Chemical Quantities

Unit 6Chapter 10, Section 10.1

The Mole: A Measurement of Matter

Objectives When you complete this presentation, you

will be able to: describe methods of measuring the amount

of something. define Avogadro’s number, N0, as it relates

to a mole of a substance. distinguish between the atomic mass of an

element and its molar mass. describe how the mass of a mole of

compound is calculated.

Measuring Matter We live in a world of quantities, of measurement.

What was your grade on the 1st Semester Exam? How many friends do you have on Facebook? How big is a “tall” cup of coffee at Starbucks?

Chemists have similar kinds of quantitative questions. How many kg of iron can we get from 100 kg of ore? How many grams of N2(g) and H2(g) must be combined

to give us 200 g of NH3(g)? What volume of CO2(g) is produced when we burn one

gallon of gasoline?

Measuring Matter To solve chemists’ problems we need to

measure the amount of matter we have. What do we mean by the “amount” of

matter? For chemists, this is not a trivial question.

Measuring Matter When we measure matter, do we mean …

the number of atoms or molecules? How many oxygen molecules combine with each

methane molecule when we burn natural gas? the mass of the elements or compounds?

How many grams of oxygen (as O2 gas) combines with ten grams of methane (as CH4 gas) when we burn natural gas?

the volumes of the matter? How many liters of oxygen (as O2 gas) combines with

one liter of methane (as CH4 gas) when we burn natural gas?

Measuring Matter Some units for measuring indicate a specific

number of items. A pair always means two. A dozen always means twelve.

Measuring Matter For example, apples are measured in three

different ways. At a fruit stand, they may be sold by the count

(3 for $2.40). In a supermarket, you buy apples by the

weight ($1.29/lb) or mass ($2.79/kg). At an orchard, you buy apples by the volume

($12.00/bushel).

Measuring Matter For example, apples are measured in three

different ways. At a fruit stand, they may be sold by the count

(3 for $2.40). In a supermarket, you buy apples by the

weight ($1.29/lb) or mass ($2.79/kg). At an orchard, you buy apples by the volume

($12.00/bushel).

Each of these may be equated to a dozen apples.

Measuring Matter For example, apples are measured in three

different ways. At a fruit stand, they may be sold by the count

(3 for $2.40). By count: 1 dozen apples = 12 apples

Measuring Matter For example, apples are measured in three

different ways. At a fruit stand, they may be sold by the count

(3 for $2.40). By count: 1 dozen apples = 12 apples

In a supermarket, you buy apples by the weight ($1.29/lb). By mass: 1dozen apples = 2.0 kg apples

Measuring Matter For example, apples are measured in three

different ways. At a fruit stand, they may be sold by the count

(3 for $2.40). By count: 1 dozen apples = 12 apples

In a supermarket, you buy apples by the weight ($1.29/lb). By mass: 1dozen apples = 2.0 kg apples

At an orchard, you buy apples by the volume ($12.00/bushel). By volume: 1dozen apples = 0.20 bushel apples

Measuring Matter Knowing how the count, mass, and volume of

apples relates to a dozen apples allows us to convert between these units. For example, we could calculate the mass of …

a bushel of apples or 90 average sized apples

… by using the following conversion factors1 dozen apples12 apples

2.0 kg apples1 dozen apples

1 dozen apples0.20 bushel apples

Sample Problem 10.1What is the mass of 90 average-sized apples if 1 dozen apples has a mass of 2.0 kg?Known: # of apples = 90 apples 12 apples = 1 dozen apples 1 dozen apples = 2.0 kg apples

Unknown: mass of 90 apples = ? kg

Process: # of apples → dozens of apples → mass of apples

mass of 90 apples =

90 apples ×

1 dozen apples12 apples × 2.0 kg

apples1 dozen apples

Sample Problem 10.1What is the mass of 90 average-sized apples if 1 dozen apples has a mass of 2.0 kg?Known: # of apples = 90 apples 12 apples = 1 dozen apples 1 dozen apples = 2.0 kg apples

Unknown: mass of 90 apples = ? kg

Process: # of apples → dozens of apples → mass of apples

mass of 90 apples =

kg apples

90 × 1 × 2.012 × 1 = 15 kg

apples

What is a Mole? Counting things as big as apples is a

reasonable way to measure the amount of something.

Would counting the grains of sand on a beach be a reasonable way to measure the amount of sand?

