Chapter 10: The MoleEditor: Kerry DemondThere are many different systems of measurment in the world, each used in a variety of ways. Teachers measure your grade in points; doctors measure your height in inches.
The mole is simply another way to measure mass. A mole contains a certain amount of particles, just as a dozen eggs contains twelve eggs. In this section, you will learn about the various things we can learn through an understanding of the mole.

10.1: The Mole-A Measurement of Matter

Measuring Matter (287-288)
Brendan Morrisey
  • There are a number of ways in which you can measure matter
  • You can often measure the amount of something by one of three different methods--by count, mass, and volume
  • Some of the units used for measuring indicate a specific number of items, ex. a pair = two and a dozen = 12
  • Apples can be measured in these three different ways
  • Each of these ways can be equated to a dozen apples
    • By count: 1 dozen apples=12 apples
    • (For average-sized apples) By mass: 1 dozen apples=2.0kg
    • (For average-sized apples) By volume: 1 dozen apples=0.20 bushel apples

  • Knowing how the count, mass, and volume of apples relate to a dozen apples allows you to convert among these units
    • Based on the unit relationships given above, you can calculate the mass of a bushel of apples or the mass of 90 average-sized apples using conversion factors such as:
      • 1 dozen apples:12 apples
      • 2.0 kg apples:1 dozen apples
      • 1 dozen apples: 0.20 bushel apples

Finding Mass from a Count (289)

Dan Lynch

In this section you learn how to find the mass of a sum of objects.
This is easy and we all learned it in class but I'll give a few examples of how to do it with simple dimensional analysis.
First start with what you're looking for, the goal.
Ex. Mass of apples
Next break it down into simple relationships that cancel out with terms on the top and bottom
Mass of apples = 90(the number of apples) x 1 dozen apples x 2.0 kg apples = 15 kg apples..
12 apples 1 dozen apples

So for 90 average sized apples the average mass is 15 kg

Next you want to make sure your answer makes sense.
A review of dimensional analysis go to pg 289 OR pg R66 in the text book, both are helpful.

What is a Mole? (290)
Siri Devlin

Chemists use a unit that is a specified number of particles. This unit is called a MOLE
Mole-(mol) of a substance is 6.02X 10^23 representative particles of that substance and is the SI unit for measuring the amount of a substance.
The number of representative particles in a mole, 6.02X 10^23, is called AVAGADRO’S NUMBER
Representative particle- the species present in a substance: usually atoms, molecules, or formula units
a mole of any substance contains Avagadro’s number of representative particles, or 6.02X 10^23 representative particles
Converting Moles to Number of Particles
(291-293) Ben Ross
Moles= representative particles × (1 mole)/(6.02X 10^23 representative particles)

Mole conversion involves a lot of math.

One example of this conversion is Carbon Dioxide, which is composed of three atoms.

Being three atoms, one mole of this element is 3 x Avogadro's number.

To find the number of atoms in a mole of a compound, follow this formula -

Representative particles = Moles X Avogadro's Number/ 1 Mole

This is dimensional analysis.


The Mass of a Mole of an Element (293-294)
Delia Calderon

  • The atomic masses are relative values based on the mass of the most common isotope of carbon.
  • Average carbon atom (atomic mass of 12 amu) is twelve times heavier than average hydrogen atom
  • 12.0 g of carbon atom and 1.0 g of hydrogen atoms contain the same number of atoms. The mass ratio of 12 carbon atoms to 1 hydrogen atom remains the same no matter what unit is used to express it.
  • Atomic masses are weighted average masses of the isotopes of each element.

  • The atomic mass of an elementexpressed in grams is the mass of a mole of the element.
  • The mass of a mole of an element is its molar mass.
  • Carbon has a molar mass of 12.0 g; atomic hydrogen has a molar mass of 1.0 g
  • 12.0 g of carbon atoms and 16.0 g of oxygen atoms contain the same number of atoms. The molar masses of any two elements must contain the same number of atoms.
  • The molar mass of any element contains 1 mol or 6.02 x 1023 atoms of that element.
  • Molar mass is the mass of 1 mol of atoms of any element.

The Mass of a Mole of a Compound (295-296)
Elaney Marcotte

  • To find the molar mass of a compound, you have to know the compound’s formula
  • First, find the compounds’ formula
  • Next, find the number of grams of each element in one mole of the compound
  • Then, add the masses of the elements in the compound
  • Example: Find the molar mass of sulfur trioxideSubstitute grams for the amu to get the molar mass
    • First, write the formula for sulfur trioxide: SO3
    • Use a periodic table to find the atomic mass of sulfur and oxygen
    • The atomic mass for sulfur is 32.1 amu and the atomic mass for oxygen is 16 amu
    • Check to see how many atoms of each element are in the compound
    • There is one atom of sulfur and three atoms of oxygen
    • Since there are three atoms of oxygen, multiply the atomic mass of oxygen by 3
    • Add the masses of the two elements
      • 32.1+48= 80.1amu

  • The molar mass of SO3 is 80.1g
Practice Problems

Find the molar mass of the following:

  1. PCl3
  2. H2O2
  3. H3PO4
  4. N2O3
  5. CaCO3
  6. Br2
  7. C4H9O2
  8. (NH4)2SO4

10.2: Mole-Mass and Mole Volume
The Mole-Mass Relationship (297-300)
Converting Moles to Mass
Marissa Chura

Problem: What is the mass of 9.45 mol of aluminum oxide?

