### Molar Mass

Science 101

### 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.2

### 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}

### 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 1023atoms.

5

### 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.}

6

### 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.### 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.9

### Example 1

### •

What is the molar mass of Zn?### •

65.41 g/mol10

### Example 2

### •

What is the molar mass of methane gas?### •

Methane is CH4, meaning each moleculehas 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

### 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

13

### Your turn

### •

Page 108 practice questions14

### 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 10}24

_{ 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.### Number of moles

*n*

*= m*

*M*

### mass

### (g)

### molar

### mass

### (g/mol)

### number

### of moles

### (mol)

17### 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}

### 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*

22
### 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.### 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.### SD in Example

*n*

*= m*

*M*

### =

### 158.52!g/mol

*6.00!g*

*=!0.03785011...!mol*

*=!0.0379!mol*

### 3 SD

### 3 SD

29### 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

### 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*

33
### mol to mass

*m*

*=nM*

34
### 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*

### 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

37

### Example 5

**•**

**Find the mass of 0.015 mol of**

**calcium chloride.**