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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

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: \(n = 25 \text{mol}\)

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 \(\text{mol}\).

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