S1.4Structure 1 — Models of the particulate nature of matter
Counting particles by mass: the mole — IB Chemistry HL Revision Notes & Topical Questions
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Lesson summary
S1.4 Counting particles by mass: the mole — IB CHEMISTRY HL notes: Use the mole, molar mass, empirical and molecular formulas, concentration and Avogadro's law to link mass, particles, solutions and gas volumes.Mole = the amount of substance containing the same number of particle…
- Avogadro constant
- Applies to
- Particle number
- What the symbols mean
- Atoms in a molecule
- Ionic compounds
Part 1 of 9The mole and the Avogadro constant
The mole and the Avogadro constant
Mole
Mole the amount of substance containing the same number of particles as there are atoms in exactly 12.00 g of carbon-12.
Avogadro constant
- NA (or L) = 6.02 × 1023 mol−1, the number of particles in one mole.
Applies to
- Applies to atoms, molecules, ions and formula units.
Particle number
- N = n × NA, so n = N / NA.What the symbols mean: N = number of particles · n = amount (mol) · NA = Avogadro constant (6.02 × 1023 mol−1)
Atoms in a molecule
- Atoms in a molecule one mole of H2 has 6.02 × 1023 molecules and twice as many atoms.
Ionic compounds
- Ionic compounds one mole of NaCl has 6.02 × 1023 formula units and twice as many ions.
Why moles
- Why moles atoms are so small that any measurable amount contains a vast number, so moles are a practical unit.
Part 2 of 9Relative atomic and formula mass
Relative atomic and formula mass
Relative atomic mass (Ar)
- Relative atomic mass (Ar) the weighted average mass of an atom of an element compared with one twelfth of a carbon-12 atom.
No units
- Ar is a ratio, so the units cancel.
Relative molecular mass (Mr)
- Relative molecular mass (Mr) the sum of the Ar values of all atoms in the formula.
Relative formula mass
- Relative formula mass the same calculation, used for compounds containing ions.
Brackets
- Brackets multiply the atoms inside the bracket by the subscript outside, for example (NH4)2SO4 contains 2 N, 8 H, 1 S and 4 O.
Part 3 of 9Molar mass
Molar mass (M)
Molar mass (M) the mass of one mole of a substance, equal numerically to Ar or Mr, in g mol−1.
Moles from mass
- Moles from mass n = m / M.What the symbols mean: n = amount of substance (mol) · m = mass (g) · M or Mr = molar mass (g mol−1, numerically equal to Mr)
Mass from moles
- Mass from moles m = n × M.
Atoms from moles
- Atoms from moles number of atoms = n × NA × atoms per molecule.
Formula triangles
- Formula triangles cover the quantity wanted to see how to calculate it (moles, particles and NA;
- moles, mass and molar mass).
Working
- Working show the working so credit can be earned even if the final answer is wrong.
Part 4 of 9Percentage composition and empirical formula
Percentage by mass
- % of an element = (atoms of the element × Ar) / Mr × 100.
Empirical formula
- Empirical formula the simplest whole-number ratio of atoms of each element in a compound.
Molecular formula
- Molecular formula the actual number of atoms of each element in a molecule;
- ethanoic acid is C2H4O2 with empirical formula CH2O.
Ionic compounds
- Ionic compounds their formula is always an empirical formula.
Organic compounds
- Organic compounds often have different empirical and molecular formulae.
1
Take the mass of each element (assume 100 g if percentages are given).
2
Divide each mass by its Ar to get moles.
3
Divide all by the smallest number of moles to get a ratio.
4
If the ratio contains fractions such as 1.5 or 1.33, multiply by the smallest integer that gives whole numbers.
Part 5 of 9Molecular formula from empirical formula
Molecular formula from empirical formula
Calculate the relative mass of the empirical formula.
Divide the relative molecular mass Mr by the empirical mass to get a whole-number multiplier k.
Multiply every subscript in the empirical formula by k.
