positive (+)	Decreases
Energy flows out of system	Negative (−)	Increases

CH_{4} (g) + 2 O_{2} (g) \to CO_{2} (g) + 2 H_{2} O (l) Δ H = - 890 kJ

Endothermic ( $q > 0$ )

The system absorbs heat from the surroundings.

The surroundings get cooler
$\Delta H > 0$ (positive)
Products have higher energy than reactants
Energy is a reactant

Examples: photosynthesis, melting ice, evaporation, dissolving $\text{NH}_4\text{NO}_3$

$\text{6CO}_2(g) + 6\text{H}_2\text{O}(l) \rightarrow \text{C}_6\text{H}_{12}\text{O}_6(s) + 6\text{O}_2(g) \quad \Delta H = +2803 \text{ kJ}$

Δ H_{forward} = - Δ H_{reverse}

If a reaction is exothermic in the forward direction, it is endothermic in reverse, and vice versa.

where $E$ is internal energy, $P$ is pressure, and $V$ is volume.

We can never measure absolute enthalpy — only the change in enthalpy:

$\Delta H = H_{\text{products}} - H_{\text{reactants}}$

At Constant Pressure

At constant pressure (open beaker, atmospheric conditions):

$\boxed{\Delta H = q_p}$

The enthalpy change equals the heat transferred at constant pressure. This is why chemists love enthalpy — it directly corresponds to the heat you can measure!

🔑 Key Insight: At constant pressure (like an open beaker), the enthalpy change IS the heat. This makes $\Delta H$ the most practically useful thermodynamic quantity.

$\Delta H$	Meaning	Type
Negative (−)	Heat released	Exothermic
Positive (+)	Heat absorbed	Endothermic

🌡️ Enthalpy Is a State Function

A state function depends only on the current state of the system, not on how it got there.

What This Means

The enthalpy change $\Delta H$ depends only on the initial and final states
It does not depend on the pathway or mechanism
The same reaction will have the same $\Delta H$ regardless of how many steps it takes

💡 Analogy: Think of altitude — your change in altitude depends only on start and end, not the trail you took. Enthalpy works the same way.

Analogy

Think of altitude: if you climb a mountain, your change in altitude depends only on your starting and ending positions — not whether you took the steep trail or the winding road. Enthalpy works the same way.

Consequences

If a reaction can occur in one step or multiple steps, $\Delta H$ is the same
This is the foundation of Hess's Law (Part 5)
We can calculate $\Delta H$ for reactions we cannot directly measure

🌡️ Standard Enthalpy

Standard conditions in thermochemistry use the symbol $°$ :

Parameter	Standard Value
Pressure	$1$ atm (or $1$ bar)
Concentration	$1$ M (for solutions)
Temperature	Usually $25°\text{C}$ ( $298$ K), but must be specified

Standard Enthalpy of Reaction ( $\Delta H°_{\text{rxn}}$ )

The enthalpy change when reactants in their standard states are converted to products in their standard states.

Standard State

The standard state of a substance is its most stable form at $1$ atm and the specified temperature:

Substance	Standard State
Oxygen	$\text{O}_2(g)$
Carbon	$\text{C}(s, \text{graphite})$
Iron

Important Relationships

If you multiply a reaction by a factor $n$ : $\Delta H_{\text{new}} = n \times \Delta H_{\text{original}}$

If you reverse a reaction: $\Delta H_{\text{reverse}} = -\Delta H_{\text{forward}}$

Enthalpy Concept Quiz 🎯

Enthalpy Scaling Practice 🧮

Given: $\text{N}_2(g) + 3\text{H}_2(g) \rightarrow 2\text{NH}_3(g) \quad \Delta H = -92 \text{ kJ}$

1) What is $\Delta H$ for $\frac{1}{2}\text{N}_2(g) + \frac{3}{2}\text{H}_2(g) \rightarrow \text{NH}_3(g)$ ? (in kJ)

2) What is $\Delta H$ for $2\text{NH}_3(g) \rightarrow \text{N}_2(g) + 3\text{H}_2(g)$ ? (in kJ)

