🎯⭐ INTERACTIVE LESSON

Moles and Molar Mass

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Moles and Molar Mass - Complete Interactive Lesson

Part 1: Introduction to the Mole

⚗️ Introduction to the Mole

Part 1 of 7 — Avogadro's Number & Counting by Weighing

Topics in This Part

Section
📖 What Is a Mole?
Putting It in Perspective
Why Such a Specific Number?
📌 Counting by Weighing
The Analogy

🔑 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

📖 What Is a Mole?

A mole (abbreviated mol) is a counting unit, just like a "dozen" means 12 items. But instead of 12, a mole is a very large number:

$\boxed{1 \text{ mol} = 6.022 \times 10^{23} \text{ particles}}$

This number is called (), named after Italian scientist Amedeo Avogadro.

📌 Counting by Weighing

It would be impossible to count individual atoms one by one. Instead, chemists count by weighing.

The Analogy

Imagine you work at a hardware store and need to sell 500 nails. You could count each one, or you could:

Weigh one nail → say it is 2.0 g
Calculate: $500 \times 2.0 \text{ g} = 1000 \text{ g} = 1.0 \text{ kg}$
Simply weigh out 1.0 kg of nails!

Chemistry works the same way. We know the mass of one mole of any element or compound, so we weigh out the right mass to get the number of particles we need.

The Core Conversion

⚖️ Mole ↔ Particle Conversions

Example 1: Moles → Particles

Problem: How many atoms are in 2.50 mol of iron (Fe)?

Solution:

$\text{atoms of Fe} = 2.50 \; \cancel{\text{mol Fe}} \times \frac{6.022 \times 10^{23} \text{ atoms Fe}}{1 \; \cancel{\text{mol Fe}}} = 1.506 \times 10^{24} \text{ atoms Fe}$

Mole Concept Quiz 🎯

Mole-Particle Conversion Drill 🧮

1) How many atoms are in 0.750 mol of aluminum (Al)? Express your answer in scientific notation as $a \times 10^{23}$ — enter only the value of $a$ (to 3 significant figures).

2) A sample contains $1.806 \times 10^{24}$ molecules of CO₂. How many moles is this? (to 3 significant figures)

Mole Concept — Fill in the Blanks 🔽

Exit Quiz — The Mole ✅

Part 2: Molar Mass

⚖️ Molar Mass

Part 2 of 7 — The Mass of One Mole

Topics in This Part

Section
📖 What Is Molar Mass?
For Elements
Key Insight
📌 Molar Mass of Compounds
Example 1: Water (H₂O)

🔑 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 Molar Mass?

The molar mass ( $M$ ) of a substance is the mass in grams of one mole of that substance.

$M = \frac{mass (g)}{moles (mol)}$

Part 3: Mole-Mass Conversions

🔄 Mole-Mass Conversions

Part 3 of 7 — Grams, Moles, and Particles

Topics in This Part

Section
⚖️ Grams → Moles
Example 1
Example 2
⚖️ Moles → Grams
Example 3

🔑 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

⚖️ Grams → Moles

To convert from grams to moles, divide by the molar mass:

$\boxed{n = \frac{m}{M}}$

Part 4: Percent Composition

📊 Percent Composition

Part 4 of 7 — What's in Your Compound?

Topics in This Part

Section
📌 Mass Percent Formula
Example 1
Example 2
🔍 Finding Empirical Formula from Percent Composition
Method

🔑 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

📌 Mass Percent Formula

The mass percent of an element in a compound is:

$\boxed{\% \text{ by mass} = \frac{\text{mass of element in 1 mol of compound}}{\text{molar mass of compound}} \times 100\%}$

Part 5: Empirical & Molecular Formulas

🔬 Empirical and Molecular Formulas

Part 5 of 7 — From Ratios to Real Formulas

Topics in This Part

Section
⚖️ Empirical vs. Molecular Formulas
Key Relationship
Examples of Empirical ↔ Molecular
📋 Step-by-Step Method
Finding the Empirical Formula from Experimental Data