Would counting individual atoms in a kilogram of a compound be a reasonable way to measure the amount of matter?

What is a Mole? Counting individual small things (such as

atoms or molecules) can be difficult. It is much easier if the things are grouped

into convenient units. Counting individual eggs could be tedious. Unless they are grouped by dozens.

What is a Mole? Chemists use a similar kind of unit to measure

amounts of matter (atoms and molecules). The unit for the amount of matter is a mole,

abbreviated as mol. 1 mole of any thing is defined as 6.02 × 1024

pieces of that thing. That is 6,020,000,000,000,000,000,000,000

pieces.

This number is called Avogadro’s number, N0.

What is a Mole? Just to be sure you understand this …

1 mol of hydrogen atoms is 6.02 × 1024 atoms 1 mol of hydrogen molecules is 6.02 × 1024

molecules 1 mol of glucose molecules is 6.02 × 1024

molecules 1 mol of pencils is 6.02 × 1024 pencils 1 mol of students is 6.02 × 1024 students 1 mol of grains of sand is 6.02 × 1024 grains

There are only 7.005 × 1020 grains of sand on earth. 1 mol of stars is 6.02 × 1024 stars

There are only 9 × 1021 stars in our universe.

What is a Mole? Let’s look at a couple of compounds a little

more closely. 1 mole of hydrogen molecules is 6.02 × 1023

molecules. Each hydrogen molecule, H2, is composed of

two atoms of hydrogen. That means there are 2 × 6.02 × 1023 = 12.04 ×

1023 hydrogen atoms in 1 mole of hydrogen molecules.

What is a Mole? Let’s look at a couple of compounds a little more

closely. 1 mole of glucose molecules is 6.02 × 1023

molecules. Each glucose molecule, C6H12O6, is composed of 6

atoms of carbon, 12 atoms of hydrogen, and 6 atoms of oxygen That means there are 6 × 6.02 × 1023 = 36.12 × 1023

carbon atoms in 1 mole of glucose molecules. That means there are 12 × 6.02 × 1023 = 72.24 ×

1023 hydrogen atoms in 1 mole of glucose molecules. That means there are 6 × 6.02 × 1023 = 36.12 × 1023

oxygen atoms in 1 mole of glucose molecules.

What is a Mole? Let’s practice converting from number of

particles to number of mols. The conversion looks like this:

Let’s try Sample Problem 10.2 (page 291).

# of moles =

# of representative particles × 6.02 × 1023 representative

particles

1 mole

Sample Problem 10.2 Magnesium is a light metal used in the manufacture

of aircraft, automobile wheels, tools, and garden furniture. How many moles of magnesium is 1.25 × 1023 atoms of magnesium?

# of moles =

# of representative particles × 6.02 × 1023 representative

particles

1 mole

Known: # of atoms = 1.25 × 1023 atoms 1 mol Mg = 6.02 × 1023 atoms Mg

Unknown: mols = ? mol Mg

Process: atoms → mols

Sample Problem 10.2 Magnesium is a light metal used in the manufacture

of aircraft, automobile wheels, tools, and garden furniture. How many moles of magnesium is 1.25 × 1023 atoms of magnesium?

# of moles =

1.25 × 1023 atoms Mg ×6.02 × 1023 atoms Mg

1 mole Mg

Known: # of atoms = 1.25 × 1023 atoms 1 mol Mg = 6.02 × 1023 atoms Mg

Unknown: mols = ? mol Mg

Process: atoms → mols

Sample Problem 10.2 Magnesium is a light metal used in the manufacture

of aircraft, automobile wheels, tools, and garden furniture. How many moles of magnesium is 1.25 × 1023 atoms of magnesium?

# of moles = 6.02 × 1023

1.25 × 1023 × 1

Known: # of atoms = 1.25 × 1023 atoms 1 mol Mg = 6.02 × 1023 atoms Mg

Unknown: mols = ? mol Mg

Process: atoms → mols

moles Mg =

0.208 moles Mg

What is a Mole? Let’s practice converting from number of

mols to number of particles . The conversion looks like this:

Let’s try Sample Problem 10.3 (page 292).

# of particles =

# of mols × 1 mol6.02 × 1023 representative

particles

Sample Problem 10.3 Propane gas is used for cooking and heating. How

many atoms are in 2.12 mol of propane (C3H8)?