3) What is $\Delta H$ for $2\text{N}_2(g) + 6\text{H}_2(g) \rightarrow 4\text{NH}_3(g)$ ? (in kJ)

Enthalpy Properties 🔽

Exit Quiz — Enthalpy ✅

Symbol	Meaning	Common Units
$q$	Heat absorbed or released	J or kJ
$m$	Mass of substance	g
$c$	Specific heat capacity	J/(g·°C)
$\Delta T$	Change in temperature ( $T_f - T_i$ )	°C or K

Specific Heat Capacity

The specific heat capacity is the amount of heat required to raise the temperature of 1 gram of a substance by 1°C.

Substance	$c$ [J/(g·°C)]
Water (liquid)	4.184
Ice	2.09
Steam	2.01
Aluminum	0.897
Iron	0.449
Copper	0.385

Water has an unusually high specific heat, meaning it can absorb a lot of heat with only a small temperature change. This is why water is used as a coolant and why coastal climates are moderate.

📌 The Coffee-Cup Calorimeter

A simple calorimeter made from a Styrofoam cup with a lid and thermometer.

How It Works

Measure the initial temperature of the solution
Mix the reactants in the cup
Record the maximum (or minimum) temperature reached
Calculate $q$ for the solution using $q = mc\Delta T$

Key Assumptions

The calorimeter is perfectly insulated (no heat escapes)
The solution has the same density and specific heat as pure water ( $c = 4.184$ J/(g·°C), $d = 1.00$ g/mL)
All heat from the reaction goes into the solution

Important Sign Convention

$\boxed{q_{\text{rxn}} = -q_{\text{solution}}}$

If the solution warms up ( $q_{\text{solution}} > 0$ ), the reaction is exothermic ( $q_{\text{rxn}} < 0$ ).

⚠️ Common AP Mistake: Don’t forget the negative sign! $q_{\text{rxn}}$ and $q_{\text{solution}}$ always have opposite signs.

Constant Pressure

A coffee-cup calorimeter operates at constant pressure (open to the atmosphere), so:

$q_p = \Delta H$

🧪 Worked Example — Coffee-Cup Calorimetry

Problem: When 50.0 mL of 1.00 M HCl is mixed with 50.0 mL of 1.00 M NaOH in a coffee-cup calorimeter, the temperature rises from 22.0°C to 28.9°C. Calculate $\Delta H$ per mole of water formed.

Given

Quantity	Value
Volume of HCl	50.0 mL of 1.00 M
Volume of NaOH	50.0 mL of 1.00 M
$T_i$	22.0°C
$T_f$	28.9°C
$c_{\text{water}}$	4.184 J/(g·°C)
$d_{\text{solution}}$	1.00 g/mL

Step-by-Step Solution

Step	Action	Calculation	Result
1	Mass of solution	$100.0 \text{ mL} \times 1.00 \text{ g/mL}$	100.0 g
2	Temperature change	$28.9 - 22.0$	$Δ$

🔑 Result: $\Delta H = -57.8$ kJ/mol. The accepted value is $-55.8$ kJ/mol — our measurement is close! The negative sign confirms the reaction is exothermic.

Calorimetry Concept Quiz 🎯

Calorimetry Calculations 🧮

1) How much heat is needed to raise the temperature of 200.0 g of water from 20.0°C to 45.0°C? (answer in kJ, to 3 significant figures; $c_{\text{water}} = 4.184$ J/(g·°C))

2) A 50.0 g piece of metal at 95.0°C is placed in 150.0 g of water at 20.0°C. The final temperature is 23.0°C. What is the specific heat of the metal? (in J/(g·°C), to 3 significant figures)

3) When 100.0 mL of 0.500 M HCl and 100.0 mL of 0.500 M NaOH are mixed, the temperature rises by 3.4°C. What is $q_{\text{rxn}}$ in kJ? (to 3 significant figures, include sign)

