Atoms and Molecules • Topic 3 of 3

Mole Concept & Molar Mass

Atoms and molecules are so small that we can never count them one by one. Yet chemistry is all about how many particles react. The solution is to count them in huge fixed-size groups, just as we count eggs in dozens. The chemist's counting unit is the mole.

Molecular mass and formula unit mass

The molecular mass of a substance is the sum of the atomic masses of all the atoms in one molecule, expressed in u. For water H2O it is 2(1) + 16 = 18 u; for carbon dioxide CO2 it is 12 + 2(16) = 44 u. For ionic compounds, which do not exist as separate molecules, we use the formula unit mass instead — the sum of the atomic masses of the atoms in one formula unit. For sodium chloride NaCl it is 23 + 35.5 = 58.5 u.

The mole and Avogadro's number

A mole is the amount of a substance that contains exactly as many particles (atoms, molecules or ions) as there are atoms in 12 g of carbon-12. This fixed number is the Avogadro number, NA = 6.022×1023. So one mole of anything always contains 6.022×1023 particles — one mole of water has 6.022×1023 water molecules, and one mole of sodium has 6.022×1023 sodium atoms.

Molar mass

The molar mass is the mass of one mole of a substance, expressed in grams. Its great convenience is that the molar mass in grams is numerically equal to the atomic or molecular mass in u. So 1 mole of water weighs 18 g, 1 mole of CO2 weighs 44 g, and 1 mole of carbon atoms weighs 12 g. This is sometimes called the gram atomic mass (for an element) or gram molecular mass (for a compound).

Interconversion: mass, moles and number of particles

Three quantities are linked by two simple bridges. To move between mass and moles, use the molar mass; to move between moles and number of particles, use the Avogadro number:

  • Number of moles n = given mass ÷ molar mass.
  • Mass = number of moles × molar mass.
  • Number of particles = number of moles × 6.022×1023.
  • Number of moles = number of particles ÷ 6.022×1023.

Think of the mole as the central hub: mass is on one side (reached through molar mass) and the number of particles is on the other (reached through the Avogadro number). To go from mass straight to number of particles you simply pass through moles in the middle.

Mass to mole to particles conversion triangleMASS (g)MOLESPARTICLES(atoms/molecules)÷ molar mass× 6.022×10²³The mole is the central hub between mass and particles
Solved Examples
1
Worked Example
Calculate the molecular mass of water H2O. (H = 1, O = 16.)
Solution
  1. Water has 2 hydrogen atoms and 1 oxygen atom.
  2. Molecular mass = 2(1) + 1(16) = 2 + 16.
  3. = 18 u.

Answer: The molecular mass of water is 18 u.

2
Worked Example
Find the molar mass of calcium carbonate CaCO3. (Ca = 40, C = 12, O = 16.)
Solution
  1. Add the atomic masses: Ca = 40, C = 12, three O = 3(16) = 48.
  2. Formula unit mass = 40 + 12 + 48 = 100 u.
  3. So the molar mass = 100 g per mole.

Answer: The molar mass of CaCO3 is 100 g mol−1.

3
Worked Example
How many moles are there in 88 g of carbon dioxide CO2? (Molar mass = 44 g mol−1.)
Solution
  1. Use n = given mass ÷ molar mass.
  2. n = 88 ÷ 44.
  3. = 2 moles.

Answer: 88 g of CO2 contains 2 moles.

4
Worked Example
Calculate the mass of 0.5 mole of sodium chloride NaCl. (Na = 23, Cl = 35.5.)
Solution
  1. Formula unit mass of NaCl = 23 + 35.5 = 58.5 u, so molar mass = 58.5 g mol−1.
  2. Mass = number of moles × molar mass = 0.5 × 58.5.
  3. = 29.25 g.

Answer: 0.5 mole of NaCl weighs 29.25 g.

5
Worked Example
How many molecules are present in 2 moles of water?
Solution
  1. One mole contains 6.022×1023 molecules.
  2. Number of molecules = number of moles × 6.022×1023.
  3. = 2 × 6.022×1023 = 1.2044×1024 molecules.

Answer: 2 moles of water contain 1.2044×1024 molecules.

6
Worked Example
Find the number of molecules in 9 g of water H2O. (Molar mass = 18 g mol−1.)
Solution
  1. First find moles: n = mass ÷ molar mass = 9 ÷ 18 = 0.5 mole.
  2. Then number of molecules = moles × 6.022×1023.
  3. = 0.5 × 6.022×1023 = 3.011×1023 molecules.

Answer: 9 g of water contains 3.011×1023 molecules.

Key Points

  • Molecular mass = sum of atomic masses of all atoms in a molecule; formula unit mass is used for ionic compounds (NaCl = 58.5 u).
  • One mole contains the Avogadro number of particles, N_A = 6.022×10²³.
  • Molar mass = mass of one mole in grams, numerically equal to the atomic or molecular mass in u (water = 18 g).
  • Mass to moles: n = given mass ÷ molar mass; moles to mass: mass = moles × molar mass.
  • Moles to particles: number of particles = moles × 6.022×10²³; the mole is the hub between mass and particles.
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.The value of the Avogadro number is:
Explanation: One mole contains 6.022×10²³ particles, which is the Avogadro number N_A.
Q2.The molar mass of CO2 (C = 12, O = 16) is:
Explanation: Molar mass = 12 + 2(16) = 12 + 32 = 44 g mol⁻¹.
Q3.The number of moles in 36 g of water (molar mass 18 g) is:
Explanation: n = mass ÷ molar mass = 36 ÷ 18 = 2 moles.
Q4.The number of atoms in 1 mole of helium is:
Explanation: One mole of any substance contains the Avogadro number, 6.022×10²³ particles.
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