The Mole Concept

The Mole Concept

Middle School

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Learning Objectives

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

• Identify the representative particle for various substances.

• Calculate the molar mass of elements and compounds.

• Convert between mass, moles, and the number of representative particles of a substance.

Key Vocabulary

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Mole (mol)

A unit for measuring substances, representing 6.02 x 10²³ representative particles of that substance.

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Avogadro's number

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

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Representative Particle

The smallest unit of a substance, such as an atom, a molecule, or a formula unit.

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Molar Mass

The mass of one mole of a substance, expressed in the unit grams per mole (g/mol).

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Measuring Matter

• In chemistry, matter is measured by its count, mass, or volume.

• ​We use conversion factors to switch between these different units of measurement.

• For example, we can relate a count of apples to its mass.

• The relationship 1 dozen apples = 2.0 kg is a conversion factor.

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Solved Example 1
Using the relationships 1 dozen apples = 12 apples and 1 dozen apples = 2.0 kg, what is the mass in kilograms of 90 apples?

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Step 1: Analyze and Sketch the Problem

• Goal: Find the mass of 90 apples in kilograms.

• Knowns: The number of apples is 90.

• Unknown: The mass of 90 apples.

• Formula: The conversion factors are 1 dozen apples = 12 apples and 1 dozen apples = 2.0 kg.

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Solved Example 1
Using the relationships 1 dozen apples = 12 apples and 1 dozen apples = 2.0 kg, what is the mass in kilograms of 90 apples?

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Step 2: Solve for the Unknown

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Solved Example 1
Using the relationships 1 dozen apples = 12 apples and 1 dozen apples = 2.0 kg, what is the mass in kilograms of 90 apples?

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Step 3: Evaluate the Answer

Multiple Choice

What is the primary function of a conversion factor in chemistry?

• To create new substances from existing matter

• To change the chemical properties of matter

• To determine the temperature at which matter changes state

• To switch between different units of measurement for matter

Multiple Choice

The statement '1 dozen apples = 2.0 kg' is an example of a conversion factor that relates which two types of measurements?

• Count and volume

• Mass and volume

• Mass and temperature

• Count and mass

Multiple Choice

If 1 dozen equals 12 apples and 1 dozen apples has a mass of 2.0 kg, what is the mass of 30 apples?

• 5.0 kg

• 2.5 kg

• 60 kg

• 15 kg

The Mole and Avogadro's Number

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Atom (Element)

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Molecule (Covalent)

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Formula Unit (Ionic)

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Solved Example 2
A sample contains 2.50 moles of silicon (Si). How many silicon atoms are in the sample?

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Step 1: Analyze and Sketch the Problem

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Solved Example 2
A sample contains 2.50 moles of silicon (Si). How many silicon atoms are in the sample?

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Step 2: Solve for the Unknown

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Solved Example 2
A sample contains 2.50 moles of silicon (Si). How many silicon atoms are in the sample?

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Step 3: Evaluate the Answer

Multiple Choice

What is the significance of Avogadro's number, 6.02 x 10²³?

• It is the total mass of all atoms in a single molecule.

• It is the number of particles in exactly one gram of a substance.

• It is the volume occupied by one mole of any gas.

• It is the number of representative particles in one mole of a substance.

Multiple Choice

Why are the representative particles for copper (Cu) and nitrogen gas (N₂) referred to by different names (atom and molecule, respectively)?

• Because copper is an element and nitrogen gas is a covalent compound.

• Because copper is a solid and nitrogen is a gas.

• Because they were discovered by different scientists.

• Because copper atoms are heavier than nitrogen molecules.

Multiple Choice

A sample contains 0.50 moles of calcium fluoride (CaF₂). How many formula units are in the sample?

• 1.51 x 10²⁴ formula units

• 3.01 x 10²³ formula units

• 1.20 x 10²⁴ formula units

• 6.02 x 10²³ formula units

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Molar Mass of Elements

• A mole has the same number of particles, but its mass varies per substance.

• An element's molar mass is the mass of one mole, in grams per mole (g/mol).

• Molar mass in g/mol is numerically equal to an element's atomic weight.

• Molar mass is used as a conversion factor between mass and moles of an element.

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Solved Example 3
Iron (Fe) is a common metal used in manufacturing. If you have a sample of iron with a mass of 15.5 grams, how many moles of iron are in the sample? (Molar mass of Fe = 55.845 g/mol)

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Step 1: Analyze and Sketch the Problem

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Solved Example 3
Iron (Fe) is a common metal used in manufacturing. If you have a sample of iron with a mass of 15.5 grams, how many moles of iron are in the sample? (Molar mass of Fe = 55.845 g/mol)

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Step 2: Solve for the Unknown

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Solved Example 3
Iron (Fe) is a common metal used in manufacturing. If you have a sample of iron with a mass of 15.5 grams, how many moles of iron are in the sample? (Molar mass of Fe = 55.845 g/mol)

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Step 3: Evaluate the Answer

• The unit of the answer is moles, which is the desired unit. Since the mass of the sample (15.5 g) is less than the molar mass (55.845 g), the number of moles should be less than one.

