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A mole (mol) is a chemical unit of measurement

commonly used in equations and is equal to both...

• Avogadro's Number: 6.022e23 particles

(602,200,000,000,000,000,000,000)

• The molar mass of a substance, found by

adding the masses of each atom in that

substance's formula.

Avogadro's number is similar to a "dozen" in that it

refers to a specific number of something. A mol of a

substance is just 6.022e23 of that substance, just as

a dozen refers to 12 of something.

The atomic masses of the periodic table are also

molar masses for those elements.

Ex. 1.00 mol C = 6.022e23 atoms C = 12.011 g C

mol Avo's # Molar Mass

8.1 Moles and Molar Masses

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Molar masses change for each element as 6.022e23

atoms of one element would not have the same

mass as 6.022e23 atoms of another.

Ex. 1 mol carbon atoms ≠ 1 mol iron atoms

g g

The same is true for compounds. A mol of CO2

would differ in mass from a mol of NaCl.

Ex. 1 mol NaCl ≠ 1 mol CO2

(22.99 g+ 35.453 g) (12.011 g + 32 g)

58.443 g 44.011 g

Overall, a mol is just a very large quantity of very

small things (atoms, ions, formula units, molecules)

which, together, equal a measurable mass in lab.

Ex. 1 mol H = 6.022e23 atoms = 1.008 g H

1mol Fe2O3 = 6.022e23 f.units = 159.69 g Fe2O3

1 mol Cl- = 6.022e23 ions = 35.453 g Cl-

1 mol H2O = 6.022e23 molec. = 18.016 g H2O

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To find the molar mass of an atom, use the atomic

mass given on the p. table. Assume ions (+/-) have

the same mass as neutral atoms. The gain/loss of

electrons has a negligible effect on mass.

Ex.1) 1 mol Fe = 6.022e23 atoms Fe = ___________

Ex.2) 1 mol Fe2+ = ________________ = ___________

Ex.3) _______ = 6.022e23 atoms Li = ___________

Ex.4) _______ = _______________ = 14.007 g N3-

For compounds, sum up the moles of each atom/ion

within the substance. The sum of these masses is

the molar mass of the entire compound, M:

Ex.5) 1 mol CO2 = 1 mol C + 2 mol O

= 12.011 g + 2(16 g)

M(CO2) = 44.011 g CO2

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Ex.6) FeCl2 Contains.... 1 mol Fe and 2 mol Cl

M(FeCl2) =

Ex.7) Cr(NO3)4 Contains...

M(Cr(NO3)4) =

Ex.8) (NH4)3N M( (NH4)3N ) =

Ex.9) iron (III) chlorate

Ex.10) NaC2H3O2 M(NaC2H3O2) =

Ex.11) magnesium sulfate

Ex.12) Li3PO4 M(Li3PO4) =

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Self-Check Problems: if you are feeling confident,

complete these problems and check them against

the posted key. Otherwise, we will do them in class.

SC.1) Na3N Contains....

M( Na3N ) =

SC.2) HClO4 Contains....

M(HClO4 ) =

Determine the molar masses of.....

SC.3) silver chloride

SC.4) zinc phosphate:

SC.5) sulfuric acid:

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When to use it: any time you need to convert

between grams and moles. Either as a single DA or

as a step within a larger problem.

Why we learn it: moles are used like "measuring

cups" in chemical reactions. This knowledge allows

you to control chemical reactions and create

specific amounts of product.

Ex.1) Give the mass of 2.40 mol pure iron, Fe(s):

Ex.2) How many mol KMnO4 are found in 4.528 g KMnO4?

8.2 Mass / Mole Conversions

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Ex.3) What is the mass of 2.00 mol hydrobromic acid, in

kg?

Ex.4) A reaction calls for 0.032 mol sodium carbonate.

How many mg do you need to measure out?

Ex.5) On average, you exhale 681 g of carbon dioxide

each day. What is this is mol?

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Self-Check Problems: if you are feeling confident,

complete these problems and check them against

the posted key. Otherwise, we will do them in class.

SC.1) What is the mass of 3.50 mol Li2O, in kg?

SC.2) How many moles are contained by 240 mg of silver

metal?

SC.3) What is the mass, in g, of 7.61 mol sodium chloride?

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SC.4) An equation calls for 4.00 g plutonium metal. What

is this in moles?

SC.5) Calculate the mass of gold (IV) nitrate, in grams,

necessary for an equation if 2.50 mol are required.

