HOW DO WE USE THE MOLE?

Chemistry Unit 9

MAIN IDEAS Chemists use the mole to count atoms,

molecules, ions and formula units. A mole always contains the same number of

particles, however, moles of different substances have different masses.

The molar mass of a compound can be calculated from its chemical formula and can be used to convert from mass to moles of that compound.

A molecular formula of a compound is a whole-number multiple of its empirical formula

MEASURING MATTER

9.1 MEASURING MATTER: OBJECTIVES Explain how a mole is used to indirectly

count the number of particles of matter. Relate the mole to a common everyday

counting unit. Convert between moles and number of

representative particles.

MOLEThe mole is the SI base unit for measure

of amount of a substance: 6.0221367 x 1023

The number of carbon atoms in exactly 12 g of pure carbon-12.

Called Avogadro’s number – Italian physicist who in 1811, determined the volume of 1 mol of gas.

By mass, we can determine the number of particles (atoms, molecules) in a sample.

We typically round to 3 sig figs – 6.02 x 1023

THE MOLE: A GOOD COMPARISONThe mole is a number. What other unit is used in a similar manner?

A dozen flowers, doughnuts or eggs. A baker’s dozen of cookies or bagels. A pair of socks or friends

If you have a dozen flowers and a dozen eggs, do they weigh the same?

THE MOLE AS A CONVERSION FACTORIn order to convert between moles and

number of particles we need to use this ratio of equivalent values (conversion factor) to express the same quantity in different units.

EXAMPLE PROBLEMS 1&2How many particles are in 3.5 mols?

How many moles of atoms are in 9.63 x 1026 atoms?

QUESTION?What does the mole measure? A. mass of a substance B. amount of a substance C. volume of a gas D. density of a gas

QUESTION?What is the conversion factor for

determining the number of moles of a substance from a known number of particles?

A.

B.

C. 1 particle 6.02 1023

D. 1 mol 6.02 1023 particles

PRACTICE PROBLEMS Page 322 #1-4; page 324 #5-14

MASS AND THE MOLE

MASS AND THE MOLE: OBJECTIVES Relate the mass of an atom to the mass

of a mole of atoms. Convert between number of moles and

the mass of an element. Convert between number of moles and

number of atoms of an element.

MOLAR MASSMolar mass is the mass in grams of one

mole of any pure substance. Units are given in g/mol Mass of the periodic table is given in

amu, but also g/mol

EXAMPLE PROBLEMS 3&4If I need 3 mols of Cu, how do I measure

the amount?

I measured 5.0g of Iron, how many atoms do I have?

CONVERSIONS

EXAMPLE PROBLEMS 5&6How many atoms of gold are in a U.S.

Eagle bullion coin with a mass of 31.1g?

How much does 5.8 x 1015 atoms of lead weigh?

QUESTIONThe mass in grams of 1 mol of any pure

substance is: A. molar mass B. Avogadro’s number C. atomic mass D. 1 g/mol

QUESTIONMolar mass is used to convert what? A. mass to moles B. moles to mass C. atomic weight D. particles

PRACTICE PROBLEMS Page 328 #15-16; page 329 #17-18 Page 331 #19-21; page 332 #22-27

MOLES OF COMPOUNDS

MOLES OF COMPOUNDS: OBJECTIVES Recognize the mole relationships shown

by a chemical formula Calculate the molar mass of a

compound. Convert between number of moles and

mass of a compound. Apply conversion factors to determine

the number of atoms or ions in a known mass of a compound

CALCULATE MOLAR MASSSteps to calculate molar mass:1. Count the number of atoms in each

molecule.2. Find the molar mass of each atom.3. Multiply the molar mass of each atom

to the number of atoms in a compound.

4. Add the total molar masses together.

EXAMPLE PROBLEM 7Find the molar mass of the following compounds/molecules. H2O

NaCl

H2SO4

EXAMPLE PROBLEM 7 CONT.. Al2O3

Fe2(SO4)3

CCl2F2

NUMBER OF ATOMS To determine the number of atoms or ions

in a known mass of a compound1. Find the molar mass of the compound.2. Use molar mass and the mole as

conversion factors to get the units needed.

EXAMPLE PROBLEM 8What is the mass of 2.5 mols of (C3H5)2 S?

EXAMPLE PROBLEM 9Calculate the number of moles of Ca(OH)2 in 325g of the compound?

EXAMPLE PROBLEM 10How many atoms are in 212g of water?

