Learning check
Once you have watched the video, check your learning with this quiz.
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 1I 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 2A 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 3What is the amount of substance in 36.0 g water? SolutionLet’s use our mathematical relation: \[M = \frac {m}{n} \Leftrightarrow n = \frac {m}{M}\] \(n_{\text{H}_2\text{O}} = \frac {m_{\text{H}_2\text{O}}}{M_{\text{H}_2\text{O}}}\) \(m_{\text{H}_2\text{O}}\) \(M_{\text{H}_2\text{O}} = 1.008\text{g/mol} \times 2 + 16.00\text{g/mol} = 18.016\text{g/mol}\) \(n_{\text{H}_2\text{O}} = \frac {36.0\text{g}}{18.016\text{g/mol}} = 1.9982238\text{mol} \approx 2.00\text{mol}\) |
