Enter the Nanoworld

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Indivisible: The Atomic Theory

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• The Mole (Notes/Practice)
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How do we observe, quantify, and draw conclusions about atoms if we cannot see them?

The Mole in Chemistry

What is a mole in chemistry?

Amedeo Avogadro (1776 - 1856)

studied quantities of gases and discovered that under the same pressure and temperature conditions, equal volumes of all gases contain the same number of molecules.

This is called Avogadro’s Hypothesis and is useful in helping chemists make predictions about ideal gases.

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The mole allows us to measure atoms, even though we cannot see them

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• The mole (mol) in chemistry is the SI Unit for the amount of a substance, whose number of particles is the same as the number of atoms of carbon in exactly 12 grams of carbon-12. Carbon-12 contains 6 protons + 6 neutrons.

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A MOLE EQUALS 3 THINGS:

• 1 mole = 6.022 x 10²³ particles

(particles: atoms, molecules, formula units, etc.)

• 1 mole = mass in grams of any pure substance (element or compound), equivalent to its atomic mass on the periodic table (units change from amu’s to grams)
• 1 mole = 22.4 L of any gas at STP

(STP is standard temperature and pressure)

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One mole of any element or compound can be determined from its mass on the Periodic Table

The Mole and Avogadro’s Number

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Link

How Big is a Mole?

• Enough soft drink cans to cover the surface of the earth to a depth of over 200 miles.
• If you had Avogadro's number of unpopped popcorn kernels, and spread them across the United States of America, the country would be covered in popcorn to a depth of over 9 miles.
• If we were able to count atoms at the rate of 10 million per second, it would take about 2 billion years to count the atoms in one mole.

Mole Day

is celebrated on

October 23,

from

6:02 a.m. until 6:02 p.m.

2019 theme

2020 theme

2021 theme

Copy and complete the table below

using a periodic table.

Molar Mass and Number of Particles in a Mole

Molar Mass and Number of Particles in a Mole

Finding Molar Mass of a Compound

To find the molar mass of H₂O:

H: 2(1.008) = 2.016 g/mol

O: 1(15.999) = 15.999 g/mol

= 18.015 g/mol

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To find the molar mass of NaCl (sodium chloride)

• The molar mass of Sodium:
• 22.990 g of Na = 1 mole of Na (Na’s atomic mass is 22.990 amu)
• The molar mass of Chlorine:
• 35.45 g of Cl = 1 mole of Cl (Cl’s atomic mass is 35.45 amu)
• The molar mass of sodium chloride:
• (22.990 g of Na + 35.45 g of Cl) = 1 mole of NaCl

or 58.44 g of NaCl = 1 mole of NaCl

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Molar Mass (cont’d.)

Determine the molar mass of the below elements, molecules, or compounds:

1. C
2. Na
3. O₂
4. Fe
5. Fe₂O₃

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Determine the molar mass of the below elements, molecules, or compounds:

• C = 12.011 g/mol, 1 mol = 12.011 g
• Na = 22.990 g/mol; 1 mol = 22.990 g
• O₂ = 31.998 g/mol; 1 mol = 31.998 g
• Fe = 55.845 g/mol; 1 mol = 55.845 g
• Fe₂O₃ = 159.687 g/mol; 1 mol = 159.687 g

Mole Conversions

Examples and Practice

Example 1: grams to moles

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How many moles are in 24.022 g of carbon?

1 mol = 12.011 g C

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24.022 g C x 1 mol C = 2.0000 mol C

12.011 g C

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Example 2: moles to grams

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How many grams is 2 moles of carbon?

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2 mol C x 12.011 g C = 24.022 g C

1 mol C

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Example 3: Liters to moles

How many moles are in 2.56 Liters?

(1 mol = 22.4 L of any gas @STP)

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2.56 L x 1 mole = 0.114 moles

22.4 L

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Example 4: moles to Liters

How many liters of helium gas are in 2.00 moles of He? (1 mol = 22.4 L of any gas @STP)

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2.00 mol x 22.4 L = 44.8 L

1 mol

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Example 5: atoms to moles

How many moles are in 7.84 x 10²⁵ atoms?

1 mol = 6.022 x 10²³ atoms (or molecules, or formula units)

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7.84 x 10²⁵ atoms x 1 mole =

6.022 X 10²³ atoms

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= 1.30 x 10² moles or 130. moles

Example 6: moles to atoms

How many atoms are in 4.00 moles?