QUESTIONHow many moles of OH— ions are in 2.50

moles of Ca(OH)2?

A. 2.00 B. 2.50C. 4.00D. 5.00

QUESTIONHow many particles of Mg are in 10 moles

of MgBr2?

A. 6.02 x 1023 B. 6.02 x 1024 C. 1.20 x 1024 D. 1.20 x 1025

PRACTICE PROBLEMS Page 335 #29-36; page 336 #37-41;

page 339 #42-46

EMPIRICAL AND MOLECULAR FORMULAS

EMPIRICAL AND MOLECULAR FORMULAS: OBJECTIVES Explain what is meant by the percent

composition of a compound. Determine the empirical and molecular

formulas for a compound from percent and actual mass data.

Explain what a hydrate is and relate the name of the hydrate to its composition.

Determine the formula of a hydrate from laboratory data.

PERCENT COMPOSITIONThe percent composition is a percent by

mass of each element in a compound.

Steps to determine percent composition of a compound:

1. Assume 1 mole of a compound.2. Calculate molar mass of each element

in the compound.3. Use each element’s molar mass to

calculate percent by mass.

PERCENT BY MASSPercent by mass is a description of the

amount of an element in a compound. Percent by mass =

EXAMPLE PROBLEM 11What is the percent by mass of each element in NaHCO3?

EMPIRICAL FORMULAThe empirical formula is the smallest

whole number ratio of elements in a compound

This ratio provides the subscripts for the elements.

May or may not be the same as the actual molecular formula. If they are different the molecular formula

will be a simple multiple of the empirical formula.

Hydrogen peroxide: HO- empirical formulaH2O2 – actual formula (molecular formula)

EMPIRICAL FORMULASteps to figure empirical formula from percent

composition:1. Assume an overall 100g sample of the

compound.2. Each element’s percentage can be used as

mass in calculations.3. Use this ‘mass’ to convert to moles. This

provides a ‘mole ratio’ for the compound.

EMPIRICAL FORMULA Since these mole ratios are not whole

numbers, we convert them to whole numbers what can be used as subscripts by dividing them all by the smallest ratio. (We assume the smallest mole ratio is a 1 in the compound)

EXAMPLE PROBLEM 12A compound has the following mass

percentages: C – 48.64%, H – 8.16%, O – 43.20%

What is the empirical formula for this molecule?

MOLECULAR FORMULAThe molecular formula specifies the

actual number of atoms of each element in one molecule/formula unit of the substance.

MOLECULAR FORMULASteps to determine the molecular

formula:1. Determine the molar mass of the

empirical formula.2. Determine the molar mass of the

actual compound. (might be given to you)

3. Divide the molar mass of the actual compound by the molar mass of the empirical formula

4. Multiply all subscripts of the empirical formula by this molar mass ratio.

EXAMPLE PROBLEM 13The mass of benzene has been

experimentally determined to be 78.12 g. We know that benzene is 92 % C by mass and 8 % H by mass. What is the molecular formula of benzene?

PRACTICE PROBLEMS Page 344 #54-57 Page 348 #58-61 Page 350 #62-66

HYDRATESHydrates are solid ionic compounds in

which water molecules are trapped. Hydrates are formed when water

molecules adhere to the ions as the solid forms.

Water molecules become a part of the crystal solid structure.

The number of water molecules associated with each molecule is written following a dot after the molecular formula:Na2CO310H2O

HYDRATES Names of these compounds are named

with a prefix representing the number of water molecules and the word hydrate.Na2CO3 10H2O – sodium carbonate

decahydratePrefixes are the same as the ones used in

naming covalent molecules

NAMING HYDRATES

ANHYDROUSAn anhydrous is a compound without

water. When a hydrate is heated, water

molecules are driven off leaving the compound.

HYDRATE FORMULASteps to determining the formula of a

hydrate:1. Determine the initial mass of the

compound prior to heating.2. Determine the final mass of the

compound after heating.3. The final mass is used to determine

the number of moles of the anhydrous compound. Grams to moles

HYDRATE FORMULA4. Calculate the difference of the initial

mass and the final mass and use this mass to determine number of moles of water, grams to moles

5. Number of hydrates per compound molecule (molar ratio – hydrate: anhydrous) = moles of H2O/moles of compound

EXAMPLE PROBLEM 14A mass of 2.50 g of blue, hydrated copper

sulfate (CuSO4) ?H2O) is place in a crucible and heated. After heating, 1.59g of white anhydrous copper sulfate (CuSO4) remains. What is the formula for the hydrate? Name the hydrate.