Calorimetry Concepts 🔽

Exit Quiz — Calorimetry ✅

The "bomb" — a rigid, sealed steel container where the reaction occurs
Water bath — surrounds the bomb, absorbs the released heat
Ignition wire — initiates combustion with an electric spark
Thermometer — measures the temperature change of the water
Stirrer — ensures uniform temperature in the water bath
Insulated jacket — minimizes heat loss to the environment

Key Feature: Constant Volume

The bomb is sealed and rigid — the volume cannot change. This means:

No $PV$ work is done ( $w = 0$ since $\Delta V = 0$ )
At constant volume: $q_v = \Delta E$ (internal energy change)
This is different from coffee-cup calorimetry where $q_p = \Delta H$

🔑 Key Distinction: Coffee-cup = constant pressure → measures $\Delta H$ . Bomb = constant volume → measures $\Delta E$ .

Relationship Between $\Delta H$ and $\Delta E$

$\Delta H = \Delta E + \Delta(PV)$

For reactions involving only solids and liquids, $\Delta H \approx \Delta E$ .

For reactions involving gases:

$\boxed{\Delta H = \Delta E + \Delta n_{\text{gas}} RT}$

where $\Delta n_{\text{gas}}$ = moles of gaseous products − moles of gaseous reactants.

📌 Heat Capacity of the Calorimeter

For a bomb calorimeter, we use the heat capacity of the entire calorimeter ( $C_{\text{cal}}$ ):

$\boxed{q_{\text{cal}} = C_{\text{cal}} \Delta T}$

Symbol	Meaning	Units
$q_{\text{cal}}$	Heat absorbed by calorimeter	kJ
$C_{\text{cal}}$

Important Distinction

Quantity	Symbol	Units	Usage
Specific heat	$c$	J/(g·°C)	Per gram
Heat capacity	$C$	J/°C or kJ/°C	For the whole calorimeter

The heat capacity $C_{\text{cal}}$ is determined by calibration — burning a substance with a known heat of combustion.

Finding $q_{\text{rxn}}$

$q_{\text{rxn}} = -q_{\text{cal}} = -C_{\text{cal}} \Delta T$

The negative sign reflects that heat released by the reaction is absorbed by the calorimeter.

🧪 Worked Example — Bomb Calorimetry

Problem: A 1.50 g sample of benzoic acid ( $\text{C}_7\text{H}_6\text{O}_2$ , molar mass = 122.12 g/mol) is burned in a bomb calorimeter with $C_{\text{cal}} = 10.34$ kJ/°C. The temperature rises from 22.45°C to 25.71°C. Calculate the molar heat of combustion.

Given

Quantity	Value
Mass of sample	1.50 g
Molar mass ( $\text{C}_7\text{H}_6\text{O}_2$ )	122.12 g/mol

Step-by-Step Solution

Step	Action	Calculation	Result
1	Temperature change	$25.71 - 22.45$	$\Delta T = 3.26°\text{C}$
2	Heat absorbed by calorimeter	$(10.34) ($

⚠️ Note: This gives $\Delta E$ (internal energy), not $\Delta H$ , because the bomb calorimeter operates at constant volume. For this reaction, $\Delta H \approx \Delta E$ because $\Delta n_{\text{gas}}$ is small.

Bomb Calorimetry Concept Quiz 🎯

Bomb Calorimetry Calculations 🧮

1) A bomb calorimeter has $C_{\text{cal}} = 8.50$ kJ/°C. If the temperature rises by 4.20°C, what is $q_{\text{rxn}}$ ? (in kJ, include sign)

2) When 0.500 g of sugar ( $\text{C}_{12}\text{H}_{22}\text{O}_{11}$ , molar mass = 342.3 g/mol) is burned in a bomb calorimeter ( $C_{\text{cal}} = 9.20$ kJ/°C), the temperature rises by 1.23°C. What is the energy released per mole? (in kJ/mol, round to nearest whole number, report as positive)

3) A calibration experiment burns 1.000 g of benzoic acid (heat of combustion = 26.38 kJ/g) and the temperature rises by 2.55°C. What is $C_{\text{cal}}$ ? (in kJ/°C, to 3 significant figures)

Bomb vs. Coffee-Cup Calorimetry 🔽

Exit Quiz — Bomb Calorimetry ✅

Δ H_{overall} = Δ H_{1} + Δ H_{2} + Δ H_{3} + \dots

🔑 Why It Works: Because enthalpy is a state function, the total $\Delta H$ depends only on the initial and final states, not the path. Whether a reaction occurs in one step or ten, $\Delta H$ is the same.