🔑 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

⚖️ Empirical vs. Molecular Formulas

Formula Type	Definition	Example (for glucose)
Empirical	Simplest whole-number ratio of atoms	CH₂O
Molecular	Actual number of atoms per molecule	C₆H₁₂O₆

Key Relationship

Part 6: Problem-Solving Workshop

🧪 Problem-Solving Workshop

Part 6 of 7 — Multi-Step Conversions & Real-World Applications

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

⚖️ The Mole Conversion Map

Here is the complete conversion roadmap you should have memorized:

$\boxed{\text{Particles} \xleftrightarrow{\times \text{ or } \div \; N_A} \text{Moles} \xleftrightarrow{\times \text{ or } \div \; M} \text{Grams}}$

Part 7: Synthesis & AP Review

🎓 Synthesis & AP Review

Part 7 of 7 — Connecting Concepts & Exam Preparation

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

🔗 Concept Connections

All of the mole concepts are interconnected:

$\boxed{\text{Percent Composition} \rightarrow \text{Empirical Formula} \xrightarrow{+\,M} \text{Molecular Formula}}$

Avogadro's number

🔑 Key Concept: The mole is the bridge between the atomic world and the laboratory — one mole always contains exactly $6.022 \times 10^{23}$ particles, regardless of the substance.

Putting It in Perspective

A dozen eggs = 12 eggs
A gross of pencils = 144 pencils
A ream of paper = 500 sheets
A mole of atoms = $6.022 \times 10^{23}$ atoms

Why Such a Specific Number?

Avogadro's number is defined so that one mole of carbon-12 atoms has a mass of exactly 12 grams. This connects the atomic mass scale (in amu) to the laboratory mass scale (in grams).

Particle	Mass of 1 atom/molecule (amu)	Mass of 1 mole (g)
H	1.008	1.008
C	12.01	12.01
O	16.00	16.00
H₂O	18.02	18.02

moles = \frac{number of particles}{6.022 \times 1 0 ^{23}}

$\boxed{\text{number of particles} = \text{moles} \times 6.022 \times 10^{23}}$

1mol Fe6.022×1023 atoms Fe

Example 2: Particles → Moles

Problem: How many moles is $3.011 \times 10^{23}$ molecules of CO₂?

$\text{mol CO}_2 = 3.011 \times 10^{23} \; \cancel{\text{molecules CO}_2} \times \frac{1 \text{ mol CO}_2}{6.022 \times 10^{23} \; \cancel{\text{molecules CO}_2}} = 0.500 \text{ mol CO}_2$

Watch Out for Polyatomic Molecules!

⚠️ Warning: Don't confuse molecules with atoms! One molecule of H₂O contains 3 atoms (2 H + 1 O). Always check whether the question asks for molecules or individual atoms.

Problem: If you have 1 mol of H₂O, how many molecules and atoms do you have?

Molecules of H₂O:

$1 \; \cancel{\text{mol H}_2\text{O}} \times \frac{6.022 \times 10^{23} \text{ molecules H}_2\text{O}}{1 \; \cancel{\text{mol H}_2\text{O}}} = 6.022 \times 10^{23} \text{ molecules of H}_2\text{O}$

$6.022 \times 10^{23} \; \cancel{\text{molecules H}_2\text{O}} \times \frac{2 \text{ atoms H}}{1 \; \cancel{\text{molecule H}_2\text{O}}} = 1.204 \times 10^{24} \text{ atoms of H}$

$6.022 \times 10^{23} \; \cancel{\text{molecules H}_2\text{O}} \times \frac{1 \text{ atom O}}{1 \; \cancel{\text{molecule H}_2\text{O}}} = 6.022 \times 10^{23} \text{ atoms of O}$

$1.204 \times 10^{24} + 6.022 \times 10^{23} = 1.807 \times 10^{24} \text{ atoms overall}$

3) How many individual oxygen atoms are in 2.00 mol of O₂? Express as $a \times 10^{24}$ — enter only $a$ (to 3 significant figures).

