Chemists need a convenient method for counting accurately the number of atoms, molecules, or formula units in a sample of a substance. MOLE The Mole:

• Chemists need a convenient method for counting accurately the number of atoms, molecules, or formula units in a sample of a substance.

MOLE

The Mole: Basic ConceptsThe Mole: Basic Concepts The Mole: Basic ConceptsThe Mole: Basic Concepts

• As you know, atoms and molecules are extremely small. There are so many of them in even the smallest sample that it’s impossible to actually count them.

• That’s why chemists created their own counting unit called the mole.

Topic 14Topic 14

• The mole, commonly abbreviated mol, is the SI base unit used to measure the amount of a substance.

Measuring Matter

• It is the number of representative particles, carbon atoms, in exactly 12 g of pure carbon-12.

The Mole: Basic ConceptsThe Mole: Basic Concepts The Mole: Basic ConceptsThe Mole: Basic Concepts Topic 14Topic 14

Click box to view movie clip.

• Through years of experimentation, it has been established that a mole of anything contains 6.022 136 7 x 1023 representative particles.

Measuring Matter

• A representative particle is any kind of particle such as atoms, molecules, formula units, electrons, or ions.


• The number 6.022 136 7 x 1023 is called Avogadro’s number in honor of the Italian physicist and lawyer Amedeo Avogadro who, in 1811, determined the volume of one mole of a gas.

Measuring Matter

• In this book, Avogadro’s number will be rounded to three significant figures— 6.02 x 1023.


• If you write out Avogadro’s number, it looks like this.

Measuring Matter

602 000 000 000 000 000 000 000


• One-mole quantities of three substances are shown, each with a different representative particle.

Measuring Matter

• The representative particle in a mole of water is the water molecule.


• The representative particle in a mole of copper is the copper atom.

Measuring Matter


• The representative particle in a mole of sodium chloride is the formula unit.

Measuring Matter


• Suppose you want to determine how many particles of sucrose are in 3.50 moles of sucrose. You know that one mole contains 6.02 x 1023 representative particles.

Converting Moles to Particles

• Therefore, you can write a conversion factor, Avogadro’s number, that relates representative particles to moles of a substance.


• You can find the number of representative particles in a number of moles just as you found the number of roses in 3.5 dozen.


• For sucrose, the representative particle is a molecule, so the number of molecules of sucrose is obtained by multiplying 3.50 moles of sucrose by the conversion factor, Avogadro’s number.


• There are 2.11 x 1024 molecules of sucrose in 3.50 moles.



• Now, suppose you want to find out how many moles are represented by a certain number of representative particles.

Converting Particles to Moles

• You can use the inverse of Avogadro’s number as a conversion factor.


• Zinc is used as a corrosion-resistant coating on iron and steel. It is also an essential trace element in your diet.


• Calculate the number of moles that contain 4.50 x 1024 atoms of zinc (Zn).


• Multiply the number of zinc atoms by the conversion factor that is the inverse of Avogadro’s number.



• The relative scale of atomic masses uses the isotope carbon-12 as the standard.

The Mass of a Mole

• Each atom of carbon-12 has a mass of 12 atomic mass units (amu).

• The atomic masses of all other elements are established relative to carbon-12.


• For example, an atom of hydrogen-1 has a mass of 1 amu.

The Mass of a Mole

• The mass of an atom of helium-4 is 4 amu.

• Therefore, the mass of one atom of hydrogen-1 is one-twelfth the mass of one atom of carbon-12.

• The mass of one atom of helium-4 is one-third the mass of one atom of carbon-12.


• You can find atomic masses on the periodic table, but notice that the values shown are not exact integers.

The Mass of a Mole

• For example, you’ll find 12.011 amu for carbon, 1.008 amu for hydrogen, and 4.003 amu for helium.

• These differences occur because the recorded values are weighted averages of the masses of all the naturally occurring isotopes of each element.


• You know that the mole is defined as the number of representative particles, or carbon-12 atoms, in exactly 12 g of pure carbon-12.

The Mass of a Mole

• Thus, the mass of one mole of carbon-12 atoms is 12 g. What about other elements?

• Whether you are considering a single atom or Avogadro’s number of atoms (a mole), the masses of all atoms are established relative to the mass of carbon-12.


• The mass of a mole of hydrogen-1 is one-twelfth the mass of a mole of carbon-12 atoms, or 1.0 g.

The Mass of a Mole

• The mass of a mole of helium-4 atoms is one-third the mass of a mole of carbon-12 atoms, or 4.0 g.


The Mass of a Mole

• The mass in grams of one mole of any pure substance is called its molar mass.

• The molar mass of any element is numerically equal to its atomic mass and has the units g/mol.