• Our answer of 0.278 mol is reasonable, and the calculation is correct: 15.5 / 55.845 ≈ 0.27755, which rounds to 0.278.

Multiple Choice

What is an element's molar mass?

• The mass of a single atom of that element.

• The total number of particles in one mole.

• The volume that one mole of an element occupies.

• The mass of one mole of that element.

Multiple Choice

What is the relationship between an element's molar mass and its atomic weight?

• The molar mass is the atomic weight multiplied by the number of atoms.

• The molar mass in g/mol is numerically equal to the element's atomic weight.

• The molar mass is half the element's atomic weight.

• The molar mass is unrelated to the element's atomic weight.

Multiple Choice

Gold (Au) has a molar mass of 197 g/mol. How many moles are in a 394-gram sample of gold?

• 2.0 moles

• 197 moles

• 0.5 moles

• 77,618 moles

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Molar Mass of Compounds

• To find a compound's molar mass, add the molar masses of all its atoms.

• In H₂SO₄, there are 2 moles H, 1 mole S, and 4 moles O.

• Multiply the moles of each element by its molar mass from the periodic table.

• Add the masses to get the total: (2x1.0)+(1x32.1)+(4x16.0) = 98.1 g/mol.

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Solved Example 4
Calculate the molar mass of glucose (C₆H₁₂O₆), given the molar masses of Carbon (C) = 12.0 g/mol, Hydrogen (H) = 1.0 g/mol, and Oxygen (O) = 16.0 g/mol.

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Step 1: Analyze and Sketch the Problem

• Goal: Find the molar mass of glucose (C₆H₁₂O₆).

• Knowns: The chemical formula is C₆H₁₂O₆. The molar mass of C is 12.0 g/mol, the molar mass of H is 1.0 g/mol, and the molar mass of O is 16.0 g/mol.

• Unknown: The molar mass of the compound.

• Formula: Molar Mass of Compound = Σ (Number of atoms of element × Molar mass of element)

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Solved Example 4
Calculate the molar mass of glucose (C₆H₁₂O₆), given the molar masses of Carbon (C) = 12.0 g/mol, Hydrogen (H) = 1.0 g/mol, and Oxygen (O) = 16.0 g/mol.

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Step 2: Solve for the Unknown

• First, calculate the total mass for each element:
  Mass of C = 6 × 12.0 g/mol = 72.0 g/mol
  Mass of H = 12 × 1.0 g/mol = 12.0 g/mol
  Mass of O = 6 × 16.0 g/mol = 96.0 g/mol

• Finally, add the masses of all the elements to find the molar mass of the compound:
  Molar Mass of C₆H₁₂O₆ = 72.0 g/mol + 12.0 g/mol + 96.0 g/mol = 180.0 g/mol

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Solved Example 4
Calculate the molar mass of glucose (C₆H₁₂O₆), given the molar masses of Carbon (C) = 12.0 g/mol, Hydrogen (H) = 1.0 g/mol, and Oxygen (O) = 16.0 g/mol.

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Step 3: Evaluate the Answer

• The calculation correctly sums the masses of all atoms in the compound and uses the correct units (g/mol).

• The final answer, 180.0 g/mol, is a reasonable molar mass for a medium-sized molecule like glucose.

Multiple Choice

How is the total molar mass of a compound determined?

• By finding the average molar mass of the atoms in the compound

• By identifying the molar mass of the most abundant element in the compound

• By summing the molar masses of each element present in the compound

• By multiplying the molar masses of all the individual atoms together

Multiple Choice

To calculate the molar mass of sulfuric acid (H₂SO₄), how is the mass contribution from the hydrogen (H) atoms determined?

• The molar mass of hydrogen is multiplied by 2.

• The molar mass of hydrogen is added to the molar mass of sulfur.

• The molar mass of hydrogen is multiplied by the molar mass of oxygen.

• The molar mass of hydrogen is divided by 2.

Multiple Choice

Given the molar masses of Calcium (Ca) = 40.0 g/mol, Carbon (C) = 12.0 g/mol, and Oxygen (O) = 16.0 g/mol, what is the molar mass of calcium carbonate (CaCO₃)?

• 52.0 g/mol

• 100.0 g/mol

• 68.0 g/mol

• 60.0 g/mol

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Common Misconceptions About the Mole

Misconception	Correction
One mole of any substance has the same mass.	Molar mass varies because the mass of individual particles differs.
The representative particle for all elements is an atom.	For diatomic elements like N2 or O2, the particle is a molecule.
Molar mass and atomic mass are identical.	Atomic mass is for one atom (amu); molar mass is for a mole (g/mol).

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Summary

• Matter can be quantified by its count, mass, or volume.

• The mole is a unit for counting 6.02 x 10²³ representative particles.

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

• Use Avogadro's number and molar mass to perform conversions.

Poll

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