- Combustion or composition data
- the empirical formula comes from masses or percentages, and the molecular formula needs Mr as well.
Part 6 of 9Molar concentration
Molar concentration
Concentration
- Concentration the amount of solute dissolved in 1 dm3 of solution.
Solute and solvent
- Solute and solvent the solute is what dissolves and the solvent is the liquid that dissolves it, often water.
Concentrated and dilute
- Concentrated and dilute a concentrated solution has a large amount of solute per unit volume and a dilute solution has a small amount.
Molar concentration
- Molar concentration c = n / V in mol dm−3, written [X], for example [NaCl].
Volume units
- Volume units convert cm3 to dm3 by dividing by 1000.
Moles in solution
- Moles in solution n = c × V.What the symbols mean: c = concentration (mol dm−3) · n = amount (mol) · V = volume (dm3; divide cm3 by 1000)
Mass concentration
- Mass concentration g dm−3 = mass of solute / volume in dm3.
Converting
- Converting g dm−3 = mol dm−3 × M, and mol dm−3 = g dm−3 / M.
Dilution
- Dilution adding solvent keeps the moles of solute constant, so c1V1 = c2V2.
Part 7 of 9Parts per million
Parts per million
Use
- Use a unit for very low concentrations such as pollutants in water or air.
Definition
- 1 ppm is 1 mg of solute in 1 dm3 (1 kg) of water, or 1 part in 106 by mass.
Conversion
- 1 mg is 10−6 kg, which is useful when finding the total mass in a large volume.
Part 8 of 9Avogadro's law and gas volumes
Avogadro's law
Avogadro's law equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.
Molar volume
- Molar volume at STP one mole of any gas occupies 22.7 dm3, written 22.7 dm3 mol−1.
- (0 °C = 273 K and 100 kPa)
Volume ratio
- Volume ratio the ratio of gas volumes in a balanced equation equals the mole ratio.
Same conditions
- Same conditions this holds only if all gases are measured at the same temperature and pressure.
Liquids
- Liquids water formed as a liquid is not included in the gas ratio.
Limiting reactant
- Limiting reactant if the gases are not in the equation ratio, divide each volume by its coefficient;
- the lowest value is the limiting reactant.
Part 9 of 9More from the specification
More from the specification
Avogadro constant (NA)
- The number of elementary entities in one mole of substance, defined as 6.022 x 1023 mol-1.
Counting atoms present in molecules
- Calculating total atoms present by multiplying moles of compound by the subscript stoichiometry and the Avogadro constant.
Limiting reactant determination
- The reactant that produces the lowest theoretical yield of product when stoichiometric ratios are evaluated.
Molar volume and mass in large systems
- Converting millions of litres or kilograms into standard molar units to determine solute concentrations.
Hydrogen
- A gas that gives a squeaky pop with a lighted splint.
Oxygen
- A gas that relights a glowing splint.
Key terms
| Term | Meaning |
|---|---|
| Mole | The amount of substance containing 6.02 × 1023 particles. |
| Avogadro constant | 6.02 × 1023 mol−1. |
| Molar mass | Mass of one mole in g mol−1. |
| Empirical formula | Simplest whole-number ratio of atoms in a compound. |
| Molecular formula | Actual number of atoms of each element in a molecule. |
| Concentration | Amount of solute per dm3 of solution. |
| Avogadro's law | Equal volumes of gases at the same conditions contain equal numbers of molecules. |
| Molar volume | 22.7 dm3 mol−1 at STP. |
Avoid these mistakes
1
Using cm3 instead of dm3 in concentration calculations — divide the volume in cm3 by 1000.
2
Counting only molecules when asked for atoms or ions — multiply by the number of atoms or ions in the formula.
3
Writing the empirical formula from an uncorrected ratio such as 1 : 1.5 — multiply to get whole numbers.
4
Applying gas-volume ratios to gases measured at different temperatures or pressures, or including liquid water.
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