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When to use it: any time you need to convert

between moles and particles. Particles = atoms,

ions, formula units, or molecules.

Why we learn it: particles are part of the abstract

"idea" of chemistry. Through moles, we can link the

ideas of chemistry to the real-world.

Conversions between moles and particles of the

same substance are easy, one-step problems which

require you to use Avogadro's number: 6.022e23.

Ex.1) How many atoms of gold are in 0.30 mol Au?

8.3 Mole and Particle Conversions

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Ex.2) Convert 2.00e5 molecules of OF2 into moles:

Ex.3) How many formula units of Fe2O3 are in 0.9 mol?

Some problems are more complex and involve

atoms/ions within larger compounds. These are

typically two-step problems involving Avo's number

and a whole number conversion:

Ex.4) How many ions of Na+ are found in 3.4 mol Na2S ?

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Ex.5) How many H+ ions are in 7 mol H3PO4?

Ex.6) How many molecules of carbon dioxide could be

assembled from 280 atoms of oxygen?

Ex.7) Calculate the number of moles of rust, Fe3O4 , which

could be formed from 8.25e25 oxygen ions:

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Self-Check Problems: if you are feeling confident,

complete these problems and check them against

the posted key. Otherwise, we will do them in class.

SC.1) How many molecules of oxygen gas, O2, would be

contained by 54.0 mol O2?

SC.2) How many oxygen atoms are contained by 0.200

mol O2 gas?

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SC.3) Calculate the number of moles of iron metal found

in 7.2e20 iron atoms:

SC.4) Determine the number of oxygen ions contained

by 120 formula units of iron (III) nitrate:

SC.5) Given 0.400 mol carbonic acid, how many atoms of

carbon do you have?

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When to use it: any time you are attempting to

convert between mass and particles. You'll have to

use moles as the "bridge" between these

measurements. Your Conversion Cheat Sheet is an

excellent tool for this chapter.

Why we learn it: you can now connect the theory

(particles) of chemistry to the real world (mass).

Ex.1) What is the mass, in mg, of a single atom of gold?

Ex.2) How many atoms of fluorine are found in 34 g ArF2?

8.4 Multi-Step Conversions

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Ex.3) After walking through the desert, you find you've

lost 172 g of mass. Assuming this is completely

water, how many molecules of water have you lost?

Ex.4) Calculate the mass, in g, of a single oxygen

molecule, O2:

Ex.5) A gallon of water is equal to 3.78 L and water has a

density of 1.00 g = 1.00 mL. Knowing this, how

many water molecules are found in 1.00 gallons of

water?

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Self-Check Problems: if you are feeling confident,

complete these problems and check them against

the posted key. Otherwise, we will do them in class.

SC.1) A pure copper penny (before 1982) has a mass of

3.10 g. Calculate the number of copper atoms used

to make a single pure copper penny.

SC.2) How many oxygen atoms are found in 1.600 kg of

sodium oxalate, Na2C2O4?

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SC.3) Determine the mass, in mg, of 1.05e19 formula

units of silver oxide:

SC.4) My skeleton has a dry mass of 20.45 kg and is

composed of calcium phosphate. How many

calcium ions are contained by my skeleton?

SC.5) How many mg of sulfuric acid could be

manufactured from 1.6e22 atoms of sulfur?

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Percent composition is a way of breaking down a

compound to show the percentage of each atom,

ion, or (for hydrates) molecule by mass.

% Composition = Total Mass of Substance

Molar Mass of Compound

Calculate the % composition of sugar, C12H22O11

Carbon: 12 x 12.011 g

342.31 g

% Carbon = 42.1%

Hydrogen: 22 x 1.008 g

342.31 g

% Hydrogen = 6.5 %

Oxygen: 11 x 16 g

342.31 g

% Oxygen = 51.4 %

8.5 Percent Composition

x 100%

x 100%

x 100%

x 100%

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The most common use of percent composition is to

determine the percent, by mass, of individual

elements within the compound:

Ex.1) Give the % composition (both Na and Cl) for table

salt, NaCl:

Ex.2) What is the percent composition of carbon within

sodium carbonate?

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You can also determine the percent water within

larger compounds, such as hydrates. Instead of

single elements, compare the mass of the dry

compound (anhydrate) against the mass of water.

CuSO4•5H2O = hydrate

CuSO4 = anhydrate

Ex.3) What is the mass percentage of water in calcium

chloride dihydrate?

