The Mole, Avogadro’s Number & Molar Mass

Packet #20

COUNTING ATOMS BY WEIGHING

Counting Atoms by Weighing I

• C(s) + O2(g) CO2 (g)

• Suppose a scientist has a small pile of carbon and wants to know how many oxygen molecules are required to convert all of the carbon into carbon dioxide.

• What can the scientist learn from the chemical equation?

• The balanced equation illustrates that one diatomic oxygen molecule (O2) is required for each carbon atom.

Counting Atoms by Weighing II

• C(s) + O2(g) CO2 (g)

• To determine how many oxygen atoms are needed by the scientist, the scientist must know how many carbon atoms are present in his/her pile.

• To determine this, the scientist must count the number of atoms through the weight of the sample provided.

AMU to grams Conversion

• AMU

• Atomic mass unit

• 1 amu = 1.66 * 10-24 g

• The periodic table provides a list of the average amu for each atom

• Aka atomic mass • Why?

• The atomic mass, listed on the periodic table, is measured in amu’s.

• These amu’s can be converted into grams using the equation provided.

Problem Example #1A

• Calculate the mass, in amu, for 1000 neutral carbon atoms

• (1000 atoms) * (12.01

amu/atom)

• (1000 atoms) * (12.01

amu/atom)

• = 12,010 amu

Problem Example 1B

• Let’s assume that when the scientist weighed the pile of natural carbon, the amount weighed was 3.00 * 1020 amu. How many carbon atoms does the scientist have?

• Remember: -1 carbon atom = 12 amu

• Conversion factor

• Calculation

• 3.00 * 1020 amu * (1 carbon atom/12 amu)

• 3.00 * 1020 amu * (1 carbon atom/12 amu)

• 2.50 * 1019 carbon atoms

Problem Examples 2 - 5

• Calculate the mass, in amu, of a sample of aluminum that contains 75 atoms.

• Calculate the mass, in amu, of a sample that contains 23 atoms.

• Calculate the number of sodium atoms present in a sample that has a mass of 1172.49 amu.

• Calculate the number of oxygen atoms in a sample that has a mass of 288 amu.

THE MOLE

Introduction

• A mole is a counting unit

• Similar to a dozen

• Dozen = 12

• A mole is equal to 6.02 * 1023 items

• This is known as Avogadro’s number

Mole

6.02 * 1023 atoms

Avogadro’s number

Counting Unit

Introduction II

• How many cars (individual cars) are found in 1 mole of cars (group)?

• 1 mole of cars = 6.02 * 1023 cars

• How many cookies (individual cookies) are found in 1 mole of cookies (group)?

• 1 mole of cookies = 6.02 * 1023 cookies.

Introduction III

• Example III

• One mole of carbon (element)

• 1 mole C = 6.02 * 1023 atoms

• Remember

• An element is a substance composed of atoms that are all the same.

MOLAR MASS

Molar Mass an of Atom

• The molar mass of an atom is equivalent to the atom’s atomic mass.

Molar Mass Example 1A

• What is the molar mass of 1 mole of oxygen (mono)?

• 16 grams

Molar Mass Example 1B

• What is the molar mass of 3 mole of oxygen?

• 3 * 16 grams

Molar Mass Example 1C

• How many moles are found within 64 grams of oxygen?

• 4 moles

Molar Mass of a Molecule/Compound

• The molar mass of a molecule/compound is equivalent of sum of the atomic masses of the all the atoms within the molecule/compound.

Molar Mass of a Molecule/Compound II

• Calculate the molar mass of one mole of sulfur dioxide (SO2).

• 1 mole of sulfur = 32.07 g

• 1 mole of diatomic oxygen (16.00 * 2 ) = 32 g

• 1 mole of SO2 = 64.07 g

Molar Mass of a Molecule/Compound II

• Calcium carbonate (calcite), CaCO3 is the principal mineral found in limestone, marble chalk, pearls and the shells of marine animals such as clams.

a. Calculate the molar mass of calcite.

• 100.09 g

b. A certain sample of calcite contains 4.86 mol. What is the mass in grams of this sample?

• 486 g of CaCO3

Molar Mass of a Molecule/Compound III

• Juglone, a dye known for centuries, is produced form the husks of black walnuts. It is also a natural herbicide that kills off competitive plants around the black walnut tree but does not affect grass and other non-competitive plants. The molecular formula is C10H6O3.

Molar Mass of a Molecule/Compound IV

• Calculate the molar mass of juglone

• 174.1 g = molar mass of juglone

• A sample of 1.56 g of juglone was extracted from black walnut husks. How many moles of juglone does this sample represent?

• 8.96 * 10-3 mol juglone

Molar Mass of a Molecule/Compound V

• Isopentyl acetate, C7H14O2, the compound responsible for the scent of bananas, can be produced commercially. Interestingly, bees release about 1 ug (1 * 10-6 g) of this compound when they sting. This attracts other bees, which join the attack. How many moles and how many molecules of isopentyl acetate are released in a typical bee sting?

• 5 * 1015 molecules

REVIEW

Example #1

• How many amu are in 1 mole of carbon?

• 12 amu

• How many amu’s are in 2 moles of carbon?

• (12 amu / 1 mole )* (2 moles)

• (12 amu / 1 mole )* (2 moles) = 24 amu

• How many grams are in 2 moles of carbon?

• Already calculated: -2 moles of carbon = 24 amu

• 1 amu = 1.66 * 1024

• (1.66 * 10^24/1 amu ) * (24 amu)

• (1.66 * 10^24/1 amu ) * (24 amu) =