M = \frac{mass (g)}{moles (mol)}

The molar mass of an element equals its atomic mass from the periodic table, but in grams per mole:

Element	Atomic Mass (amu)	Molar Mass (g/mol)
Hydrogen (H)	1.008	1.008
Carbon (C)	12.01	12.01
Oxygen (O)	16.00	16.00
Sodium (Na)	22.99	22.99
Iron (Fe)	55.85	55.85

💡 Tip: To find the molar mass of any element, simply look up its atomic mass on the periodic table and change the units from amu to g/mol.

🔑 Key Concept: The number on the periodic table does double duty — it tells you the mass of one atom in amu and the mass of one mole of atoms in grams.

📌 Molar Mass of Compounds

For a compound, add up the molar masses of all atoms in the formula.

Example 1: Water (H₂O)

Problem: What is the molar mass of water (H₂O)?

Solution:

$M_{\text{H}_2\text{O}} = 2(1.008) + 1(16.00) = 2.016 + 16.00 = 18.02 \text{ g/mol}$

Example 2: Sodium Chloride (NaCl)

Problem: What is the molar mass of sodium chloride (NaCl)?

Solution:

$M_{\text{NaCl}} = 22.99 + 35.45 = 58.44 \text{ g/mol}$

Example 3: Calcium Carbonate (CaCO₃)

Problem: What is the molar mass of calcium carbonate (CaCO₃)?

Solution:

$M_{\text{CaCO}_3} = 40.08 + 12.01 + 3(16.00) = 40.08 + 12.01 + 48.00 = 100.09 \text{ g/mol}$

Example 4: Glucose (C₆H₁₂O₆)

Problem: What is the molar mass of glucose (C₆H₁₂O₆)?

Solution:

$M_{\text{C}_6\text{H}_{12}\text{O}_6} = 6(12.01) + 12(1.008) + 6(16.00) = 72.06 + 12.10 + 96.00 = 180.16 \text{ g/mol}$

💡 Watch for Parentheses!

💡 Tip: When parentheses appear in a formula like Ca(OH)₂, the subscript outside multiplies everything inside — both the O and the H.

Problem: What is the molar mass of calcium hydroxide, Ca(OH)₂?

Solution:

$M = 40.08 + 2(16.00 + 1.008) = 40.08 + 2(17.008) = 40.08 + 34.02 = 74.10 \text{ g/mol}$

Molar Mass Concept Quiz 🎯

Molar Mass Calculation Drill 🧮

Given Atomic Masses (g/mol):

H C N O Na
1.008 12.01 14.01 16.00 22.99

S Cl K Ca Fe
32.07 35.45 39.10 40.08 55.85

1) Calculate the molar mass of ammonia (NH₃) in g/mol. (to 3 significant figures)

2) Calculate the molar mass of potassium permanganate (KMnO₄) in g/mol. (Mn = 54.94; to 3 significant figures)

3) Calculate the molar mass of iron(III) oxide (Fe₂O₃) in g/mol. (to 3 significant figures)

Molar Mass Concepts — Fill in the Blanks 🔽

Exit Quiz — Molar Mass ✅

where $n$ = moles, $m$ = mass in grams, $M$ = molar mass in g/mol.

🔑 Key Concept: This is the most important equation in mole chemistry — always set up dimensional analysis so that units cancel properly.

Problem: How many moles are in 36.04 g of water (H₂O)?

