The Mole Concept

The Mole Concept

High School

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Learning Objectives

• Define the mole as a counting unit and state Avogadro's number.

• Explain how to determine the molar mass of elements and compounds.

• Describe the relationship between the mole, particles, mass, and volume of a gas.

• Perform calculations to convert between moles, mass, particles, and volume.

Key Vocabulary

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Mole (mol)

A fundamental counting unit in chemistry, a mole is equal to 6.02 x 10²³ particles.

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Avogadro's Number

The number of particles in one mole of a substance, approximately 6.02 x 10²³ particles.

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Molar Mass

The total mass in grams of one mole of a substance, calculated using atomic masses.

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Standard Molar Volume

The volume occupied by one mole of any gas at standard temperature and pressure (STP), 22.4 L.

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What is a Mole?

• The mole (mol) is a fundamental unit for measuring quantities of a substance.

• ​One mole of any substance contains 6.02 x 10²³ representative particles.

• This value is known as Avogadro's Number, named after scientist Amedeo Avogadro.

• The mole conveniently bridges the microscopic and macroscopic scales in chemistry.

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Solved Example 1
How many atoms of gold (Au) are present in a 2.5-mole sample? Avogadro's number is 6.02 x 10²³ particles/mol.

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Step 1: Analyze and Sketch the Problem

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Solved Example 1
How many atoms of gold (Au) are present in a 2.5-mole sample? Avogadro's number is 6.02 x 10²³ particles/mol.

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Step 2: Solve for the Unknown

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Solved Example 1
How many atoms of gold (Au) are present in a 2.5-mole sample? Avogadro's number is 6.02 x 10²³ particles/mol.

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Step 3: Evaluate the Answer

Multiple Choice

Which of the following best describes the primary function of the mole in chemistry?

• A unit used to measure the mass of a substance in grams.

• A counting unit representing 6.02 x 10²³ particles of a substance.

• A number named in honor of the scientist who discovered it.

• A unit representing the volume of a substance in liters.

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Calculating Molar Mass

• Molar mass is the mass in grams of one mole of a substance.

• For an element, it equals the atomic mass on the periodic table (g/mol).

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

• For H₂O: (2 x 1.01) + (1 x 16.00) equals 18.02 g/mol.

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Solved Example 2
Calculate the molar mass of calcium nitrate, Ca(NO₃)₂. Use the following atomic masses: Ca = 40.08 g/mol, N = 14.01 g/mol, and O = 16.00 g/mol.

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Step 1: Analyze and Sketch the Problem

• Goal: Find the molar mass of Ca(NO₃)₂.

• Knowns: The formula indicates 1 Ca atom, 2 N atoms, and 6 O atoms. Atomic masses: Ca = 40.08 g/mol, N = 14.01 g/mol, O = 16.00 g/mol.

• Unknown: The total molar mass of the compound.

• Formula: The molar mass of a compound is the sum of the atomic masses of its atoms.

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Solved Example 2
Calculate the molar mass of calcium nitrate, Ca(NO₃)₂. Use the following atomic masses: Ca = 40.08 g/mol, N = 14.01 g/mol, and O = 16.00 g/mol.

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Step 2: Solve for the Unknown

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Solved Example 2
Calculate the molar mass of calcium nitrate, Ca(NO₃)₂. Use the following atomic masses: Ca = 40.08 g/mol, N = 14.01 g/mol, and O = 16.00 g/mol.

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Step 3: Evaluate the Answer

• The calculation correctly sums the masses of all atoms based on the chemical formula.

• The subscript ₂ outside the parentheses was correctly distributed to the nitrogen and oxygen atoms.

• The final answer of 164.10 g/mol is reasonable and has the correct units for molar mass.

Multiple Choice

Given that the molar mass of Hydrogen (H) is 1.01 g/mol and Oxygen (O) is 16.00 g/mol, what is the molar mass of hydrogen peroxide (H₂O₂)?

• 33.01 g/mol

• 18.02 g/mol

• 17.01 g/mol

• 34.02 g/mol

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Molar Volume of Gases at STP

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Solved Example 3
What is the volume in liters occupied by 2.5 moles of nitrogen gas (N₂) at Standard Temperature and Pressure (STP)?

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Step 1: Analyze and Sketch the Problem

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Solved Example 3
What is the volume in liters occupied by 2.5 moles of nitrogen gas (N₂) at Standard Temperature and Pressure (STP)?

