The Mole

Q: how long would it take to spend a mole of $1 coins if they were being spent at a rate of 1 billion per second?

Background: atomic masses• Look at the “atomic masses” on the periodic

table. What do these represent?• E.g. the atomic mass of C is 12 (atomic # is 6)• We know there are 6 protons and 6 neutrons• Protons and neutrons have roughly the same

mass. So, C weighs 12 u (atomic mass units).• What is the actual mass of a C atom?• Answer: approx. 2 x 10-23 grams (protons and

neutrons each weigh about 1.7 x10-24 grams)Two problems1. Atomic masses do not convert easily to grams2. They can’t be weighed (they are too small)

The MoleWith these problems, why use atomic mass at all?1. Masses give information about # of p+, n0, e–

2. It is useful to know relative massE.g. Q - What ratio is needed to make H2O?

A - 2:1 by atoms, but 2:16 by mass• It is useful to associate atomic mass with a mass

in grams. It has been found that1 g H, 12 g C, or 23 g Na have 6.02 x 1023 atoms

• 6.02 x 1023 is a “mole” or “Avogadro’s number”• “mol” is used in equations, “mole” is used in

writing; one gram = 1 g, one mole = 1 mol.• Read 4.3 (167-9). Stop after text beside fig 2.• Do Q1-6. Challenge: 1st slide (use reasonable units)

The Mole: Answers1. A mole is a number (like a dozen). Having

this number of atoms allows us to easily convert atomic masses to molar masses.

2. 6.02 x 1023

3. 602 000 000 000 000 000 000 0004. 3.00 x 6.02 x 1023 = 18.06 x 1023 or 1.81 x 1024

(note: there are 3 moles of atoms in one mole of CO2 molecules. In other words, there are 5.42 x 1024 atoms in 3.00 mol CO2)

5. 3.01 x 1023

6. a) 1.43 kg 12 = 0.119 kg per orangeb) 1.01 g 6.02 x 1023 = 1.68 x 10

–24 g

MollionaireQ: how long would it take to spend a mole of

$1 coins if they were being spent at a rate of 1 billion per second?

A: $ 6.02 x 1023 / $1 000 000 000 = 6.02 x 1014 payments = 6.02 x 1014 seconds

6.02 x 1014 seconds / 60 = 1.003 x 1013 minutes1.003 x 1013 minutes / 60 = 1.672 x 1011 hours1.672 x 1011 hours / 24 = 6.968 x 109 days6.968 x 109 days / 365.25 = 1.908 x 107 years

A: It would take 19 million years

Comparing sugar (C12H22O11) & H2O

No, sugar has more (45:3 ratio)

Yes (6.02 x 1023 in each)

Yes.

No, molecules have dif. masses

No, molecules have dif. sizes.

1 mol each

Yes, that’s what grams are.

mass?

No, they have dif. molar masses# of moles?

No, they have dif. molar masses

# of molecules?

No# of atoms?

No, they have dif. densities.

volume?

1 gram eachSame

Molar mass• The mass of one mole is called “molar mass”• E.g. 1 mol Li = 6.94 g Li• This is expressed as 6.94 g/mol• What are the following molar masses?

S SO2

Cu3(BO3)2

32.06 g/mol 64.06 g/mol308.27 g/mol

Calculate molar masses (to 2 decimal places) CaCl2 (NH4)2CO3

O2

Pb3(PO4)2

C6H12O6

Cu x 3 = 63.55 x 3 = 190.65B x 2 = 10.81 x 2 = 21.62O x 6 = 16.00 x 6 = 96.00

308.27

Molar mass• The mass of one mole is called “molar mass”• E.g. 1 mol Li = 6.94 g Li• This is expressed as 6.94 g/mol• What are the following molar masses?

S SO2

Cu3(BO3)2

32.06 g/mol 64.06 g/mol308.27 g/mol

Calculate molar masses (to 2 decimal places) CaCl2 (NH4)2CO3

O2

Pb3(PO4)2

C6H12O6

110.98 g/mol (Ca x 1, Cl x 2)96.11 g/mol (N x 2, H x 8, C x 1, O x 3)32.00 g/mol (O x 2)

811.54 g/mol (Pb x 3, P x 2, O x 8)180.18 g/mol (C x 6, H x 12, O x 6)

Converting between grams and moles• If we are given the # of grams of a compound

we can determine the # of moles, & vise-versa• In order to convert from one to the other you

must first calculate molar massg = mol x g/molmol = g g/mol

• This can be represented in an “equation triangle”

g

mol

g/mol

g= g/mol x mol0.25HCl

53.15H2SO4

3.55NaCl1.27Cu

Equationmol (n)gg/molFormula9.136.46

mol= g g/mol0.541998.08g= g/mol x mol20758.44mol= g g/mol0.020063.55

Simplest and molecular formulaeConsider NaCl (ionic) vs. H2O2 (covalent)

Cl Na

Na Cl

Cl

Cl

Na

Na

• Chemical formulas are either “simplest” (a.k.a. “empirical”) or “molecular”. Ionic compounds are always expressed as simplest formulas.

• Covalent compounds can either be molecular formulas (I.e. H2O2) or simplest (e.g. HO)

Q - Write simplest formulas for propene (C3H6), C2H2, glucose (C6H12O6), octane (C8H14)

Q - Identify these as simplest formula, molecularformula, or both H2O, C4H10, CH, NaCl

HOO

H HOO H H

OO H

AnswersQ - Write simplest formulas for propene (C3H6),

C2H2, glucose (C6H12O6), octane (C8H14)

Q - Identify these as simplest formula, molecularformula, or both H2O, C4H10, CH, NaCl

A - CH2

A - H2O is both simplest and molecular

C4H10 is molecular (C2H5 would be simplest)

CH is simplest (not molecular since CH can’t form a molecule - recall Lewis diagrams)

NaCl is simplest (it’s ionic, thus it doesn’t form molecules; it has no molecular formula)

CH CH2O C4H7

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