Converting Mass to Moles

• A roll of copper wire has a mass of 848 g. • How many moles of copper are in the roll? • Use the atomic mass of copper given on the

periodic table to apply a conversion factor to the mass given in the problem.


Converting Moles to Mass

• Calculate the mass of 0.625 moles of calcium.

• Use the molar mass of calcium to apply a conversion factor to the number of moles given in the problem.

• According to the periodic table, the atomic mass of calcium is 40.078 amu, so the molar mass of calcium is 40.078 g.


Converting Moles to Mass


Converting Mass to Number of Particles

• Calculate the number of atoms in 4.77 g lead.

• To find the number of atoms in the sample, you must first determine how many moles are in 4.77 g lead.



• According to data from the periodic table, the molar mass of lead is 207.2 g/mol. Apply a conversion factor to convert mass to moles.



• Now use a second conversion factor to convert moles to number of particles.



• You can also convert from number of particles to mass by reversing the procedure above and dividing the number of particles by Avogadro’s number to determine the number of moles present.


Moles of Compounds• Recall that a mole is Avogadro’s number

(6.02 x 1023) of particles of a substance. • If the substance is a molecular compound,

such as ammonia (NH3), a mole is 6.02 x 1023 molecules of ammonia.

• If the substance is an ionic compound, such as baking soda (sodium hydrogen carbonate, NaHCO3), a mole is 6.02 x 1023 formula units of sodium hydrogen carbonate.


Moles of Compounds

• In either case, a mole of a compound contains as many moles of each element as are indicated by the subscripts in the formula for the compound.

• For example, a mole of ammonia (NH3) consists of one mole of nitrogen atoms and three moles of hydrogen atoms.


Molar mass of a compound

• The molar mass of a compound is the mass of a mole of the representative particles of the compound.

• Because each representative particle is composed of two or more atoms, the molar mass of the compound is found by adding the molar masses of all of the atoms in the representative particle.



• In the case of NH3, the molar mass equals the mass of one mole of nitrogen atoms plus the mass of three moles of hydrogen atoms.



• You can use the molar mass of a compound to convert between mass and moles, just as you used the molar mass of elements to make these conversions.

Molar mass of NH3 = molar mass of N + 3(molar mass of H)

Molar mass of NH3 = 14.007 g + 3(1.008 g) = 17.031 g/mol


Converting Mass of a Compound to Moles

• At 4.0°C, water has a density of 1.000 g/mL.

• How many moles of water are in 1.000 kg of water (1.000 L at 4.0°C)?




• Before you can calculate moles, you must determine the molar mass of water (H2O).

• A mole of water consists of two moles of hydrogen atoms and one mole of oxygen atoms.


• Now you can use the molar mass of water as a conversion factor to determine moles of water.

• Notice that 1.000 kg is converted to 1.000 x 103 g for the calculation.

molar mass H2O = 2(molar mass H) + molar mass O




Basic Assessment QuestionsBasic Assessment Questions

Question 1

Calculate the number of molecules in 15.7 mol carbon dioxide.

Topic 14Topic 14


Answer

9.45 x 1024 molecular CO2

Topic 14Topic 14


Question 2

Calculate the number of moles in 9.22 x 1023 atom iron.

Topic 14Topic 14


Answer

1.53 mol Fe

Topic 14Topic 14


Question 3

Calculate the mass of 6.89 mol antimony.

Topic 14Topic 14


Answer

839g Sb

Topic 14Topic 14


Question 4

A chemist needs 0.0700 mol selenium for a reaction. What mass of selenium should the chemist use?

Topic 14Topic 14


Answer

5.53g Se

Topic 14Topic 14


Question 5

Calculate the number of moles in 17.2 g of benzene (C6H6).

Topic 14Topic 14


Answer

0.220 mol C6H6

Topic 14Topic 14

The Mole: Additional ConceptsThe Mole: Additional Concepts The Mole: Additional ConceptsThe Mole: Additional Concepts Topic 14Topic 14

Additional Concepts

Molecular formulas

• For many compounds, the empirical formula is not the true formula.

• Chemists have learned, though, that acetic acid is a molecule with the formula C2H4O2, which is the molecular formula for acetic acid.

• A molecular formula tells the exact number of atoms of each element in a molecule or formula unit of a compound.

The Mole: Additional ConceptsThe Mole: Additional Concepts The Mole: Additional ConceptsThe Mole: Additional Concepts Topic 14Topic 14

Chemists need a convenient method for counting accurately the number of atoms, molecules, or formula units in a sample of a substance. MOLE The Mole:

Documents

basic concepts topic

mole of copper

mole of water

number of moles

mole quantities

number of molecules

number of atoms

particles of sucrose