Ex.4) Determine the % by mass of the anhydrate in cobalt

(II) chloride tetrahydrate:

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Self-Check Problems: if you are feeling confident,

complete these problems and check them against

the posted key. Otherwise, we will do them in class.

SC.1) What is the % composition of perchloric acid?

SC.2) What is the % water within magnesium sulfate

pentahydrate?

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When to use it: as a method to predict the formula

of an unknown compound in lab.

Why we learn it: you can use your lab data to

determine chemical formulas. Historically, much of

what we know about chemical bonding and

compounds was developed using empirical

formulas.

An empirical formula represents the simplest whole

number ratios between elements within a

compound. Essentially, it's a simplified version of a

molecular (full, covalent) formula:

Ex.1) (Molecular/Full) (Empirical)

Glucose: C6H12O6 → CH2O

Octane: C8H18 →

Oxalic Acid: H2C2O4 →

Fructose: C5H10O5 →

8.6 Empirical and Molecular Formulas

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Ionic compounds are already simplified. Their

normal formulas ARE their empirical formulas:

Ex.2) Table Salt: NaCl →

Iron (III) oxide: Fe2O3 →

Zinc phosphate: Zn3(PO4)2 →

Empirical formulas can be calculated from lab data,

allowing us to identify unknown compounds:

STEP 1: Assume mass percentages represent masses, in g:

Ex. 50.0% C = 50.0 g C

STEP 2: Divide each element's mass by their respective

molar masses, turning them into moles.

Ex. 50.0 g C / 12.011 g C = 4.263 mol C

STEP 3: Divide all moles by the lowest number of moles in

the formula thus far. These numbers will give you

the ratios in the empirical formula. You may have

to multiply to get whole numbers.

Ex. 4.263 mol C : 8.526 mol O

4.263 4.263

1 mol C : 2 mol O = CO2

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Ex.3) Determine the empirical formula for a compound

known to be 75% carbon and 25% hydrogen:

Mass Ratio:

Mole Ratio:

Empirical Formula:

Ex.4) A compound contains 13.5 g Ca, 10.8 g O, and 0.675

g hydrogen. What is its empirical formula?

Mass:

Mole:

Empirical Formula:

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Occasionally, your mole ratios (after step 3) will be

fractional instead of whole numbers. Ends in 0.25 -

multiply by 4. Ends in 0.50, multiply by 2. Ends in

0.33 or 0.67, multiply by 3.

Ex.5) 1.335 mol C : 1.998 mol H : 1.000 mol O

Ex.6) 4.501 mol C : 4.996 mol H : 1.002 mol O

Ex.7) Analysis of an aspirin tablet gives 60.00% C, 4.48%

H, and 35.52% O. Give the empirical formula for

aspirin:

Mass:

Moles:

Empirical Formula:

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You can combine empirical formula calculations

with molar masses to "scale up" and determine the

original molecular formulas for a substance:

Ex.8) A compound's empirical formula is C2H5 and the

molar mass is experimentally determined to be

approximately 58 g. Give the molecular formula for

this compound:

Ex.9) Empirical: Molecular:

Formula Mass Formula Mass

N2O 176 g

CH4 16 g

CH2O 180 g

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Ex.10) Determine the molecular formula for a compound if

it contains 50.05% sulfur and 49.95% oxygen by

mass and has a molar mass of 192 g/mol.

Mass Ratios:

Mole Ratios:

Empirical Formula:

Molecular Formula:

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These calculations can also be applied to determine

the number of water molecules within a hydrate:

Ex.11) Copper (II) sulfate (M = 159.612) exists as a hydrate.

In lab, a 2.60 g sample of the hydrate is heated in a

crucible for several minutes, allowing the water (M

= 18.016) to be vaporized from the sample. When

cooled, the mass of the sample is now 1.66 g.

Calculate formula and name for this hydrate:

Determine the mass of the CuSO4 :

Determine the mass of the water :

Determine the ratio of CuSO4 to water:

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Self-Check Problems: if you are feeling confident,

complete these problems and check them against

the posted key. Otherwise, we will do them in class.

SC.1) Calculate the empirical formula for a compound

which is 13.6% phosphorus and 86.4% selenium:

SC.2) Determine the empirical and molecular formulae for

a compound which is 39.14% carbon and 60.86%

nitrogen if it has a molar mass of 460 g/mol:

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SC.3) A 5.00 g sample of a sodium sulfate hydrate is

placed in a crucible and heated to drive off the

water. If the dry (anhydrous) compound has a mass

of 2.20 g, give the formula and name of this

hydrate: