Counting Particles By Mass: The Mole

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The Mole and Avogadro's Constant

The mole is the amount of substance that contains the same number of fundamental units as there are atoms in exactly 12.00 g of carbon-12.
The Avogadro constant (N_A or L) is the number of particles equivalent to the relative atomic mass (A_r) or relative molecular mass (M_r) of a substance in grams.
The value of the Avogadro constant is 6.02 × 10²³ mol^-1.
The Avogadro constant applies to atoms, molecules and ions.
One mole of any substance contains 6.02 × 10²³ fundamental units.
The mass of a substance with this number of particles is called the molar mass.

Relative Atomic and Molecular Mass

The relative atomic mass (A_r) of an element is the weighted average mass of one atom compared to one twelfth the mass of a carbon-12 atom.
A_r is determined using the weighted average mass of the isotopes of the element.
A_r has no units because it is a ratio and the units cancel.
Relative molecular mass (M_r) is the sum of the relative atomic masses of the atoms in a molecule.
For compounds containing ions, the term relative formula mass (M_r) is used and is calculated in the same way.
Example: M_r of H2O = (2 × 1.01) + 16.00 = 18.02.

Moles and Mass Calculations

The number of moles can be calculated using: moles = mass (g) ÷ molar mass (g mol^-1).
The molar mass of a substance is its relative atomic mass (A_r) or relative formula mass (M_r) expressed in grams.
Molar mass is given in units of g mol^-1.
To find the mass of a substance: mass = moles × molar mass.
Always show your workings in calculations to check for errors and possibly gain credit.

Moles, mass and molar mass

Moles and Particles

The number of particles can be calculated using: number of particles = moles × Avogadro constant.
To find the number of moles from particles: moles = number of particles ÷ Avogadro constant.
When calculating the number of atoms in a molecule, multiply the number of moles of molecules by the number of atoms in one molecule.
Example: 0.010 moles of CH3CHO contains 0.040 moles of H atoms, which is 2.4 × 10²² H atoms.

Empirical Formula

The empirical formula gives the simplest whole-number ratio of atoms of each element in a compound.
The molecular formula shows the actual number and type of atoms in a molecule.
The empirical formula can be determined from percentage composition by mass data.
To find the empirical formula: divide the mass or percentage of each element by its atomic mass, then divide by the smallest value to get the simplest ratio.
The formula of an ionic compound is always written as an empirical formula.
Organic compounds often have different empirical and molecular formulae.

Molecular Formula

To determine the molecular formula from the empirical formula: divide the relative molecular mass (M_r) by the relative mass of the empirical formula.
This gives a whole number multiplier.
Multiply the empirical formula by this number to get the molecular formula.
Example: If empirical formula is C4H10S and M_r = 180.42, the multiplier is 2, so molecular formula is C8H20S2.

Molar Concentration

Concentration tells us how much solute is dissolved in a solvent to make a solution.
It is usually measured as the amount of solute in 1 dm³ of solution.
The solute is the substance being dissolved; the solvent is the liquid that does the dissolving.
Concentration can be expressed as moles per unit volume (mol dm^-3), mass per unit volume (g dm^-3), or parts per million (ppm).
Formula: concentration (mol dm^-3) = moles of solute (mol) ÷ volume of solution (dm³).
To convert cm³ to dm³, divide by 1000.
To convert from mol dm^-3 to g dm^-3, multiply the molar concentration by the molar mass.
To convert from g dm^-3 to mol dm^-3, divide the mass concentration by the molar mass.

Concentration, moles and volume

Parts Per Million (ppm)

ppm is used for very low concentrations, such as pollutants in water or air.
1 ppm is defined as 1 mg of solute dissolved in 1 dm³ of water.
Since 1 dm³ of water weighs 1 kg, 1 ppm is also 1 mg dissolved in 1 kg of water.
This is equivalent to 10^-3 g in 10³ g, or a concentration of 1 in 10⁶.