$\text{mol H}_2\text{O} = 36.04 \; \cancel{\text{g H}_2\text{O}} \times \frac{1 \text{ mol H}_2\text{O}}{18.02 \; \cancel{\text{g H}_2\text{O}}} = 2.000 \text{ mol H}_2\text{O}$

Problem: How many moles are in 100.0 g of NaCl? ( $M = 58.44$ g/mol)

$\text{mol NaCl} = 100.0 \; \cancel{\text{g NaCl}} \times \frac{1 \text{ mol NaCl}}{58.44 \; \cancel{\text{g NaCl}}} = 1.711 \text{ mol NaCl}$

⚖️ Moles → Grams

To convert from moles to grams, multiply by the molar mass:

$\boxed{m = n \times M}$

Problem: What is the mass of 0.250 mol of glucose ( $\text{C}_6\text{H}_{12}\text{O}_6$ , $M = 180.16$ g/mol)?

$\text{g C}_6\text{H}_{12}\text{O}_6 = 0.250 \; \cancel{\text{mol C}_6\text{H}_{12}\text{O}_6} \times \frac{180.16 \text{ g C}_6\text{H}_{12}\text{O}_6}{1 \; \cancel{\text{mol C}_6\text{H}_{12}\text{O}_6}} = 45.04 \text{ g C}_6\text{H}_{12}\text{O}_6$

📋 Multi-Step Conversions: Grams ↔ Moles ↔ Particles

Often you need to go from grams to particles (or vice versa). This requires two steps:

$\text{grams} \xrightarrow{\div M} \text{moles} \xrightarrow{\times N_A} \text{particles}$

$\text{particles} \xrightarrow{\div N_A} \text{moles} \xrightarrow{\times M} \text{grams}$

⚠️ Warning: Always check your units! A common error is multiplying when you should divide (or vice versa). If your answer has nonsensical units, retrace your conversion factors.

Example: Grams → Particles

Problem: How many molecules are in 9.01 g of H₂O?

Solution:

Step 1: Convert grams to moles:

$\text{mol H}_2\text{O} = 9.01 \; \cancel{\text{g H}_2\text{O}} \times \frac{1 \text{ mol H}_2\text{O}}{18.02 \; \cancel{\text{g H}_2\text{O}}} = 0.500 \text{ mol H}_2\text{O}$

Step 2: Convert moles to molecules:

$\text{molecules of H}_2\text{O} = 0.500 \; \cancel{\text{mol H}_2\text{O}} \times \frac{6.022 \times 10^{23} \text{ molecules H}_2\text{O}}{1 \; \cancel{\text{mol H}_2\text{O}}} = 3.011 \times 10^{23} \text{ molecules H}_2\text{O}$

Example: Particles → Grams

Problem: What is the mass of $1.505 \times 10^{24}$ atoms of iron (Fe, $M = 55.85$ g/mol)?

Solution:

Step 1: Convert atoms to moles:

$n = 1.505 \times 10^{24} \; \cancel{\text{atoms Fe}} \times \frac{1 \text{ mol Fe}}{6.022 \times 10^{23} \; \cancel{\text{atoms Fe}}} = 2.50 \text{ mol Fe}$

Step 2: Convert moles to grams:

$m = 2.50 \; \cancel{\text{mol Fe}} \times \frac{55.85 \text{ g Fe}}{1 \; \cancel{\text{mol Fe}}} = 139.6 \text{ g Fe}$

Conversion Concept Quiz 🎯

Mole-Mass Conversion Drill 🧮

Given Atomic Masses (g/mol):

H C O Na Cl Ca
1.008 12.01 16.00 22.99 35.45 40.08

1) How many moles are in 25.0 g of CaCO₃ ( $M = 100.09$ g/mol)? (to 3 significant figures)

2) What is the mass (in grams) of 0.400 mol of NaCl ( $M = 58.44$ g/mol)? (to 3 significant figures)

3) How many molecules are in 5.00 g of CO₂ ( $M = 44.01$ g/mol)? Express as $a \times 10^{22}$ — enter $a$ (to 3 significant figures).

Conversion Roadmap — Fill in the Blanks 🔽

Exit Quiz — Mole-Mass Conversions ✅

% by mass=molar mass of compoundmass of element in 1 mol of compound×100%

🔑 Key Concept: Percent composition tells you what fraction of a compound's mass comes from each element — essential for identifying unknown compounds.