Rules for Manipulating Equations

Operation	Effect on $\Delta H$
Reverse the reaction	Change the sign
Multiply by a factor $n$	Multiply $\Delta H$ by $n$
Add reactions together	Add $\Delta H$ values

🛠️ Problem-Solving Strategy

Step-by-Step Approach

Write the target reaction — the one you need $\Delta H$ for
Examine the given reactions — look for each substance in your target
Manipulate given reactions so that when added, they equal the target:
- Reverse reactions if a reactant needs to be a product (or vice versa)
- Multiply reactions to match the coefficients in the target
Add the manipulated reactions — substances on opposite sides cancel
Add the adjusted $\Delta H$ values to get $\Delta H_{\text{overall}}$

Worked Example

Problem: Find $\Delta H$ for: $\text{C}(s) + \frac{1}{2}\text{O}_2(g) \rightarrow \text{CO}(g)$

Solution:

Keep reaction 1 as written (has C as reactant ✓)
Reverse reaction 2 (need CO as product): $\text{CO}_2(g) \rightarrow \text{CO}(g) + \frac{1}{2}\text{O}_2(g) \quad \Delta H = +283.0$ kJ

Add:

$\text{C}(s) + \text{O}_2(g) + \text{CO}_2(g) \rightarrow \text{CO}_2(g) + \text{CO}(g) + \frac{1}{2}\text{O}_2(g)$

Cancel $\text{CO}_2$ and simplify $\text{O}_2$ :

$\text{C}(s) + \frac{1}{2}\text{O}_2(g) \rightarrow \text{CO}(g)$

$\Delta H = -393.5 + 283.0 = -110.5 \text{ kJ}$

Hess's Law Concept Quiz 🎯

Hess's Law Calculations 🧮

Given:

(1) $\text{S}(s) + \text{O}_2(g) \rightarrow \text{SO}_2(g) \quad \Delta H_1 = -296.8$ kJ
(2) $2\text{SO}_2(g) + \text{O}_2(g) \rightarrow 2\text{SO}_3(g) \quad \Delta H_2 = -197.8$ kJ

Find $\Delta H$ for: $2\text{S}(s) + 3\text{O}_2(g) \rightarrow 2\text{SO}_3(g)$

1) What must you multiply reaction (1) by? (enter the number)

2) What must you multiply reaction (2) by? (enter the number)

3) What is $\Delta H$ for the target reaction? (in kJ, to 3 significant figures)

Hess's Law Strategy 🔽

Exit Quiz — Hess's Law ✅

$\text{C}(s, \text{graphite}) + \text{O}_2(g) \rightarrow \text{CO}_2(g) \quad \Delta H°_f = -393.5 \text{ kJ/mol}$

$\text{H}_2(g) + \frac{1}{2}\text{O}_2(g) \rightarrow \text{H}_2\text{O}(l) \quad \Delta H°_f = -285.8 \text{ kJ/mol}$

$\frac{1}{2}\text{N}_2(g) + \frac{3}{2}\text{H}_2(g) \rightarrow \text{NH}_3(g) \quad \Delta H°_f = -45.9 \text{ kJ/mol}$

🔑 AP Must-Know: $\Delta H°_f$ of any element in its standard state = 0. This is the #1 rule for formation enthalpy calculations.

Element	Standard State	$\Delta H°_f$
$\text{O}_2(g)$	Standard	0 kJ/mol
$\text{N}_2(g)$	Standard	0 kJ/mol
$\text{C}(s, \text{graphite})$	Standard	0 kJ/mol
$\text{Fe}(s)$	Standard	0 kJ/mol
$\text{Br}_2(l)$	Standard	0 kJ/mol

This makes sense: an element doesn't change to form itself!

