The Mole: A Measurement of Matter

Sand Activity

• Is it practical to count each grain of sand?

• How else might you measure or quantify the sand?

• mass, volume

• just a small amount of sand contains millions of smaller particles, just like chemical substances

The Mole: A Measurement of Matter

Scientists answer questions such as:

• How many kilograms of iron can be obtained from one kilogram of iron ore?

• How many grams of the elements hydrogen and nitrogen must be combined to make 200 grams of the fertilizer ammonia (NH3)?

• How do we measure matter?• by counting• determine its mass and volume

The Mole: A Measurement of Matter• There are ways that

everyday things are measured

• how many is a couple?

• how many is one dozen?

• how many is a few?• how many sodas

are in one case?• how many are in

one gross?

Example: apples can be measured three different ways, all of which can be equated to a dozen apples

By count:• 1 dozen apples = 12 apples• for average-sized apples the

following approximations can be used:

• By mass:• 1 dozen apples = 2.0 kg

apples• By volume:• 1dozen apples = 0.20 bushel

apples

The Mole: A Measurement of Matter

• Knowing how the count, mass, and volume of apples relate to a dozen apples allows you to convert between these units. For example, you could calculate the mass of a bushel of apples or the mass of 90 average-sized apples using conversion factors based on the unit relationships given above.

The Mole: A Measurement of Matter• In chemistry you will do calculations using

a measuring unit called a mole. The mole, the SI unit that measures the amount of substance, is a unit just like the dozen.

• The mole can be related to the number of particles (a count), the mass, and the volume of an element or a compound just as a dozen was related to these three units for apples

The Mole: A Measurement of Matter

Knowns:

Number of apples = 90 apples12 apples = 1 dozen apples1 dozen apples = 2.0 kg apples

Unknowns:

Mass of 90 apples = ? kg

Example:What is the mass of 90 average-sized apples?

Convert:Number of apples to mass of applesThis conversion can be carried out by performing the following sequence of conversions:

number dozens mass of apples

The Mole: A Measurement of Matter

• Calculate:

• First conversion factor: 1 dozen apples/ 12 apples

• Second conversion factor: 2.0 kg apples/ 1 dozen apples

• Multiplying the original number of apples by these two conversion factors yields the answer in kilograms,

The Mole and Molar Mass• The mole is the standard method in chemistry

for communicating how much of a substance is present (just like one dozen is equal to the quantity twelve).

• Definition: • The mole is the amount of substance of a

system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

The Mole and Molar Mass• One mole contains as many entities as

there are in 12 grams of carbon-12 (or 0.012 kilogram)

• In one mole, there are 6.023 x 1023 atoms. Here's another way: there are 6.023 x 1023 atoms of carbon in 12 grams of carbon-12

• Let's say that clearly: one mole of ANYTHING contains 6.023 x 1023 entities.

The Mole and Molar Mass• The word "entities" is simply a generic

word. For example, if we were discussing atoms, then we would use "atoms" and if molecules were the subject of discussion, the word entities would be replaced in actual use by "molecules."

• The mole has been very carefully measured in a number of ways over many decades. The symbol for mole is "mol."

The Mole and Molar Mass

• One mole of ANY specified entity contains 6.022 x 1023 of that entity. For example:

• One mole of donuts contains 6.022 x 1023 donuts

• One mole of H2O contains 6.022 x 1023 molecules

• One mole of nails contains 6.022 x 1023 nails • One mole of Fe contains 6.022 x 1023 atoms • One mole of dogs contains 6.022 x 1023 dogs • One mole of electrons contains 6.022 x 1023

electrons • One mole of 11th grade chemistry students

contains 6.022 x 1023 poor, suffering (I mean happy, joyful) Monaca students

The Mole and Molar Mass• 6.023 x 1023 is so important in

chemistry that it has a name. It is called Avogadro's Number and has the symbol N.

• It is so named in honor of Amedeo Avogadro, an Italian chemist, who, in 1811, made a critical contribution (recognized only in 1860 after his death) which helped greatly with the measurement of atomic weights.

The Mole and Molar Mass• Avogadro's Number has a unit

associated with it. It is mol¯1, as in 6.022 x 1023 mol¯1.

• The superscripted minus one means the unit mol is in the denominator. There is an understood numerator of one, as in 1/mol.

The Mole and Molar Mass• 6.022 x 1023 mol¯1• Why is there no unit

in the numerator? There could be, but it would vary based on the entity involved. If we were discussing an element, we might write atoms/mol.

• If we were discussing a compound, we would say "molecules per mol." What is in the numerator depends on what "entity" (atom, molecule, ion, electron, etc.) is being used in the problem.

The Mole and Molar Mass

Examples

• Atoms/mol• Molecules/mol• Ions/mol• Electrons/mol• Pencils/mol• Chairs/mol• etc

• Getting back to Avogadro's Number and its role in chemistry; please note that counting atoms or molecules is very difficult since they are so small. However, we can "count" atoms or molecules by weighing large amounts of them on a balance.

Molar Mass• When we weigh one mole of a substance

on a balance, this is called a "molar mass" and has the units g/mol (grams per mole). This idea is very critical because it is used all the time.

• A molar mass is the weight in grams of one mole.

• One mole contains 6.023 x 1023 entities.

• Therefore, a molar mass is the mass in grams of 6.023 x 1023 entities.

Molar Mass• OK. How does one calculate a molar

mass?• The molar mass of a substance is the

molecular weight in grams. The molecular weight of a substance is the weight in atomic mass units of all the atoms in a given formula.

• All you need to do is calculate the molecular weight and place the unit "g/mol" after the number and that is the molar mass for the substance in question.

Molar Mass

• Calculate the molar mass of Al(NO3)3

• Al(1 x 26.98) + N(3 x 14.007) + O(9 x 16.00) = 213.00 g/mol

• 213.00 grams is the mass of one mole of aluminum nitrate.

• 213.00 grams of aluminum nitrate contains 6.022 x 1023 entities of Al(NO3)3

Review

• Calculate the molar mass of Pb(ClO2)2

• Pb( 1 x 207.2) + Cl( 2 x 35.4527) + O( 4 x 15.9994) = 342.10 g/mol

• Calculate the molar mass of NH4MnO4

• N( 1 x 14.0067) + H( 4 x 1.01) + Mn( 1 x 54.9380) + O( 4 x 15.9994)

• = 136.97 g/mol

• A bottle filled with exactly 18.02 g water will contain 6.02 x 1023 water molecules.  The concept of fractions and multiples described above also applies to molecules: 9.01 g of water would contain 1/2 mole, or 3.01 x 1023 molecules. 

Mole and Weight Relationships of Water and its Parts

2 moles H

+ 1 mole O =1 mole water

2 * 1.01 g + 16.00 g = 18.02 g