## The mole

What's the mass of one molecule of H2?

• Let’s have a look at the periodic table!
• One hydrogen atom weighs 1.008 u.
• One hydrogen molecule, H2, weighs 2 × 1.008u = 2.016u.

Hydrogen is up to the left of the periodic table, and oxygen is up to the right.

What’s the mass of 6.022 × 1023 H2-molecules?

• 1 u is the equivalent of 1.6605 × 10–24 g
• A single H2-molecule weighs 2.016 u =
= 2.016 u × 1.6605 × 10–24 g/u = 3.347568 × 10–24 g
• 6.022 × 1023 H2-molecules weigh 6.022 × 1023 × 3.347568 × 10–24 g =
= 2.01590545 g ≈ 2.016 g

What’s the mass of one molecule of O2?

• Let’s have a look at the periodic table again!
• One oxygen atom weighs 16.00 u.
• One oxygen molecule, O2, weighs 2 × 16.00u = 32.00u.

What’s the mass of 6.022 × 1023 O2-molecules?

• 1 u is the equivalent of 1.6605 × 10–24 g
• A single O2-molecule weighs 32.00 u =
= 32.00 u × 1.6605 × 10–24 g/u = 5.3136 × 10–23 g
• 6.022 × 1023 O2-molecules weigh 6.022 × 1023 × 5.3136 × 10–23 g =
= 31.9984992 g ≈ 32.00 g
 1 molecule weighs 6.022 × 1023 molecules weigh H2 2.016 u 2.016 g O2 32.00 u 32.00 g

6.022 × 1023 = 1 mol

• ”Mole” (symbol: mol) is a ”word of quantity”
• More ”words of quantities”:
• 1 pair (couple) = 2 pcs
• 1 dozen = 12 pcs
• score = 20 pcs
• gross = 144 pcs
• grand = 1,000 pcs
• myriad = 10,000 pcs
• 1 mol = 6.022 × 1023 pcs

How do you use the number 6.022 × 1023?

• The number 6.022 × 1023 is a conversion factor from u → g
• The number 6.022 × 1023 is called Avogadro’s constant. It’s written $$N_\text{A}$$ and has the unit $$1/\text{mol}$$.
• We write: $$N_{\text{A}} = 6.022 \times 10^{23}/\text{mol}$$

## Amount of substance

The amount of substance answers the question, ”How many moles of the substance is there?”

• Written $$n$$, has the unit mol.
• Example: $$n = 25 \text{mol}$$

### Example 1

I have a piece of iron that I know contains 2.5 moles of iron atoms. How many iron atoms is that?

#### Solution

$$N_{\text{Fe}} = n_{\text{Fe}} \times N_{\text{A}} =$$

$$2.5\text{mol} \times 6.022 \times 10^{23}/\text{mol} = 1.5055 \times 10^{24} \approx 1.5 \times 10^{24}$$

### Example 2

A piece of gold that I have in my lab consists of 6.1 × 1021 gold atoms. What is the amount of substance of gold, i.e. how many moles of gold are there?

#### Solution

$$n_{\text{Au}} = \frac {N_{\text{Au}}}{N_{\text{A}}} = \frac {6.2 \times 10^{21}}{6.022 \times 10^{23}/\text{mol}} = 0.0101295\text{mol} \approx 10 \times 10^{-3}\text{mol}$$

## Molar mass

1 mole of something is 6.022 × 1023 pcs.

• The molar mass of something tells us how much one mole of that substance weighs.
• The molar mass is written $$M$$ and has the unit $$\text{g/mol}$$.

What is the molar mass of hydrogen gas, H2?

$$M_{\text{H}_2} = m_{\text{1 H}_2\text{ molecule}} \times N_{\text{A}}$$

$$m_{\text{1 H}_2\text{ molecule}} = 2.016\text{u} \times 1.6605 \times 10^{-24}\text{g/u} = 3.347568 \times 10^{-24}\text{g}$$

$$M_{\text{H}_2} = 3.347568 \times 10^{-24}\text{g} \times 6.022 \times 10^{23}/\text{mol} ≈ 2.016\text{g/mol}$$

### A mathematical relation

The molar mass indicates how much 1 mol of something weighs.

• Thus, we can write:

$\text{molar mass} = \frac{\text{mass}}{\text{amount of substance}}$

• Or, preferably:

$M = \frac{m}{n}$

Where

$$M$$ is the molar mass in $$\text{g/mol}$$.

$$m$$ is the mass in $$\text{g}$$.

$$n$$ is the amount of substance in $$\text{mol}$$.

### Example 3

What is the amount of substance in 36.0 g water?

#### Solution

Let’s use our mathematical relation:

$M = \frac {m}{n} \Leftrightarrow n = \frac {m}{M}$

$$n_{\text{H}_2\text{O}} = \frac {m_{\text{H}_2\text{O}}}{M_{\text{H}_2\text{O}}}$$

$$m_{\text{H}_2\text{O}}$$

$$M_{\text{H}_2\text{O}} = 1.008\text{g/mol} \times 2 + 16.00\text{g/mol} = 18.016\text{g/mol}$$

$$n_{\text{H}_2\text{O}} = \frac {36.0\text{g}}{18.016\text{g/mol}} = 1.9982238\text{mol} \approx 2.00\text{mol}$$