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### 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 problems

- Atomic masses do not convert easily to grams
- They can’t be weighed (they are too small)

The Mole

Withtheseproblems,whyuseatomicmassatall?

- Masses give information about # of p+, n0, e–
- It is useful to know relative mass

E.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 that

1gH,12gC,or 23gNahave6.02x1023atoms

- 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: Answers

- A mole is a number (like a dozen). Having this number of atoms allows us to easily convert atomic masses to molar masses.
- 6.02x1023
- 602 000 000 000 000 000 000 000
- 3.00 x 6.02x1023 = 18.06x1023 or 1.81x1024

(note: there are 3 moles of atoms in one mole of CO2 molecules. In other words, there are 5.42x1024 atoms in 3.00 mol CO2)

- 3.01x1023
- a) 1.43 kg 12 = 0.119 kg per orange

b) 1.01 g 6.02x1023 = 1.68 x 10–24 g

Mollionaire

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?

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 minutes

1.003 x 1013 minutes / 60 = 1.672 x 1011 hours

1.672 x 1011 hours / 24 = 6.968 x 109 days

6.968 x 109 days / 365.25 = 1.908 x 107 years

A: It would take 19 million years

Comparing sugar (C12H22O11) & H2O

Same

1 gram each

1 mol each

volume?

No, they have dif. densities.

No, molecules have dif. sizes.

mass?

Yes, that’s what grams are.

No, molecules have dif. masses

# of moles?

No, they have dif. molar masses

Yes.

# of molecules?

No, they have dif. molar masses

Yes (6.02x1023 in each)

# of atoms?

No, sugar has more (45:3 ratio)

No

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/mol

308.27 g/mol

Calculate molar masses (to 2 decimal places)

CaCl2

(NH4)2CO3

O2

Pb3(PO4)2

C6H12O6

Cu x 3 = 63.55 x 3 = 190.65

B x 2 = 10.81 x 2 = 21.62

O 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/mol

308.27 g/mol

Calculate molar masses (to 2 decimal places)

CaCl2

(NH4)2CO3

O2

Pb3(PO4)2

C6H12O6

110.98 g/mol (Cax1, Clx2)

96.11g/mol(Nx2, Hx8, Cx1, Ox3)

32.00 g/mol (Ox2)

811.54 g/mol (Pbx3, Px2, Ox8)

180.18 g/mol (Cx6, Hx12, Ox6)

mol

g/mol

Formula

g/mol

g

mol (n)

Equation

HCl

0.25

g= g/mol x mol

H2SO4

53.15

NaCl

3.55

Cu

1.27

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 mass

g = mol x g/mol

mol = g g/mol

- Thiscanberepresentedinan“equationtriangle”

36.46

9.1

98.08

0.5419

mol= g g/mol

58.44

207

g= g/mol x mol

63.55

0.0200

mol= g g/mol

H

H

H

H

H

Na

Na

Na

Na

Cl

Cl

Cl

Cl

O

O

O

O

O

O

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

- 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, molecular
- formula, or both H2O, C4H10, CH, NaCl

For more lessons, visit www.chalkbored.com

AnswersQ - Write simplest formulas for propene (C3H6),

C2H2, glucose (C6H12O6), octane (C8H14)

Q - Identify these as simplest formula, molecular

formula, 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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