Avogadro's number: from atoms to grams

A number big enough to weigh

Carbon burns in oxygen: 2C + O₂ → 2CO. Two atoms of carbon react with one molecule of oxygen. Single atoms are far too light to weigh.

Multiplying every particle by the same number keeps the ratio 2 : 1 : 2. So the book multiplies by 6.022 × 10²³, chosen because 1.00 g equals 6.022 × 10²³ amu.

Now each mass in amu becomes the same number in grams: 24 g of carbon reacts with 32 g of oxygen to give 56 g of carbon monoxide.

6.022 × 10²³ is called Avogadro's number, N_A, after the Italian chemist Amedeo Avogadro. It is the number of units in one mole.

N_A particles of a substance weigh its formula mass in grams: 12 g of carbon atoms, 32 g of O₂ molecules.

Key terms

Avogadro's number (N_A)

Counting particles by weighing.

amu

Masses of single atoms and molecules.

1.00 g

The link between amu and grams.

Mass ratio

Measuring reactants in the lab.

Short questions with model answers

1. Q1. What mass of carbon is 2 × 6.022 × 10²³ atoms? (p. 58)

   • 2 × 6.022 × 10²³ × 12.0 amu
   • 6.022 × 10²³ amu = 1.00 g
   • 2 × 12.0 g = 24.0 g

   24 g of carbon

2. Q2. Check that mass is conserved in 2C + O₂ → 2CO in grams. (p. 58)

   • 24 g + 32 g = 56 g
   • 2 × 28 g = 56 g

   56 g on both sides: mass is conserved.

Common mistakes

• ✗ Multiplying the particles by a huge number changes the reacting ratio.

  ✓ Every particle is multiplied by the same number, so 2 : 1 : 2 stays.

• ✗ N_A atoms of any element weigh the same.

  ✓ They weigh the atomic mass in grams: 12 g of C, 16 g of O atoms.

• ✗ 32 g of oxygen has more molecules than 28 g of CO because it is heavier.

  ✓ Both are one N_A: each molecule of O₂ is simply heavier.

MCQs

1. 1. Avogadro's number is:

   1. (a) 6.022 × 10²³
   2. (b) 6.022 × 10²²
   3. (c) 1.66 × 10⁻²⁴
   4. (d) 12.0
   Show answer

   (a) p. 58.

2. 2. 1.00 g is equal to:

   1. (a) 12 amu
   2. (b) 6.022 × 10²³ amu
   3. (c) 1 amu
   4. (d) 32 amu
   Show answer

   (b) p. 58: that is why this number was chosen.

3. 3. How many atoms are in 12 g of carbon?

   1. (a) 12
   2. (b) 2 × 6.022 × 10²³
   3. (c) 6.022 × 10²³
   4. (d) 3.01 × 10²³
   Show answer

   (c) One N_A of carbon atoms weighs 12 g.

4. 4. Which holds the same number of molecules as 32 g of O₂?

   1. (a) 56 g CO
   2. (b) 14 g CO
   3. (c) 28 g CO
   4. (d) 64 g CO
   Show answer

   (c) 28 g of CO is also one N_A of molecules.

5. 5. Atoms in 6 g of carbon:

   1. (a) 6.022 × 10²³
   2. (b) 3.011 × 10²³
   3. (c) 12.04 × 10²³
   4. (d) 6
   Show answer

   (b) 6 g is half of 12 g, so half of N_A (MCQ vi, p. 64).

Quick revision

• N_A = 6.022 × 10²³, the number of units in one mole.
• 1.00 g = 6.022 × 10²³ amu, so N_A particles weigh their formula mass in grams.
• Scaling up keeps the ratio: 24 g C + 32 g O₂ → 56 g CO.