A dozen. Molar Mass. Mass of atoms

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Molar Mass

Science 10

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A dozen…

is a number of objects.

A dozen eggs, a dozen cars, and a dozen people are all 12 objects.

But a dozen cars has a much greater mass than a dozen eggs because the mass of each car is much greater than the mass of each egg.

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Mass of atoms

An Au atom contains 79 p+ and 118 n°.

An H atom contains one p+.

The mass of an Au atom is about 197 times greater than the mass of an H atom.

A dozen…

A dozen Au atoms have a mass that is about 197 times greater than the mass of a dozen H atoms.

But atoms are very small…

A gold atom has a mass of about 3 x 10-22 g or

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The mole

Because atoms are so small it is not practical to talk about individual atoms.

Chemists talk about moles of atoms.

Like a dozen, a mole is a number of atoms.

One mole of atoms is about 6.02 x 1023

atoms.

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Avogadro’s number

Just like 12 eggs is called a dozen eggs, 6.02!x!1023 atoms is a mole of atoms.

6.02 x 1023 is known as Avogadro’s number.

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Power of the mole

A mole of Au has 6.02 x 1023 atoms.

A mole of Mg has 6.02 x 1023 atoms.

The mole allows easy comparisons of amounts of atoms in the same way that the dozen allows easy comparisons of amounts of eggs.

Why 6.02 x 10

23

?

An oxygen atom has 8 p+ and 8 n°.

Its atomic mass number is 8 + 8 = 16.

6.02 x 1023 oxygen atoms have a mass of

16!grams.

16 grams of oxygen atoms is a convenient amount of oxygen, whereas 16 atoms is impractical.

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Molar mass

is the mass of one mole of a substance.

The atomic mass numbers of an element on the periodic table is the average mass, in grams, of one mole of that element’s atoms.

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Example 1

What is the molar mass of Zn?

65.41 g/mol

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Example 2

What is the molar mass of methane gas?

Methane is CH4, meaning each molecule

has one C atom and 4 H atoms.

Each C: 12.01 g/mol

Each H: 1.01 g/mol

Total: 12.01 g/mol + (4 x 1.01 g/mol) =

16.05 g/mol

Example 3

What is the molar mass of water? H2O:

H: 2 x 1.01 g/mol = 2.02 g/mol O: 1 x 16.00 g/mol = 16.00 g/mol

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Example 4

What is the molar mass of iron (III) oxide? Fe2O3:

Fe: 2 x 55.85 g/mol = 111.70 g/mol O: 3 x 16.00 g/mol = 48.00 g/mol

M = 159.70 g/mol

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Your turn

Page 108 practice questions

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Number of moles

One mole of Cu has a mass of 63.55 g.

The molar mass (M) for Cu is 63.55 g/mol.

63.55 g of Cu would be composed of 6.02!x!1023 atoms.

127.10 g of Cu would be two moles of Cu, or 2 x 6.02 x 1023 = 1.204 x 1024 atoms.

Number of moles

We can find the number of moles in a sample of any substance if we know (or can determine) the substance’s molar mass, and we know the mass of the sample.

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Number of moles

n

= m

M

mass

(g)

molar

mass

(g/mol)

number

of moles

(mol)

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Example 1

Find the number of moles in 2.00!g of helium.

Find the molar mass:

He: 1 x 4.00 g/mol = 4.00 g/mol M = 4.00 g/mol 18

Example 1

n

= m

M

= 2.00!g

4.00!g/mol

=!0.5!mol

Example 1

What does 0.5 mol mean?

one mol = 6.02 x 1023 atoms

0.5 mol = 0.5 x 6.02 x 1023 atoms

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Example 2

Find the number of moles in 6.00 g of strontium chloride.

Find the molar mass: SrCl2: Sr: 1 x 87.62 g/mol = 87.62 g/mol Cl: 2 x 35.45 g/mol = 70.90 g/mol M = 158.52 g/mol 21

Example 2

n

= m

M

=

158.52!g/mol

6.00!g

=!0.03785011...!mol

=!0.0379!mol

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Significant Digits

… are a way of representing how accurate a measurement is.

SD Rules

The digits 1 through 9 are always significant.

Leading zeros are not significant.

All other zeros are significant.

In scientific notation, the digits before the “x!10” are significant.

Exact numbers have unlimited significant digits.

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3 SD examples

1.23

0.123

0.0123

103

120

12.0 25

Examples of 2 SD

9.0

15

0.43

5.0 x 104

10 26

Exact Numbers

These are exact numbers:

15 students

$5.25

SD Rules Part 2

In multiplication or division calculations, the answer should be rounded to the least number of SD from the numbers used.

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SD in Example

n

= m

M

=

158.52!g/mol

6.00!g

=!0.03785011...!mol

=!0.0379!mol

3 SD

3 SD

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Example 2

Find the number of moles in 9.50!g of ethanol. C: 2 x 12.01 g/mol = 24.02 g/mol

M = 46.08 g/mol

C2H5OH: H: 6 x 1.01 g/mol = 6.06 g/mol O: 1 x 16.00 g/mol = 16.00 g/mol 30

Example 2

Find the number of moles in 9.50!g of ethanol.

n

= m

M

=

46.08!g/mol

9.50!g

=0.2061631...!mol

=0.206!mol

Example 3

Find the number of moles in 1.1!kg of gold (II) phosphate.

Au: 3 x 196.97 g/mol = 590.91 g/mol

M = 780.85 g/mol

Au3(PO4)2:

P: 2 x 30.97 g/mol = 61.94 g/mol O: 8 x 16.00 g/mol = 128.00 g/mol

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Example 3

Find the number of moles in 1.1!kg of gold (II) phosphate.

n

= m

M

=

780.85!g/mol

1100!g

=1.4087212...!mol

=1.4!mol

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mol to mass

m

=nM

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Example 4

Find the mass of 0.205 mol of sodium carbonate.

Na: 2 x 22.99 g/mol = 45.98 g/mol

M = 105.99 g/mol

Na2CO3:

C: 1 x 12.01 g/mol = 12.01 g/mol O: 3 x 16.00 g/mol = 48.00 g/mol

Example 4

Find the mass of 0.205 mol of sodium carbonate.

=21.72795!g

=!21.7!g

m

=nM

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Example 5

Find the mass of 0.015 mol of calcium chloride.

Ca: 1 x 40.08 g/mol = 40.08 g/mol

M = 110.98 g/mol

CaCl2:

Cl: 2 x 35.45 g/mol = 70.90 g/mol

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Example 5

Find the mass of 0.015 mol of calcium chloride.

=!1.6647!g

=!1.7!g

m

=nM

=0.015!mol!x!110.98!g/mol

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Figure

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References

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