📌 The Master Equation

$\boxed{\Delta H°_{\text{rxn}} = \sum n \cdot \Delta H°_f(\text{products}) - \sum m \cdot \Delta H°_f(\text{reactants})}$

where $n$ and $m$ are the stoichiometric coefficients.

How to Use It

Look up $\Delta H°_f$ for every compound in the reaction
Remember: $\Delta H°_f = 0$ for elements in their standard states
Multiply each by its coefficient

Worked Example

Calculate $\Delta H°_{\text{rxn}}$ for: $\text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(l)$

Substance	$\Delta H°_f$ (kJ/mol)	Coefficient
$\text{CH}_4(g)$

$\Delta H°_{\text{rxn}} = [(-393.5) + 2(-285.8)] - [(-74.8) + 2(0)]$

Formation Enthalpy Concept Quiz 🎯

Formation Enthalpy Calculations 🧮

Given:

Substance	$\Delta H°_f$ (kJ/mol)
$\text{CO}_2(g)$	$-393.5$
$\text{H}_2\text{O}(l)$	$-285.8$
$\text{C}_2\text{H}_6(g)$	$-84.7$
$\text{NH}_3(g)$	$-45.9$
$\text{NO}(g)$	$+90.3$
$\text{O}_2, \text{N}_2, \text{H}_2$	$0$

1) Calculate $\Delta H°_{\text{rxn}}$ for: $\text{C}_2\text{H}_6(g) + \frac{7}{2}\text{O}_2(g) \rightarrow 2\text{CO}_2(g) + 3\text{H}_2\text{O}(l)$ (in kJ, to 3 significant figures)

2) Calculate $\Delta H°_{\text{rxn}}$ for: $4\text{NH}_3(g) + 5\text{O}_2(g) \rightarrow 4\text{NO}(g) + 6\text{H}_2\text{O}(l)$ (in kJ, to 3 significant figures)

Formation Enthalpy Concepts 🔽

Exit Quiz — Formation Enthalpies ✅

Concept	Key Relationship	Notes
Exothermic	$\Delta H < 0$	System releases heat
Endothermic	$\Delta H > 0$	System absorbs heat
Reverse reaction	$\Delta H_{\text{rev}} = -\Delta H_{\text{fwd}}$	Sign change
Scaled reaction	$\Delta H_{\text{new}} = n \cdot \Delta H$	Linear scaling

Hess's Law & Formation

Method	Equation
Hess's Law	$\Delta H_{\text{total}} = \sum \Delta H_{\text{steps}}$
Formation enthalpies	$\Delta H°_{\text{rxn}} = \sum n \cdot \Delta H°_f(\text{products}) - \sum m \cdot \Delta H°_f(\text{reactants})$

🎯 AP Exam Strategies

Common AP Question Types

Calorimetry calculation — given mass, specific heat, ΔT → find q → find ΔH per mole
Hess's Law — manipulate 2-3 reactions to find ΔH for a target reaction
Formation enthalpy — use the master equation with a table of $\Delta H°_f$ values
Conceptual — identify exo/endothermic, explain sign conventions, predict temperature changes

Common Mistakes to Avoid

Forgetting to flip the sign of ΔH when reversing a reaction
Using specific heat ( $c$ ) when heat capacity ( $C$ ) is given (or vice versa)
Forgetting that $\Delta H°_f = 0$ for elements in their standard states
Mixing up $q_{\text{rxn}}$ and $q_{\text{solution}}$ (they have opposite signs)
Not converting between J and kJ

⚠️ Unit Warning: $q = mc\Delta T$ gives joules. $\Delta H°_f$ values are in kJ/mol. Always check your units before combining!