Problem: Find the percent composition of water (H₂O, $M = 18.02$ g/mol).

Mass of H in 1 mol H₂O: $2(1.008) = 2.016$ g
Mass of O in 1 mol H₂O: $1(16.00) = 16.00$ g

$\%\text{H} = \frac{2.016 \text{ g H}}{18.02 \text{ g H}_2\text{O}} \times 100\% = 11.19\%$

$\%\text{O} = \frac{16.00 \text{ g O}}{18.02 \text{ g H}_2\text{O}} \times 100\% = 88.79\%$

Check: $11.19 + 88.79 = 99.98\% \approx 100\%$ ✓ (small rounding difference is fine)

Problem: Find the percent composition of glucose (C₆H₁₂O₆, $M = 180.16$ g/mol).

$\%\text{C} = \frac{6(12.01) \text{ g C}}{180.16 \text{ g C}_6\text{H}_{12}\text{O}_6} \times 100\% = \frac{72.06}{180.16} \times 100\% = 40.00\%$

$\%\text{H} = \frac{12(1.008) \text{ g H}}{180.16 \text{ g C}_6\text{H}_{12}\text{O}_6} \times 100\% = \frac{12.10}{180.16} \times 100\% = 6.71\%$

$\%\text{O} = \frac{6(16.00) \text{ g O}}{180.16 \text{ g C}_6\text{H}_{12}\text{O}_6} \times 100\% = \frac{96.00}{180.16} \times 100\% = 53.28\%$

🔍 Finding Empirical Formula from Percent Composition

If you know the percent composition, you can determine the empirical formula (simplest whole-number ratio of atoms).

Method

💡 Tip: By assuming exactly 100 g, every percentage converts directly to grams — making the math much simpler!

Assume 100 g of the compound (so percentages become grams directly)
Convert grams to moles for each element: $n = m/M$
Divide all by the smallest mole value to get the ratio
Round to the nearest whole number (or multiply if you get values like 1.5, 2.5, etc.)

Example

Problem: A compound is 40.0% C, 6.7% H, and 53.3% O by mass. Find the empirical formula.

Solution:

Step 1: Assume 100 g → 40.0 g C, 6.7 g H, 53.3 g O

Step 2: Convert to moles:

C: $40.0 / 12.01 = 3.33$ mol
H: $6.7 / 1.008 = 6.65$ mol
O: $53.3 / 16.00 = 3.33$ mol

Step 3: Divide by smallest (3.33):

C: $3.33/3.33 = 1.00$
H: $6.65/3.33 = 2.00$
O: $3.33/3.33 = 1.00$

Step 4: Ratio = 1 : 2 : 1 → Empirical formula: CH₂O

Percent Composition Concept Quiz 🎯

Percent Composition Calculation Drill 🧮

Given: H = 1.008, C = 12.01, N = 14.01, O = 16.00, S = 32.07

1) What is the percent by mass of nitrogen in ammonia (NH₃, $M = 17.03$ g/mol)? (to 3 significant figures)

2) What is the percent by mass of sulfur in SO₃ ( $M = 80.07$ g/mol)? (to 3 significant figures)

3) A compound is 85.7% C and 14.3% H by mass. What is the ratio of C to H in the empirical formula? (Enter as a single number: if the ratio is C₁H₂, enter 2)

Percent Composition — Fill in the Blanks 🔽

Exit Quiz — Percent Composition ✅

$\boxed{\text{Molecular formula} = n \times (\text{Empirical formula})}$

$\boxed{n = \frac{M_{\text{molecular}}}{M_{\text{empirical}}}}$

$n$ must be a positive integer (1, 2, 3, ...).

🔑 Key Concept: The molecular formula is always a whole-number multiple of the empirical formula. If $n = 1$ , they are the same!