Avogadro's Law and Gas Volumes

Avogadro's Law states that equal volumes of gases under the same conditions of temperature and pressure contain the same number of molecules.
At standard temperature and pressure (STP), one mole of any gas occupies 22.7 dm³.
STP conditions are defined as 0 °C (273 K) and 100 kPa pressure.
The volume ratio of gaseous reactants and products in a balanced equation is the same as the mole ratio.
Example: In C3H8(g) + 5O2(g) → 3CO2(g) + 4H2O(l), 50 cm³ of propane requires 250 cm³ of O2 and produces 150 cm³ of CO2.
Gas volume relationships are only valid if all gases are measured under the same conditions of temperature and pressure.
If gases are not in the same ratio as the balanced equation, use limiting reactant principles to determine the actual amount of product formed.

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1.Which statement defines the mole?
Easy
- AThe amount of substance that contains 6.02 × 10²³ elementary entities.
- BThe mass of one atom of carbon-12.
- CThe volume occupied by one gram of any gas at room temperature.
- DThe number of particles in one gram of any substance.
2.What is the value of the Avogadro constant?
Easy
- A6.02 × 10²³ mol⁻¹
- B6.02 × 10⁻²³ mol⁻¹
- C12.00 g mol⁻¹
- D22.7 dm³ mol⁻¹
3.Which statement about relative atomic mass (Ar) is correct?
Easy
- AIt is the weighted average mass of an atom compared to one-twelfth the mass of a carbon-12 atom.
- BIt is the mass of one mole of an element in grams.
- CIt is the number of atoms in one mole of an element.
- DIt is the mass of one atom of an element in kilograms.
4.Which of the following is the relative formula mass (Mr) of ammonium sulfate, (NH₄)₂SO₄? (Ar: N=14.01, H=1.01, S=32.07, O=16.00)
Easy
- A132.17
- B114.11
- C68.14
- D100.17
5.The empirical formula of a compound gives the simplest whole-number ratio of atoms of each element in the compound.
Easy
True or false?
6.How many moles are present in 2.64 g of sucrose, C₁₂H₂₂O₁₁ (Mr = 342.3)?
Medium
- A7.71 × 10⁻³ mol
- B7.71 × 10⁻² mol
- C0.771 mol
- D1.30 × 10² mol
7.Which of the following statements about concentration are correct? (select all that apply)
Medium
- AConcentration in mol dm⁻³ is calculated as moles of solute divided by volume of solution in dm³.
- B1 ppm is equivalent to 1 mg of solute dissolved in 1 dm³ of water.
- CTo convert cm³ to dm³, divide by 1000.
- DA concentrated solution contains a small amount of solute per unit volume.
- EThe units of concentration can be mol dm⁻³, g dm⁻³ or ppm.
8.Match each term with its correct description.
Medium
- Mole
- Molar mass
- Empirical formula
- Avogadro's Law
- The amount of substance containing 6.02 × 10²³ particles
- The mass of one mole of a substance in grams
- The simplest whole-number ratio of atoms in a compound
- Equal volumes of gases at the same temperature and pressure contain the same number of molecules