# of atoms =

# of mols ×

Known:# of mols = 2.12 mols1 mol C3H8 = 6.02 × 1023 molecules C3H81 molecule C3H8 = 11 atoms (3 C + 8 H)

Unknowns:# atoms = ? atoms

Process:mols → molecules → atoms

1 molecule

# of atoms1 mol

6.02 × 1023 molecules ×

Sample Problem 10.3 Propane gas is used for cooking and heating. How

many atoms are in 2.12 mol of propane (C3H8)?

# of atoms =

2.12 mols ×

Known:# of mols = 2.12 mols1 mol C3H8 = 6.02 × 1023 molecules C3H81 molecule C3H8 = 11 atoms (3 C + 8 H)

Unknowns:# atoms = ? atoms

Process:mols → molecules → atoms

1 molecule

11 atoms1 mol

6.02 × 1023 molecules ×

Sample Problem 10.3 Propane gas is used for cooking and heating. How

many atoms are in 2.12 mol of propane (C3H8)?

# of atoms =

Known:# of mols = 2.12 mols1 mol C3H8 = 6.02 × 1023 molecules C3H81 molecule C3H8 = 11 atoms (3 C + 8 H)

Unknowns:# atoms = ? atoms

Process:mols → molecules → atoms

1 × 12.12 × 6.02 × 1023

× 11 atoms = 1.40 × 1025 atoms

The Mass of a Mole What is so special about Avogadro’s Number?

Why do we use “6.02 × 1023” any way?

The Mass of a Mole If we measure out 6.02 × 1023 atoms of an

element, the mass is equal to the atomic mass of that element. For 6.02 × 1023 atoms of H, mass = 1.01 g For 6.02 × 1023 atoms of C, mass = 12.01 g For 6.02 × 1023 atoms of O, mass = 16.00 g

If we measure out 6.02 × 1023 molecules of a compound, the mass is equal to the molar mass of that compound. For 6.02 × 1023 molecules of CO2, mass = 44.01 g For 6.02 × 1023 molecules of C6H12O6, mass =

180.16 g

The Mass of a Mole The atomic mass of an element is the mass

of 1 mol of that element. The molar mass of a compound is the mass

of 1 mol of that compound.

The Mass of a Mole To calculate the molar mass of a compound

find the number of grams of each element in one mole of the compound

add the masses of the elements in the compound

For example: for glucose, C6H12O6:

mass of C = 6 × 12.01 g = 72.06 g mass of H = 12 × 1.00794 g = 12.09528 g mass of O = 6 × 16.00 g = 96.00 g mass of C6H12O6 = (72.06 + 12.10 + 96.00) g =

180.16 g

The Mass of a Mole To calculate the molar mass of a compound

find the number of grams of each element in one mole of the compound

add the masses of the elements in the compound

For example: for water, H2O:

mass of H = 2 × 1.00794 g = 2.01588 g mass of O = 1 × 16.00 g = 16.00 g mass of H2O = (12.02 + 16.00) g = 18.02 g

The Mass of a Mole To calculate the molar mass of a compound

find the number of grams of each element in one mole of the compound

add the masses of the elements in the compound

For example: for methane, CH4:

mass of C = 1 × 12.01 g = 12.01 g mass of H = 4 × 1.00794 g = 4.03177 g mass of CH4 = (12.01 + 4.03) g = 16.04 g

The Mass of a Mole Try some on your own: find the molar mass of

…

NH3

CO2

NaCl

H2SO4

KOH

Fe2O3

17.02 g/mol

44.01 g/mol

58.44 g/mol

98.08 g/mol

56.11 g/mol

159.69 g/mol

Summary When chemists measure matter, they

measure … the numbers of atoms or molecules the mass of the elements or compounds the volumes of the matter

The unit for the amount of matter is a mole. 1 mole of any thing is defined as 6.02 × 1023

pieces of that thing. This number is called Avogadro’s Number, N0.

Summary To convert from numbers of particles to

number of mols, we use the conversion…

To convert form number of mols to number of particles, we use the conversion …

# of moles =

# of representative particles × 6.02 × 1023 representative

particles

1 mole

# of particles =

# of mols × 1 mol6.02 × 1023 representative

particles

Summary The atomic mass of an element is the mass

of 1 mol of that element. The molar mass of a compound is the mass

of 1 mol of that compound. To calculate the molar mass of a compound

find the number of grams of each element in one mole of the compound and add the masses of the elements in the compound.