Examples of Empirical ↔ Molecular

Empirical	$M_{\text{emp}}$ (g/mol)	$M_{\text{mol}}$ (g/mol)	$n$	Molecular
CH₂O	30.03	30.03	1	CH₂O (formaldehyde)
CH₂O	30.03	60.05	2	C₂H₄O₂ (acetic acid)
CH₂O	30.03	180.16	6	C₆H₁₂O₆ (glucose)
CH	13.02	78.11	6	C₆H₆ (benzene)

📋 Step-by-Step Method

Finding the Empirical Formula from Experimental Data

Start with mass or percent of each element
Convert to moles: $n_i = m_i / M_i$
Divide all by the smallest mole value
If needed, multiply to get whole numbers

Finding the Molecular Formula

Calculate the molar mass of the empirical formula ( $M_{\text{emp}}$ )
Divide the given molecular molar mass by $M_{\text{emp}}$ : $n = M_{\text{mol}} / M_{\text{emp}}$

Worked Example

Problem: A compound is 40.0% C, 6.7% H, and 53.3% O by mass. Its molar mass is 180.2 g/mol. Find the molecular formula.

Solution:

Step 1–4 (from Part 4): Empirical formula = CH₂O

Step 5: $M_{\text{emp}} = 12.01 + 2(1.008) + 16.00 = 30.03$ g/mol

Step 6:

$n = \frac{M_{\text{mol}}}{M_{\text{emp}}} = \frac{180.2 \text{ g/mol}}{30.03 \text{ g/mol}} = 6.00$

Step 7: Molecular formula = $\text{C}_{1 \times 6}\text{H}_{2 \times 6}\text{O}_{1 \times 6} = \text{C}_6\text{H}_{12}\text{O}_6$ (glucose!)

Empirical & Molecular Formula Quiz 🎯

Empirical & Molecular Formula Drill 🧮

Given: H = 1.008, C = 12.01, N = 14.01, O = 16.00, P = 30.97

1) A compound is 43.6% P and 56.4% O by mass. What is the mole ratio of P to O? Give as the number of O per 1 P (to 3 significant figures).

2) The empirical formula from question 1 is P₂O₅. Calculate $M_{\text{emp}}$ in g/mol. (to 3 significant figures)

3) If the molar mass of the compound is 283.88 g/mol, what is $n$ (the multiplier to get the molecular formula)? (whole number)

Formulas — Fill in the Blanks 🔽

Exit Quiz — Empirical & Molecular Formulas ✅

Particles× or ÷NAMoles× or ÷MGrams

🔑 Key Concept: Moles are always at the center of conversions — you must pass through moles to convert between grams and particles.

Key Formulas Summary

Conversion	Formula
Grams → Moles	$n = m / M$
Moles → Grams	$m = n \times M$
Moles → Particles	$N = n \times N_A$
Particles → Moles	$n = N / N_A$
Grams → Particles	$N = (m/M) \times N_A$
Particles → Grams	$m = (N/N_A) \times M$

Strategy for Multi-Step Problems

💡 Tip: When stuck on a multi-step problem, write down the units of what you have and what you need, then build a conversion path through moles.

Identify what you are given and what you need to find
Plan the conversion path (grams → moles → particles, etc.)
Set up conversion factors so units cancel
Calculate and check significant figures
Verify — does the answer make sense?

📌 Lab Scenario: Analyzing an Unknown

A student in the lab weighs out 11.0 g of an unknown white solid. Analysis shows it is pure calcium carbonate (CaCO₃, $M = 100.09$ g/mol).

Questions to Answer

a) How many moles?

$\text{mol CaCO}_3 = 11.0 \; \cancel{\text{g CaCO}_3} \times \frac{1 \text{ mol CaCO}_3}{100.09 \; \cancel{\text{g CaCO}_3}} = 0.1099 \text{ mol CaCO}_3$

b) How many formula units?