Step One: Analyze
Identify your given information, as well as your destination.
We are given that there are 9.45 moles of aluminum oxide.
We don't know that mass of the aluminum oxide, so that is the destination.

Step Two: Calculate
First determine the molar mass of aluminum oxide. It is 102.0 gAl2O3
Multiply the given number of moles by the conversion factor, relating moles to grams.
mass=9.45moles x 102.0g / 1 mol

Answer: 964g Al2O3

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Use the molar mass of an element or compound to covert between the mass of a substance and the moles of a substance.
Molar mass = 1 mole
The formula for molar mass is as follows:
Mass(grams) = number of moles x mass(grams)/1 mole

Converting Mass to Moles
Kati West

Problem: Rust is iron (III) oxide, of Fe2O3. How many moles of iron (III) oxide are contained in 92.2g of Fe2O3

Step 1: Analyze
We know the mass is 92.2g Fe2O3.
We don't know how many moles of Fe2O3 this contains.
This makes the conversion factor is mass to moles.

Step 2: Calculate
The molar mass of Fe2O3 is 159.6g Fe2O3
Multiply the given mass by the conversion factor.
Moles = 92.2g Fe2O3 x 1 mol Fe2O3/159.6 g Fe2O3 = 0.578 mol Fe2O3

Answer: 0.578 mol Fe2O3

The Mole-Volume Relationship (300)
Kendall Lavin-Parsons
  • Moles of solid and liquids are not even
  • Gases are even more different
  • Volume of moles of gases are more predictable
  • Avogadro’s hypothesis = equal volume of gases at the same temperature and pressure contain equal numbers of particles
  • All particles in gas are very spread apart with a large gap of time in between
  • This stands true for both large and small particles
  • Volume of gas varies with change in temperature

EX: when you take a balloon of helium outside and it shrinks

  • Standard temperature and pressure (STP) = temperature of 0 degrees Celsius, pressure of 101.3 kPa, 1 atmosphere (atm)

EX: in STP 6.02 x 10 ^23 representative particles of gasses occupies a volume of 22.4 Liters

  • The quantity in Liters is known as the Molar Volume

Calculating Volume at STP (301)
Phil Royal
- The mole volume is used to convert a number of moles of gas to the volume of gas at STP
- The relationship between 22.4 = 1 molecule at STP provides us a conversion factor

Example Problem

- Destination: volume of gas at STP
- Volume of 02 =3.75 mol x 22.4/ 1 mol
- Answer: 8.40

Sample Problem 10.7

Determine the volume in liters of .60 mol of SO2 at STP.

What do we know?

- moles = 0.60 mole SO(2)
- 1 mole of SO2 = 22.4 L So(2)

What don't we know?

- Volume = ?L

Solve for the unknown!

volume = 0.60 mol of SO2 x 22.4 L SO2/ 1 mole SO2= 13 L SO2

Does it make sense?

-Yes, as .60 is very close to half of a mole and half a mole multiplied by 22.4 would be 11.7 L SO2

The Opposite Conversion:

- Same as the operations being preformed about, but with the conversion factor switched.

Calculating Molar Mass from Density:

- Different gasses have different densities
- Density of gas at STP and the molar volume at STP is used below

Calculating the Molar Mass of a Gas at STP:

What we know:
- Desity = 1.964 g/l
- 1 mol (gas at STP) = 22.4 L
- Conversion Factor to convert density to molar mass= 22.4 L / 1 mol

What we don't:

- Molar Mass = ? g/mol


Molar Mass = 1.964 g/ 1 l x 22.4 L /1 mol= 44.0 g/mol

Does it make sense?

Yes, as the density is very close to 2.0 and multiplied by 22.4, is 44.8.
Thus the answer is reasonable.

