Relative masses & moles
Relative masses & moles
Relative atomic and molecular 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 the Periodic Table supplied with the question. These are given to one decimal place, for example Cl = 35.5. Keep any more precise isotopic masses explicitly given in a mass-spectrum question.
- Relative atomic mass, Ar
- The weighted mean mass of an atom of an element relative to one-twelfth of the mass of one carbon-12 atom.
- Relative molecular mass, Mr
- The mean mass of a molecule relative to one-twelfth of the mass of one carbon-12 atom.
- Relative formula mass
- The sum of the relative atomic masses in the formula unit of an ionic compound. Ionic substances do not contain separate molecules.
- Molar mass
- The mass per mole of specified entities. Its unit is g mol−1; its numerical value matches the corresponding relative mass.
Ar relative atomic mass; no unit; Σ sum of all the indicated contributions.
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Work on paper. Attempt each question before opening its answer. These are original CrackingChem questions, written in AQA style.
(a) Define relative atomic mass, Ar. (2 marks)
(b) Define relative molecular mass, Mr. (2 marks)
(c) State the relative-mass term used for an ionic compound. (1 mark)
(d) State the unit of Ar, Mr and relative formula mass. (1 mark)
(e) Explain the difference between relative molecular mass and molar mass. (2 marks)
Total: 8 marks
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(a) Ar is the weighted mean mass of an atom of an element [1] relative to one-twelfth of the mass of one carbon-12 atom. [1]
(b) Mr is the mean mass of a molecule [1] relative to one-twelfth of the mass of one carbon-12 atom. [1]
(c) Relative formula mass. [1]
(d) Ar, Mr and relative formula mass have no unit. [1]
(e) Molar mass is the mass of one mole of specified entities [1] and has unit g mol−1. [1] Its numerical value is normally the same as the corresponding relative mass.
A mass spectrum of a copper sample gives the following ion counts for its two isotopes.
| Relative isotopic mass | 62.930 | 64.928 |
|---|---|---|
| Number of ions detected | 1383 | 617 |
(a) Calculate the relative atomic mass of copper. Give your answer to four significant figures. (3 marks)
(b) A student reports 63.929 by taking the unweighted mean of the two masses. Explain why this method is invalid. (2 marks)
(c) State the unit of the relative atomic mass you calculated. (1 mark)
Total: 6 marks
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(a) Ar = [(62.930 × 1383) + (64.928 × 617)] ÷ (1383 + 617). [1] Total ions = 2000; calculator value = 63.546383. [1] To four significant figures, Ar = 63.55. [1]
(b) The isotope abundances are unequal, so an unweighted mean gives each isotope the same influence. [1] Weight each isotopic mass by its ion count and divide the sum by the total ion count. [1]
(c) No unit. [1]
Calculate formula masses, including brackets
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The formula tells you how many atoms of each element are present. 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 discrete molecules. For compounds such as ionic solids that do not contain molecules, use relative formula mass. Give no unit for a relative mass. The same numerical value used as a molar mass has units of g mol⁻¹.
Sulfuric acid
Find Mr(H2SO4). Use H 1.0, S 32.1 and O 16.0.
Worked answer
Relative molecular/formula mass = sum of the Aᵣ contributions of every atom
| Quantity | H | S | O |
|---|---|---|---|
| Number | 2 | 1 | 4 |
| Ar | 1.0 | 32.1 | 16.0 |
| Contribution | Contribution = atom count × Aᵣ 2.0 | Contribution = atom count × Aᵣ 32.1 | Contribution = atom count × Aᵣ 64.0 |
Calcium nitrate
Find the relative formula mass of Ca(NO3)2. Use Ca 40.1, N 14.0 and O 16.0.
Worked answer
The formula contains one Ca, two N and six O atoms.
Relative molecular/formula mass = sum of the Aᵣ contributions of every atom
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Work on paper. Attempt each question before opening its answer. These are original CrackingChem questions, written in AQA style.
Use H = 1.0, N = 14.0, O = 16.0, Al = 27.0 and S = 32.1.