$\text{formula units} = 0.1099 \; \cancel{\text{mol CaCO}_3} \times \frac{6.022 \times 10^{23} \text{ formula units CaCO}_3}{1 \; \cancel{\text{mol CaCO}_3}} = 6.62 \times 10^{22} \text{ formula units CaCO}_3$

c) How many total atoms? (CaCO₃ has 5 atoms per formula unit: 1 Ca + 1 C + 3 O)

$\text{atoms} = 6.62 \times 10^{22} \; \cancel{\text{formula units CaCO}_3} \times \frac{5 \text{ atoms}}{1 \; \cancel{\text{formula unit CaCO}_3}} = 3.31 \times 10^{23} \text{ atoms}$

d) How many grams of calcium are in the sample?

$\text{g Ca} = 0.1099 \; \cancel{\text{mol CaCO}_3} \times \frac{1 \; \cancel{\text{mol Ca}}}{1 \; \cancel{\text{mol CaCO}_3}} \times \frac{40.08 \text{ g Ca}}{1 \; \cancel{\text{mol Ca}}} = 4.41 \text{ g Ca}$

Or using percent composition: $\%\text{Ca} = 40.08/100.09 \times 100 = 40.04\%$ ; $m_{\text{Ca}} = 0.4004 \times 11.0 = 4.40$ g.

Multi-Step Problem Quiz 🎯

Multi-Step Calculation Drill 🧮

Given: H = 1.008, C = 12.01, N = 14.01, O = 16.00, Na = 22.99, Cl = 35.45, Fe = 55.85

1) How many grams of iron (Fe) contain the same number of atoms as 12.01 g of carbon (C)? (to 3 significant figures)

2) A chemist has 25.0 g of NaCl ( $M = 58.44$ ). How many chloride ions ( $\text{Cl}^-$ ) are present? Express as $a \times 10^{23}$ — enter $a$ (to 3 significant figures).

3) How many hydrogen atoms are in 36.04 g of water ( $M_{\text{H}_2\text{O}} = 18.02$ )? Express as $a \times 10^{24}$ — enter (to 3 significant figures).

Problem-Solving Strategy — Fill in the Blanks 🔽

Exit Quiz — Problem-Solving Workshop ✅

Percent Composition→Empirical Formula+MMolecular Formula

$\boxed{\text{Mass (g)} \xleftrightarrow{M} \text{Moles} \xleftrightarrow{N_A} \text{Particles}}$

🔑 Key Concept: Everything in quantitative chemistry flows through the mole — master these conversions and you can solve virtually any stoichiometry problem.

The mole bridges the atomic and macroscopic worlds
Molar mass connects mass (measurable) to amount (moles)
Percent composition reveals the elemental makeup of compounds
Empirical formulas come from mole ratios of elements
Molecular formulas require knowing the molar mass

Converting between grams, moles, and particles
Calculating molar mass of compounds
Determining empirical and molecular formulas
Percent composition calculations
Multi-step conversion problems

📌 Common Mistakes to Avoid ⚠️

1. Confusing Atomic Mass and Molar Mass Units

⚠️ Warning: The numbers are the same but the units differ! Atomic mass → amu (for single atoms), Molar mass → g/mol (for one mole).

2. Forgetting Subscripts in Molar Mass Calculations

⚠️ Warning: Don't forget that subscripts outside parentheses multiply everything inside! $M_{\text{Ca(OH)}_2} \neq 40.08 + 16.00 + 1.008$ . Correct: $M_{\text{Ca(OH)}_2} = 40.08 + 2(16.00) + 2(1.008) = 74.10$ g/mol ✓

3. Atoms vs. Molecules

⚠️ Warning: 1 mol H₂O = $6.022 \times 10^{23}$ molecules (not atoms!). Total atoms in 1 mol H₂O = $3 \times 6.022 \times 10^{23} = 1.807 \times 10^{24}$ atoms (3 per molecule).

4. Rounding Mole Ratios Too Soon

⚠️ Warning: Do not round non-integer mole ratios! 1.33 = $4/3$ (multiply by 3), 1.50 = $3/2$ (multiply by 2), 1.25 = $5/4$ (multiply by 4).

