Chimica

Moles and molar mass: solved exercises step by step

What a mole is, how to calculate molar mass and how to convert between grams, moles and number of particles, with five solved exercises of increasing difficulty and verified answers.

Recommended for: Grade 9 · Grade 10

A mole is the amount of substance that contains 6.022 × 10²³ particles, a value known as Avogadro’s number; the molar mass is the mass of one mole of that substance, measured in grams per mole (g/mol). These two definitions give you the only formulas most exercises need: n = m / M to go from grams to moles, and N = n × Nₐ to go from moles to number of particles.

Why chemists use the mole

Atoms are far too small to be counted one by one, yet in the lab substances are handled by weighing them. The mole bridges the two worlds: it is a “package” of particles large enough that its mass becomes a convenient number of grams. Saying “one mole of iron” is the same as saying “6.022 × 10²³ iron atoms”, exactly as “a dozen eggs” is the same as “twelve eggs”.

How to calculate molar mass

Molar mass is found by adding up the atomic masses of every atom in the formula, each multiplied by its subscript. The atomic masses come straight from the periodic table. For H₂SO₄, for instance, you add hydrogen twice, sulfur once and oxygen four times. The result carries the same number as the molecular mass in u, but it is written in g/mol.

The three steps that keep coming back

Almost every exercise is a chain linking three quantities: grams, moles and number of particles. Moles sit in the middle and act as the compulsory stopover. Grams become moles by dividing by M, moles become particles by multiplying by Nₐ, and going the other way you simply invert both operations. If a question asks for the atoms of one specific element inside a compound, add one more step: multiply the moles of the compound by that element’s subscript in the formula.

The exercises below grow in difficulty along exactly that line, from a plain molar mass calculation to the full journey from particles to grams. Every solution has been rechecked step by step, significant figures included.

Solved exercises

1. Calculate the molar mass of carbon dioxide, CO₂. (C = 12.01 u ; O = 16.00 u) base

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  1. Read the formula: one CO₂ molecule contains 1 carbon atom and 2 oxygen atoms.
  2. Multiply each atomic mass by the number of atoms: 1 × 12.01 and 2 × 16.00.
  3. 1 × 12.01 = 12.01 ; 2 × 16.00 = 32.00.
  4. Add the two contributions: 12.01 + 32.00 = 44.01.
  5. Molar mass is expressed in grams per mole → M(CO₂) = 44.01 g/mol.

Answer: M(CO₂) = 44.01 g/mol

2. How many moles are there in 36.0 g of water, H₂O? (H = 1.008 u ; O = 16.00 u) base

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  1. First the molar mass: 2 × 1.008 + 16.00 = 2.016 + 16.00 = 18.02 g/mol.
  2. You have grams and want moles, so use n = m / M.
  3. n = 36.0 g ÷ 18.02 g/mol.
  4. 36.0 ÷ 18.02 = 1.998.
  5. Round to the three significant figures of the data → n ≈ 2.00 mol.

Answer: n ≈ 2.00 mol

3. What is the mass of 0.25 mol of sodium chloride, NaCl? (Na = 22.99 u ; Cl = 35.45 u) intermedio

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  1. Molar mass: 22.99 + 35.45 = 58.44 g/mol.
  2. Here you know the moles and want grams, so rearrange the formula: m = n × M.
  3. m = 0.25 mol × 58.44 g/mol.
  4. 0.25 × 58.44 = 14.61.
  5. The value 0.25 has two significant figures → m ≈ 14.6 g.

Answer: m ≈ 14.6 g

4. In 49.0 g of sulfuric acid, H₂SO₄, how many moles are present and how many oxygen atoms? (H = 1.008 u ; S = 32.06 u ; O = 16.00 u ; Nₐ = 6.022 × 10²³ mol⁻¹) intermedio

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  1. Molar mass: 2 × 1.008 + 32.06 + 4 × 16.00 = 2.016 + 32.06 + 64.00 = 98.08 g/mol.
  2. Moles of acid: n = 49.0 ÷ 98.08 = 0.4996 ≈ 0.500 mol.
  3. Each molecule contains 4 oxygen atoms, so the moles of O are 4 × 0.500 = 2.00 mol.
  4. Convert moles into atoms: N = 2.00 mol × 6.022 × 10²³ mol⁻¹.
  5. N = 1.2044 × 10²⁴ ≈ 1.20 × 10²⁴ oxygen atoms.

Answer: n ≈ 0.500 mol ; about 1.20 × 10²⁴ oxygen atoms

5. A sample contains 1.50 × 10²³ molecules of glucose, C₆H₁₂O₆. What is its mass in grams? (C = 12.01 u ; H = 1.008 u ; O = 16.00 u) avanzato

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  1. The route is molecules → moles → grams: two steps, not one.
  2. Molar mass: 6 × 12.01 + 12 × 1.008 + 6 × 16.00 = 72.06 + 12.096 + 96.00 = 180.16 g/mol.
  3. From molecules to moles: n = N / Nₐ = 1.50 × 10²³ ÷ 6.022 × 10²³ = 0.249 mol.
  4. From moles to grams: m = n × M = 0.249 × 180.16 = 44.88.
  5. Round to three significant figures → m ≈ 44.9 g.

Answer: m ≈ 44.9 g

FAQ

What is the difference between atomic mass and molar mass?

Atomic mass is measured in atomic mass units (u) and refers to a single particle; molar mass is measured in grams per mole (g/mol) and refers to 6.022 × 10²³ particles. The number is the same — carbon has an atomic mass of 12.01 u and a molar mass of 12.01 g/mol — but the scale changes: the first is microscopic, the second can be read on a laboratory balance.

Does one mole of different substances always have the same mass?

No. One mole always contains the same number of particles, but the mass depends on how heavy each particle is: one mole of hydrogen H₂ weighs about 2.02 g, one mole of water about 18.02 g, one mole of glucose about 180.2 g. It is the same reason a dozen feathers and a dozen bricks do not weigh the same.

How do I know whether to multiply or divide by the molar mass?

Look at the unit of the value you start from. If you start from grams and want moles, divide (n = m / M); if you start from moles and want grams, multiply (m = n × M). The quick check is on the units: g ÷ (g/mol) leaves mol, while mol × (g/mol) leaves g.