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Step 2: Solve for the Unknown

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Solved Example 3
What is the volume in liters occupied by 2.5 moles of nitrogen gas (N₂) at Standard Temperature and Pressure (STP)?

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Step 3: Evaluate the Answer

• Since one mole of gas at STP occupies 22.4 L, 2.5 moles should occupy 2.5 times that volume, which is 56 L.

• The unit for the answer is Liters, which is a unit of volume. The answer is reasonable and the calculation is correct.

Multiple Choice

At Standard Temperature and Pressure (STP), what volume would be occupied by 1 mole of Helium (He) gas compared to 1 mole of Nitrogen (N₂) gas?

• They would both occupy 22.4 L.

• Helium would occupy less volume because its atoms are lighter.

• Nitrogen would occupy more volume because its molecules are larger.

• Their volumes cannot be compared without knowing their masses.

Mole Conversions

• Convert between mass and moles using the substance's molar mass (g/mol).

• Convert between particles and moles using Avogadro's number (6.02 x 10²³).

• Convert between gas volume and moles using standard molar volume (22.4 L/mol).

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Solved Example 4
How many molecules of water (H₂O) are in a 36.04-gram sample? The molar mass of H₂O is 18.02 g/mol.

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Step 1: Analyze and Sketch the Problem

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Solved Example 4
How many molecules of water (H₂O) are in a 36.04-gram sample? The molar mass of H₂O is 18.02 g/mol.

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Step 2: Solve for the Unknown

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Solved Example 4
How many molecules of water (H₂O) are in a 36.04-gram sample? The molar mass of H₂O is 18.02 g/mol.

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Step 3: Evaluate the Answer

• The initial mass (36.04 g) is double the molar mass (18.02 g/mol), so it makes sense that we have 2 moles.

• The final answer is double Avogadro's number, which is consistent with the 2 moles calculated. The units cancel correctly, leaving "molecules".

Multiple Choice

According to the relationships described, which two conversion factors are required to convert the given mass of a substance in grams into its equivalent number of atoms?

• Standard molar volume and Avogadro's number

• Molar mass and standard molar volume

• Only molar mass is required

• Molar mass and Avogadro's number

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Common Misconceptions about the Mole

Misconception	Correction
One mole of different substances has the same mass.	One mole has the same number of particles, but their masses are different.
The mole is a direct unit of mass or volume.	The mole is a counting unit, representing a specific number of items.
Amedeo Avogadro discovered the number 6.02 x 1023.	The number is named in his honor; he did not determine the constant.

Multiple Choice

How does understanding that a 'mole' is a counting unit help explain why one mole of gold (Au) and one mole of lithium (Li) have different masses?

• It explains that because both samples have 6.02 x 10²³ atoms, the difference in mass must come from the difference in mass of individual gold and lithium atoms.

• It proves that gold is denser than lithium.

• It shows that the counting unit changes depending on the element being measured.

• It doesn't; it only tells us they have the same number of atoms.

Multiple Choice

If you have 44.8 L of an unknown gas at STP, what can you determine about the quantity of the gas?

• The gas is composed of diatomic molecules.

• The sample contains exactly two moles of gas particles.

• The gas has a mass of 44.8 grams.

• The sample contains 6.02 x 10²³ atoms of the gas.

Multiple Choice

A chemist has a 50-gram sample of substance A (molar mass = 25 g/mol) and a 100-gram sample of substance B (molar mass = 100 g/mol). Predict which sample contains more particles and justify the prediction.

• It is impossible to predict without knowing Avogadro's number.

• Substance B, because its mass is greater.

• Substance A, because it contains more moles within its given mass.

• They contain the same number of particles.

Multiple Choice

To obtain 1.204 x 10²⁴ molecules of water (H₂O) for an experiment, what is the most practical first step to take in a lab, and what key piece of information is essential?

• Measure 2.0 moles by mass; the molar mass of water is required.

• Prepare 2.0 grams of water; only a scale is needed.

• Measure 44.8 L of water vapor; this requires the reaction to be at STP.

• Count the molecules individually; no other information is needed.

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Summary

• One mole of a substance contains 6.02 x 10²³ particles (Avogadro's number).

• Molar mass converts between the mass of a substance and the number of moles.

• One mole of any gas at STP occupies a standard volume of 22.4 liters.

• The mole is used to convert between mass, particles, and volume of a gas.

Poll

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