QUESTIONWhat is the empirical formula for the

compound C6H12O6?

A. CHO B. C2H3O2

C. CH2O

D. CH3O

QUESTIONWhich is the empirical formula for

hydrogen peroxide? A. H2O2

B. H2O

C. HO D. none of the above

QUESTIONHeating a hydrate causes what to

happen? A. Water is driven from the hydrate. B. The hydrate melts. C. The hydrate conducts

electricity.D. There is no change in the

hydrate.

QUESTIONA hydrate that has been heated and the

water driven off is called: A. dehydrated compound B. antihydrated compound C. anhydrous compound D. hydrous compound

PRACTICE PROBLEMS Page 353 #74-75; page 354 #76-82

ACCUMULATING CONTENT AND

SKILLS

ACCUMULATING CONTENT How does the mole apply to balanced

equations?

EXAMPLE PROBLEM 15How many grams of each reactant are needed to run the following reaction? How many grams of each product are produced? (Hint: complete, balance, convert) CuSO4 �5H2O(aq) + CaCl2(aq)

EXAMPLE PROBLEM 16From the reaction above, how much is needed of each reactant in the net ionic equation to produce the balanced amount of the precipitate? How much precipitate is produced?

KEY CONCEPTS

KEY CONCEPTS The mole is a unit used to count

particles of matter indirectly. One mole of a pure substance contains Avogadro’s number of particles.

Representative particles include atoms, ions, molecules, formula units, electrons, and other similar particles.

KEY CONCEPTS One mole of carbon-12 atoms has a

mass of exactly 12 g.

Conversion factors written from Avogadro’s relationship can be used to convert between moles and number of representative particles.

The mass in grams of 1 mol of any pure substance is called its molar mass.

KEY CONCEPTS The molar mass of an element is

numerically equal to its atomic mass. The molar mass of any substance is

the mass in grams of Avogadro’s number of representative particles of the substance.

Molar mass is used to convert from moles to mass. The inverse of molar mass is used to convert from mass to moles.

KEY CONCEPTS Subscripts in a chemical formula

indicate how many moles of each element are present in 1 mol of the compound.

The molar mass of a compound is calculated from the molar masses of all of the elements in the compound.

Conversion factors based on a compound’s molar mass are used to convert between moles and mass of a compound.

KEY CONCEPTS The percent by mass of an element in a

compound gives the percentage of the compound’s total mass due to that element.

The subscripts in an empirical formula give the smallest whole-number ratio of moles of elements in the compound.

The molecular formula gives the actual number of atoms of each element in a molecule or formula unit of a substance.

The molecular formula is a whole-number multiple of the empirical formula.

KEY CONCEPTS The formula of a hydrate consists of

the formula of the ionic compound and the number of water molecules associated with one formula unit.

The name of a hydrate consists of the compound name and the word hydrate with a prefix indicating the number of water molecules in 1 mol of the compound.

Anhydrous compounds are formed when hydrates are heated.

QUESTIONWhat does Avogadro’s number represent?

A. the number of atoms in 1 mol of

an element B. the number of molecules in

1 mol of a compound C. the number of Na+ ions in

1 mol of NaCl (aq) D. all of the above

QUESTIONThe molar mass of an element is

numerically equivalent to what? A. 1 amu B. 1 mole C. its atomic mass D. its atomic number

QUESTIONHow many moles of hydrogen atoms are

in one mole of H2O2?

A. 1 B. 2C. 3D. 0.5

QUESTIONWhat is the empirical formula of Al2Br3?

A. AlBr B. AlBr3

C. Al2Br

D. Al2Br3

QUESTIONWhat is an ionic solid with trapped water

molecules called? A. aqueous solution B. anhydrous compound C. hydrate D. solute

QUESTIONHow many water molecules are

associated with 3.0 mol of CoCl2 • 6H2O?

A. 18 B. 1.1 1025 C. 3.6 1024 D. 1.8 1024

QUESTIONHow many moles of Al are in 2.0 mol of

Al2Br3?

A. 2 B. 4C. 6D. 1

QUESTIONHow many atoms of hydrogen are in

3.5 mol of H2S?

A. 7.0 1023 B. 2.1 1023 C. 6.0 1023 D. 4.2 1024

QUESTIONWhich is not the correct formula for an

ionic compound? A. CO2

B. NaCl C. Na2SO4

D. LiBr2