5. Forgetting to Use the Mole Ratio (Not Mass Ratio)

⚠️ Warning: In stoichiometry, always convert to moles first — never work directly with grams!

AP-Style Multiple Choice 🎯

AP-Style Free Response Calculations 🧮

A student analyzes a pure sample of hydrated copper(II) sulfate, CuSO₄·5H₂O.

Given: Cu = 63.55, S = 32.07, O = 16.00, H = 1.008

1) Calculate the molar mass of CuSO₄·5H₂O in g/mol. (to 3 significant figures)

2) What is the percent by mass of water in CuSO₄·5H₂O? (to 3 significant figures)

3) If the student has 50.0 g of CuSO₄·5H₂O, how many moles of water molecules are present? (to 3 significant figures)

Comprehensive Review — Fill in the Blanks 🔽

Final Exit Quiz — Moles & Molar Mass ✅

18.02g H2O1 mol H2O=

1mol H2O6.022×1023 molecules H2O=

6.022×1023atoms Fe1 mol Fe=

n = M_{mol} / M_{emp}

Multiply all subscripts in the empirical formula by

n

30.03 g/mol180.2 g/mol=

1mol CaCO36.022×1023 formula units CaCO3=

1022 formula units CaCO3

1formula unit CaCO35 atoms=

Moles and Molar Mass

Moles and Molar Mass - Complete Interactive Lesson

Part 1: Introduction to the Mole

⚗️ Introduction to the Mole

Topics in This Part

What You'll Master in Part 1

📖 What Is a Mole?

📌 Counting by Weighing

The Analogy

The Core Conversion

⚖️ Mole ↔ Particle Conversions

Example 1: Moles → Particles

Part 2: Molar Mass

⚖️ Molar Mass

Topics in This Part

What You'll Master in Part 2

📖 What Is Molar Mass?

Part 3: Mole-Mass Conversions

🔄 Mole-Mass Conversions

Topics in This Part

What You'll Master in Part 3

⚖️ Grams → Moles

Part 4: Percent Composition

📊 Percent Composition

Topics in This Part

What You'll Master in Part 4

📌 Mass Percent Formula

Part 5: Empirical & Molecular Formulas

🔬 Empirical and Molecular Formulas

Topics in This Part

What You'll Master in Part 5

⚖️ Empirical vs. Molecular Formulas

Key Relationship

Part 6: Problem-Solving Workshop

🧪 Problem-Solving Workshop

Practice Makes Perfect

What You'll Master in Part 6

⚖️ The Mole Conversion Map

Part 7: Synthesis & AP Review

🎓 Synthesis & AP Review

Bringing It All Together

What You'll Master in Part 7

🔗 Concept Connections

Putting It in Perspective

Why Such a Specific Number?

Example 2: Particles → Moles

Watch Out for Polyatomic Molecules!

For Elements

Key Insight

📌 Molar Mass of Compounds

Example 1: Water (H₂O)

Example 2: Sodium Chloride (NaCl)

Example 3: Calcium Carbonate (CaCO₃)

Example 4: Glucose (C₆H₁₂O₆)

💡 Watch for Parentheses!

Example 1

Example 2

⚖️ Moles → Grams

Example 3

📋 Multi-Step Conversions: Grams ↔ Moles ↔ Particles

Example: Grams → Particles

Example: Particles → Grams

Example 1

Example 2

🔍 Finding Empirical Formula from Percent Composition

Method

Example

Examples of Empirical ↔ Molecular

📋 Step-by-Step Method

Finding the Empirical Formula from Experimental Data

Finding the Molecular Formula

Worked Example

Key Formulas Summary

Strategy for Multi-Step Problems

📌 Lab Scenario: Analyzing an Unknown

Questions to Answer

The Big Ideas

Common Exam Topics

📌 Common Mistakes to Avoid ⚠️

1. Confusing Atomic Mass and Molar Mass Units