Relative masses & the mole
Relative masses & the mole
Relative isotopic and atomic masses
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Atoms are too small for ordinary gram measurements to be convenient. Relative masses compare them with a shared reference: one-twelfth of the mass of one carbon-12 atom.
Relative isotopic mass describes an atom of one particular isotope. Relative atomic mass, Aᵣ, is a weighted mean for the element, allowing for its isotope abundances.
Because each relative mass is a ratio of two masses, it has no unit. Keep that separate from molar mass, which is normally expressed in g mol⁻¹. The definitions below give the precise exam wording.
Use the Aᵣ values on your supplied Periodic Table, which gives values to one decimal place, for example Cl = 35.5. Use the exact data given in a question, including any more precise isotopic masses.
- Relative isotopic mass
- The mass of an atom of an isotope compared with one-twelfth of the mass of an atom of carbon-12.
- Relative atomic mass, Ar
- The weighted mean mass of an atom of an element compared with one-twelfth of the mass of an atom of carbon-12.
🧪 TEST IT
Work on paper. Attempt each question before opening its answer. These are original CrackingChem questions, written in OCR A style.
(a) State the definition of relative isotopic mass. [2 marks]
(b) State the definition of relative atomic mass, Ar. [2 marks]
Total: 4 marks
Show answer & marking points
(a) Relative isotopic mass: the mass of an atom of an isotope compared with one-twelfth of the mass of an atom of carbon-12: atom of an isotope [1]; carbon-12 comparison [1].
(b) Relative atomic mass: the weighted mean mass of an atom of an element compared with one-twelfth of the mass of an atom of carbon-12: weighted mean [1]; carbon-12 comparison [1].
Marking note: For Ar, average on its own is not enough. OCR requires weighted mean. Do not attach a unit to either relative mass.
Calculate relative molecular and formula masses
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A formula is an atom-counting instruction. To find a relative molecular or formula mass, add the Aᵣ contribution of every atom in the formula.
- Write down how many atoms of each element are present.
- Multiply the count of each element by its Aᵣ.
- Add the contributions.
Brackets are the usual trap. In Al₂(SO₄)₃, the outside 3 multiplies both S and O, giving Al₂S₃O₁₂. It does not multiply the Al.
Use relative molecular mass for separate molecules and relative formula mass for a formula describing a giant structure. Give no unit for a relative mass. The same numerical value used as a molar mass has units of g mol⁻¹.
Ar relative atomic mass; no unit.
Brackets and subscripts
Calculate the relative formula mass of Ca(NO3)2. Use Ca 40.1, N 14.0 and O 16.0.
Worked answer
Relative molecular/formula mass = sum of the Aᵣ contributions of every atom
| Quantity | Ca | N | O |
|---|---|---|---|
| Number of atoms | 1 | 2 | 6 |
| Ar | 40.1 | 14.0 | 16.0 |
| Contribution | Contribution = atom count × Aᵣ 40.1 | Contribution = atom count × Aᵣ 28.0 | Contribution = atom count × Aᵣ 96.0 |
🧪 TEST IT
Work on paper. Attempt each question before opening its answer. These are original CrackingChem questions, written in OCR A style.
Use H = 1.0, C = 12.0, N = 14.0, O = 16.0 and Mg = 24.3.
(a) Calculate Mr of C2H5OH. [2 marks]
(b) Calculate the relative formula mass of Mg(NO3)2. [3 marks]
(c) State why neither answer has a unit. [1 mark]
Total: 6 marks
Show answer & marking points
Relative molecular/formula mass = sum of the Aᵣ contributions of every atom
(a) Mr(C2H5OH) = (2 × 12.0) + (6 × 1.0) + 16.0 [1] = 46.0 [1].
(b) Relative formula mass of Mg(NO3)2 = 24.3 + (2 × 14.0) + (6 × 16.0) [2] = 148.3 [1].
(c) Relative masses are comparison values, so they have no unit. [1]
Relative mass and molar mass
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Relative mass and molar mass often have the same numerical value, but they describe different quantities.
Relative molecular or formula mass is a comparison with the carbon-12 reference and has no unit. Molar mass, M, is the mass of one mole and is usually given in g mol⁻¹.
For water, Mᵣ = 18.0 and M = 18.0 g mol⁻¹. Use the molar mass when calculating n = m/M, with mass in grams. Do not put g mol⁻¹ on Mᵣ itself.
| Quantity | Meaning | Unit |
|---|---|---|
| Ar | Relative mass for an element’s atoms | None |
| Mr / relative formula mass | Relative value for a molecule or formula unit | None |
| M | Mass per mole of the stated substance | g mol−1 |
Water: the same number, different quantities
Use H 1.0 and O 16.0 to compare Mr(H2O), M(H2O) and the mass of 2.00 mol H2O.
Worked answer
m = 2.00 × 18.0 = 36.0 g
🧪 TEST IT
Work on paper. Attempt each question before opening its answer. These are original CrackingChem questions, written in OCR A style.
Use Ca = 40.1, O = 16.0 and H = 1.0 for calcium hydroxide, Ca(OH)2.
(a) Calculate its relative formula mass. [2 marks]
(b) State its molar mass, including the unit. [1 mark]
(c) Explain why the two numerical values are equal but the units are different. [2 marks]
Total: 5 marks
Show answer & marking points
(a) Relative formula mass = 40.1 + (2 × 16.0) + (2 × 1.0) [1] = 74.1 [1].
(b) M(Ca(OH)2) = 74.1 g mol−1. [1]
(c) The numerical value is the same because one mole has a mass in grams equal to the relative formula mass [1]. Relative formula mass is unitless, whereas molar mass is mass per mole in g mol−1 [1].
The mole and Avogadro constant
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One mole contains exactly 6.02214076 × 1023 specified entities. The exact Avogadro constant is 6.02214076 × 1023 mol−1. For calculations, use the supplied rounded value, NA = 6.02 × 1023 mol−1.
A mole is a unit for measuring amount of substance, rather like a dozen is a unit for counting items. You can have one mole, two moles or half a mole.
The mole and the Avogadro constant do different jobs. mol is the unit; NA tells you how many specified particles there are per mole. Think of “dozen” and 12: the word names the counting unit, while the number tells you how many items it contains.
Use NA = 6.02 × 10²³ mol⁻¹, rounded to three significant figures. So 1 mol contains approximately 6.02 × 10²³ specified particles. Use a different value if a question explicitly supplies one.
The amount of substance has symbol n and unit mol. Name what you are counting: atoms, molecules, formula units, ions or electrons. One mole of each contains the same number of entities, but their masses differ. One mole of O₂ molecules contains two moles of oxygen atoms.
| Substance | Basic entity |
|---|---|
| Ne | Atom |
| O2 | Molecule |
| NaCl | Formula unit |
| Al3+ | Ion |
N number of the specified particles; a count with no unit; NA Avogadro constant, 6.02 × 10²³ mol⁻¹; n amount of the specified substance or particles, in mol.
🧪 TEST IT
Work on paper. Attempt each question before opening its answer. These are original CrackingChem questions, written in OCR A style.
(a) State the symbol and unit for amount of substance. (2 marks)
(b) Explain the difference between a mole and the Avogadro constant. (2 marks)
Total: 4 marks
Show answer & marking points
(a) Symbol n [1]; unit mol. [1]
(b) The mole is the unit for amount of substance. [1] The Avogadro constant is the number of specified entities per mole and has unit mol−1. [1] Its exact value is 6.02214076 × 1023 mol−1; the OCR A calculation value, 6.02 × 1023 mol−1, is rounded. The exact numerical value is not required for these questions.