(a) Calculate the relative molecular mass of HNO3. (2 marks)
(b) Calculate the relative formula mass of Al2(SO4)3. (3 marks)
Total: 5 marks
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Relative molecular/formula mass = sum of the Aᵣ contributions of every atom
(a) Mr(HNO3) = 1.0 + 14.0 + 3(16.0) [1] = 63.0. [1]
(b) Al2(SO4)3 contains Al2S3O12. [1] Relative formula mass = 2(27.0) + 3(32.1) + 12(16.0) [1] = 342.3. [1]
The mole and the Avogadro constant
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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; L 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 L = 6.022 × 10²³ mol⁻¹, rounded to four significant figures. So 1 mol contains approximately 6.022 × 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.
| Concept | What it means | Think of a dozen |
|---|---|---|
| Mole (mol) | The unit used to measure amount of substance. You can have 1 mol, 2 mol or part of a mole. | The word “dozen” names a counting unit. |
| Avogadro constant, L | The number of specified particles per mole. Use L = 6.022 × 1023 mol−1 (4 significant figures). | 12 tells you how many items are in one dozen; L tells you how many particles are in one mole. |
N is the number of particles, such as atoms, molecules, ions, formula units or electrons. n is the amount of substance in mol, and L is the Avogadro constant in mol⁻¹.
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Work on paper. Attempt each question before opening its answer. These are original CrackingChem questions, written in AQA style.
Use L = 6.022 × 10²³ mol⁻¹.
- Explain the difference between the mole and the Avogadro constant, L. (2 marks)
- Name the entity counted in each case: Fe, O₂, NaCl, Cl⁻ and transferred charge in a half-equation. (5 marks)
- Calculate the number of CO₂ molecules in 0.250 mol CO₂. (2 marks)
Total: 9 marks
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(a) The mole, mol, is the unit of amount of substance. [1] L is the number of specified entities per mole, with unit mol⁻¹. [1]
(b) Atoms; molecules; formula units; ions; electrons, respectively. [1 each]
(c) N = nL = 0.250 × 6.022 × 10²³ [1] = 1.51 × 10²³ CO₂ molecules. [1]
Choose the correct particle or entity
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Before using a formula, decide what the question wants you to count. A molecule, an atom and an ion are not interchangeable labels.
Use molecules for substances made of separate molecules, such as water. For an ionic compound such as NaCl, use formula units rather than molecules.
Then look inside the formula. One H₂O molecule contains two H atoms and one O atom. One formula unit of an ionic compound may contain more than one of a particular ion. Apply that multiplier only when the question asks for those component particles.
| Substance or symbol | Entity to count |
|---|---|
| Fe | Atoms |
| O2, CO2, H2O | Molecules |
| NaCl, MgCl2 | Formula units |
| Na+, Cl−, SO42− | Ions |
| Transferred charge in a half-equation | Electrons |
One sample, three different amounts
A sample contains 0.250 mol H2O. Find the amount in moles of molecules, hydrogen atoms and all atoms.
Worked answer
| Quantity | H2O molecules | H atoms | All atoms |
|---|---|---|---|
| Multiplier | 1 | 2 | 2 + 1 = 3 |
| Amount / mol | 0.250 | 0.500 | 0.750 |
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Work on paper. Attempt each question before opening its answer. These are original CrackingChem questions, written in AQA style.
A sample contains 0.250 mol H2SO4 molecules. Use L = 6.022 × 1023 mol−1.
(a) Calculate the number of H2SO4 molecules. (2 marks)
(b) Calculate the number of hydrogen atoms. (2 marks)
(c) Calculate the total number of atoms of all elements. (3 marks)
Total: 7 marks
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(a) N(H₂SO₄ molecules) = nL
N(H2SO4 molecules) = 0.250 × 6.022 × 1023 [1] = 1.51 × 1023 molecules. [1]
(b) Moles of hydrogen atoms = moles of H₂SO₄ × hydrogen atoms per molecule
n(H atoms) = 2 × 0.250 = 0.500 mol [1], so N = nL
N = 0.500 × 6.022 × 1023 = 3.01 × 1023 H atoms. [1]
(c) One H2SO4 molecule contains 2 + 1 + 4 = 7 atoms. [1] Total moles of atoms = moles of H₂SO₄ × total atoms per molecule
n(total atoms) = 7 × 0.250 = 1.75 mol [1], so N = nL
N = 1.75 × 6.022 × 1023 = 1.05 × 1024 atoms. [1]