Comprehensive AP Review Quiz 🎯

Integration Problems 🧮

1) 150.0 mL of 2.00 M HCl reacts with excess NaOH in a coffee-cup calorimeter. The temperature rises by 13.4°C. Assume the solution's mass is 150.0 g and $c = 4.184$ J/(g·°C). What is $\Delta H$ per mole of HCl? (in kJ/mol, to 3 significant figures, include sign)

2) Using the $\Delta H°_f$ values below, calculate $\Delta H°_{\text{rxn}}$ for $\text{C}_3\text{H}_8(g) + 5\text{O}_2(g) \rightarrow 3\text{CO}_2(g) + 4\text{H}_2\text{O}(l)$ . (in kJ)

Substance	$\Delta H°_f$ (kJ/mol)
$\text{CO}_2(g)$

Comprehensive Concept Review 🔽

Final Exit Quiz — Thermochemistry Mastery ✅

$\text{C}(s) + \text{O}_2(g) \rightarrow \text{CO}_2(g) \quad \Delta H_1 = -393.5$ kJ
$\text{CO}(g) + \frac{1}{2}\text{O}_2(g) \rightarrow \text{CO}_2(g) \quad \Delta H_2 = -283.0$ kJ

Subtract the sum of reactants from the sum of products

= [-393.5 - 571.6] - [-74.8]

= -965.1 + 74.8 = -890.3 \text{ kJ}

Enthalpy and Calorimetry

Enthalpy and Calorimetry - Complete Interactive Lesson

Part 1: Enthalpy & ΔH

🔥 Energy, Systems, and Surroundings

Topics in This Part

What You'll Master in Part 1

📌 System and Surroundings

Energy Transfer

📌 Endothermic vs. Exothermic Processes

Exothermic (q<0q < 0q<0)

📌 Energy Diagrams

Exothermic Diagram

Endothermic Diagram

Key Relationship

Part 2: Exothermic & Endothermic

🌡️ Enthalpy (ΔH) — The Heat of Reaction

Topics in This Part

What You'll Master in Part 2

📖 What Is Enthalpy?

Part 3: Coffee Cup Calorimetry

☕ Calorimetry — Measuring Heat

Topics in This Part

What You'll Master in Part 3

📌 The Heat Equation

Part 4: Bomb Calorimetry

💣 Bomb Calorimetry

Topics in This Part

What You'll Master in Part 4

🏗️ Bomb Calorimeter Structure

Part 5: Hess's Law

🔄 Hess's Law — Adding Enthalpy Changes

Topics in This Part

What You'll Master in Part 5

📏 Hess's Law

Part 6: Problem-Solving Workshop

🏗️ Standard Enthalpies of Formation

Practice Makes Perfect

What You'll Master in Part 6

🌡️ Standard Enthalpy of Formation (ΔH°f\Delta H°_fΔH°f​)

Part 7: Synthesis & AP Review

🎯 Synthesis & AP Review — Enthalpy and Calorimetry

Bringing It All Together

What You'll Master in Part 7

📌 Complete Concept Map

Energy and Heat

Sign Conventions

Endothermic (q>0q > 0q>0)

At Constant Pressure

Key Signs

🌡️ Enthalpy Is a State Function

What This Means

Analogy

Consequences

🌡️ Standard Enthalpy

Standard Enthalpy of Reaction (ΔH°rxn\Delta H°_{\text{rxn}}ΔH°rxn​)

Standard State

Important Relationships

Specific Heat Capacity

📌 The Coffee-Cup Calorimeter

How It Works

Key Assumptions

Important Sign Convention

Constant Pressure

🧪 Worked Example — Coffee-Cup Calorimetry

Given

Step-by-Step Solution

Key Feature: Constant Volume

Relationship Between ΔH\Delta HΔH and ΔE\Delta EΔE

📌 Heat Capacity of the Calorimeter

Important Distinction

Finding qrxnq_{\text{rxn}}qrxn​

🧪 Worked Example — Bomb Calorimetry

Given

Step-by-Step Solution

Rules for Manipulating Equations

🛠️ Problem-Solving Strategy

Step-by-Step Approach

Worked Example

Examples

Critical Rule

Exothermic ( $q < 0$ )

🌡️ Standard Enthalpy of Formation ( $\Delta H°_f$ )

Endothermic ( $q > 0$ )

Standard Enthalpy of Reaction ( $\Delta H°_{\text{rxn}}$ )

Relationship Between $\Delta H$ and $\Delta E$

Finding $q_{\text{rxn}}$