1 mol = 6.022 x 10²³ atoms (or molecules, or formula units)

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4.00 moles x 6.022 X 10²³ atoms =

1 mole

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= 2.41 x 10²⁴ atoms

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When using the exponent button, the program puts in the power of ten.

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2nd

EE

EE

EXP

x10^x

Practice 1: Convert grams to moles

14.1g of Na = ? moles

1 mol Na = 22.990 g Na

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Practice 1 Solution: grams to moles

14.1g of Na = ? moles

1 mol Na = 22.990 g Na

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14.1 g Na 1 mol Na = 0.613 mol Na

22.990 g Na

Practice 2: moles to grams

How many grams in 1.5 moles sulfur?

( 1 mol S = 32.06g)

Solution to Practice 2:

How many grams in 1.5 moles sulfur?

( 1 mol S = 32.06g)

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1.5 mol S x 32.06 g S = 48.09 g S

1 mol S

Practice 3: Liters to moles

How many moles are in 5.30 Liters?

(1 mol = 22.4 L of any gas @STP)

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5.30 L x ? = ?

?

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Practice 3 Solution: Liters to moles

How many moles are in 5.30 Liters?

(1 mol = 22.4 L of any gas @STP)

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5.30 L x 1 mole = 0.237 moles

22.4 L

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Practice 4: moles to Liters

How many liters of helium gas are in 1.40 moles of He? (1 mol = 22.4 L of any gas @STP)

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Practice 4 Solution: moles to Liters

How many liters of helium gas are in 1.40 moles of He? (1 mol = 22.4 L of any gas @STP)

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1.40 mol x 22.4 L = 31.4 L

1 mol

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Practice 5: particles to moles

How many moles are in 6.38 x 10²⁴ particles?

Practice 5 Solution: moles to particles

How many moles are in 6.38 x 10²⁴ particles?

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6.38 x 10²⁴ particles x 1 mole =

6.022 X 10²³ particles

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= 10.6 moles

Example 6: L to particles

How many particles are in 12.6 Liters?

Conversion Factors: 1 mole = 22.4 L ; 1 mole = 6.022 x 10²³ particles

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Example 6: How many particles are in 12.6 Liters?

12.6 L x 1 mole

22.4 L

x 6.02 X 10²³particles

1 mole

= 3.39 x 10²³ particles

Example 7: grams to atoms �

How many atoms of sodium are found in 25.24 grams of sodium?

How many atoms of sodium are found in 25.24 grams of sodium?

1 mole of Na = 22.990 g of Na

1 mole of Na = 6.022 x 10²³ atoms�

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25.24 g Na ? ?

? ?

Example 7: grams to atoms

Example 7 Solution:

How many atoms of sodium are found in 25.24 grams of sodium?

22.990 g of Na = 1 mole of Na = 6.022 x 10²³ atoms�

25.24 g Na 1 mol Na 6.022 x 10²³ atoms Na

22.990 g Na 1 mol Na

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= 6.611 x 10²³ atoms Na

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Practice 8:

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Convert 7.5 x 10²⁴ atoms Ca to moles

(1 mole Ca = 6.022 x 10²³ atoms Ca)

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Practice 8 Solution:

Convert 7.5 x 10²⁴ atoms Ca to moles

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7.5 x 10²⁴ atoms Ca 1 mol Ca

6.022 x 10²³ atoms Ca

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= 12 moles Ca

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Bell Work:

1. Convert 1.5 x 10²⁴ atoms Ca to grams Ca

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2. Convert 62.0 g Mg to atoms Mg

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Bell Work:

• Convert 1.5 x 10²⁴ atoms Ca to grams Ca

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1.5 x 10²⁴ atoms Ca

2. Convert 62.0 g Mg to atoms Mg

Solving using molar mass:

• How many moles of Na are in a sample of 14.1g of Na. (More dimensional analysis…)

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• Use the conversion rules to solve this problem:

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• How many particles are found in this same sample of Na?

Remember:

• The atomic mass of substance from the periodic table in grams = 1 mole of a substance
• For example:
• The molar mass of Sodium:
• 22.990 g of Na = 1 mole of Na
• Which contains Avogadro’s number of atoms
• 1 mole of Na = 6.022 x 10²³ atoms�

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Mole Conversion Activity

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Chapter 21 Objectives and Vocabulary handout