The Mole Road Map (303)
Austin Burlone
-Mole is at center of chemical calculations
-Mole is used as "intermediate step" when converting one unit to the next
-The conversion factor is different depending on what the person is looking to calculate
external image molar_roadmap.GIF

Practice Problems
Frank Morley

Calculate the volume: Assume these are all the moles of gaseous elements: 1 mole fills 22.4 L at STP
.375 moles
.780 moles
.60 moles
.75 moles
,85 moles
.450 moles
50 moles
7.5 moles
9.2 moles
7.8 moles
122 moles
12.25 moles
10.75 moles
60.7 moles
1.1 moles
.123 moles

Calculate mass:

All gaseous elements occupy 22.4 L. assume all are densities of gaseous elemnts

10.3: Percent Composition and Chemical Formulas
The Percent Composition of a Compound (305-306)
Brett Chatfield
- If you have ever had experience with cutting grass, you know that the percent of fertilizer used is very important. In the spring, you may use a fertilizer with a high concentration of nitrogen to make it green. In the fall, you may want potassium to strengthen it.
- The relative amounts of the elements in a compound are expressed as the percent composition or the percent by mass of each element in the compound. The percent composition of a compound is the percent value of each element in the compound.
- For example, in K2CrO4, K=40.3% Cr= 26.8% and O = 32.9%. They all add to 100 %

How to Calculate Percent Composition

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Percent Composition from Mass Data

- Pretend to be a chemist who has just discovered a new compound. Now you have it in the crystalline solid form in a jar. You must verify the composition of the compound. To do this you must determine the molecular formula. You can solve this by a certain series of steps

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For Additional Help:

A Practice Worksheet
Percent Composition from the Chemical Formula (307)
Chris Hart
  • You can calculate the percent composition of a compound if you know only its chemical formula.
  • The subscripts in the formula of the compound are used to calculate the mass of each element in a mole of that compound.
  • The sum of these masses is the molar mass.
  • Using the individual masses of the elements and the molar mass you can calculate the percent by mass of each element in one mole of the compound.
  • Divide the mass of each element by the molar mass and multiply the result by 100%.

%mass = mass of element in 1 mol compound x 100%
molar mass of compound

The percent composition of a compound is always the same.

Percent Composition as a Conversion Factor (308)
Abbey Salvas

-Percent composition can be used to calculate the number of grams of any element in a specific mass of a compound

-multiply the mass of the compound by a conversion factor based on the percent composition of the element in the compound

Sample Problem:

How much carbon and hydrogen are contained in 82.0 g of propane?

Propane is 81.8% carbon and 18% hydrogen.

You can use the ratio 81.8 g C/100 g C3H8 to calculate the mass of carbon contained in 82.0 g of propane (C3H8).

82.0g C3H8 X 81.8g C/100g C3H8= 67.1g C

Using the ratio 18g H/100g C3H8, you can calculate the mass of hydrogen

82.0g C3H8 X 18g H/100g C3H8= 15g H

The sum of the two masses equals 82g, the sample size, to two significant figures.

Empirical Formulas (309-310)
Randy Melanson

Just as formulas for cooking call for certain ratios, formulas for molecules appear in ratios too. The basic ratio of the elements in a compound is called the empirical formula. For example the empirical formula for carbon dioxide is CO2. The empirical formula shows the kinds and lowest relative counts of atoms or moles of atoms in a molecule or formula units of a compound. Multiply the empirical formula by any factor can produce the formulas for other compounds.
  • Microscopic Interpretation- CO2 molecule is composed of 1 carbon atom and 2 oxygen atoms.
  • Macroscopic Interpretation- 1 mos CO2 is composed of (6.02x10^23) carbon atoms (1 mole C atoms), and 2x(6.02x10^23) oxygen atoms (2 mole O atoms).
  • Empirical formulas may be interpreted at the microscopic (atomic) or macroscopic (molar) level.

An empirical formula may not be the same as a molecular formula. For example the molecule hydrogen peroxide is composed of two hydrogen atoms and two oxygen atoms or H2O2. Thus the lowest ratio of hydrogen to oxygen is 1:1 which makes the empirical formula HO. The actual molecular formula of hydrogen peroxide has twice the number of atoms as the empirical formula.
  • The empirical formula of a compound shows the smallest whole-number ratio of the atoms in the compound.
  • The molecular formula tells the actual number of each kind of atom present in the molecule of the compound.

Molecular Formulas (311-312)
Nic Cunha
Many chemicals have the same empirical formulas such as ethyne and benzene, both have the empirical formula CH. But these compounds, as well as many others, have different molar masses. Their molar masses are simple whole number multiples of the molar masses of the empirical formula, CH. The Molecular Formula od a compound I either the same as its experimentally determined empirical formula, or it’s a simple whole number multiple of its empirical formula. Once you have determined the empirical formula of your compound, you can determine its molecular formula, but you must know its molar mass. From the Empirical formula you can calculate the empirical formula mass (efm)à simply the molar mass represented by the empirical formula. Then you can divide the experimentally determined molar mass by the efm. This gives the number of empirical formula units in a molecule of the compound and is the multiplier to convert the empirical formula to the molecular formula.

For example:
Empirical formula of hydrogen peroxide is HO. Its efm is 17.0 g/mol. The molar mas of H­2O2 is 34.0 g/mol.
34.0g/mol = 2
17.0 g/mol
To obtain the molecular formula of hydrogen peroxide from its empirical formula, multiply the subscripts in the empirical formula by 2 (the number above). (HO) x2= H­2O2.