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9.Place the steps for determining the molecular formula from percentage composition data in the correct order.
Medium
- Calculate the empirical formula from percentage composition.
- Calculate the relative mass of the empirical formula.
- Divide the relative molecular mass by the relative empirical mass to get a whole-number multiplier.
- Multiply the empirical formula by the multiplier to obtain the molecular formula.
10.Which of the following statements about the mole and the Avogadro constant are correct? (select all that apply)
Medium
- AOne mole of any substance contains 6.02 × 10²³ fundamental units.
- BThe Avogadro constant applies to atoms, molecules and ions.
- COne mole of H₂ contains 6.02 × 10²³ hydrogen atoms.
- DThe molar mass of a substance is its relative atomic or formula mass expressed in grams per mole.
- EOne mole of NaCl contains 6.02 × 10²³ ions in total.
11.Which of the following statements about Avogadro's Law are correct? (select all that apply)
Medium
- AEqual volumes of gases at the same temperature and pressure contain the same number of molecules.
- BAt STP, one mole of any gas occupies 22.7 dm³.
- CThe volume ratio of gaseous reactants and products in a balanced equation is the same as the mole ratio.
- DThe volume of a gas is directly proportional to its molar mass at constant temperature and pressure.
- EAt STP, one mole of any gas has a mass of 22.7 g.
12.The empirical formula of an ionic compound is always written as the simplest whole-number ratio of ions.
Easy
True or false?
13.The relative atomic mass of an element has units of grams per mole.
Easy
True or false?
14.Match each term with its correct definition.
Medium
- Mole
- Molar mass
- Empirical formula
- Molecular formula
- The mass of one mole of a substance in grams
- The actual number and type of atoms in a molecule
- The amount of substance containing 6.02 × 10²³ particles
- The simplest whole-number ratio of atoms of each element in a compound
15.Match each substance with the number of particles it contains in 1 mole.
Medium
- Na (sodium metal)
- H₂ (hydrogen gas)
- NaCl (sodium chloride)
- H₂O (water)
- 6.02 × 10²³ formula units
- 1.204 × 10²⁴ atoms
- 6.02 × 10²³ molecules
- 6.02 × 10²³ atoms
16.Arrange the steps for calculating the mass of solute needed to prepare a solution of known concentration and volume in the correct order.
Medium
- Convert the volume from cm³ to dm³ by dividing by 1000.
- Calculate the number of moles using moles = concentration × volume.
- Calculate the molar mass of the solute.
- Multiply the number of moles by the molar mass to find the mass.
17.A 2.450 g sample of camphor (C, H and O only) was burned in excess oxygen, producing 7.081 g of carbon dioxide and 2.320 g of water. What is the empirical formula of camphor? (Ar: C = 12.01, H = 1.01, O = 16.00)
Medium
- AC₁₀H₁₆O
- BC₅H₈O
- CC₁₀H₁₆O₂
- DC₃H₄O
18.A commercial 11.2 g nasal spray pump delivers a metered dose of exactly 400 micrograms of nitroglycerin, C₃H₅N₃O₉. How many moles are present in one dose? (Mr of nitroglycerin = 227.09)
Medium
- A1.76 × 10⁻⁶ mol
- B1.76 × 10⁻³ mol
- C2.27 × 10⁻⁴ mol
- D9.08 × 10⁻⁸ mol
19.Which change of state and energy change occur when a nasal spray pump is used to vaporise nitroglycerin?
Medium
- ALiquid to gas, with energy absorbed from the surroundings
- BGas to liquid, with energy released to the surroundings
- CLiquid to gas, with energy released to the surroundings
- DSolid to liquid, with energy absorbed from the surroundings
20.A 0.146 g sample of carvone (C, H and O only) was vaporised and had a volume of 0.0341 dm³ at 150 °C and 100.2 kPa. Which of the following statements are correct? (select all that apply) (R = 8.31 J K⁻¹ mol⁻¹)
Hard
- AThe molar mass of carvone is approximately 150.2 g mol⁻¹
- BThe number of moles of carvone in the sample is 1.03 × 10⁻³ mol
- CThe molar mass of carvone is approximately 1.50 g mol⁻¹
- DThe number of molecules of carvone in 0.146 g is 6.20 × 10²⁰
- EThe temperature must be converted to kelvin before using the ideal gas equation
21.Which statement about the Avogadro constant is correct?
Medium
- AIt is the number of particles in one mole of a substance.
- BIt is the mass of one mole of a substance in grams.
- CIt is the number of atoms in 12.00 g of carbon-12.
- DIt is the volume occupied by one mole of any gas at STP.
22.Which statement about the molar volume of a gas at STP is correct?
Medium
- AOne mole of any gas occupies 22.7 dm³ at 0 °C and 100 kPa.
- BOne mole of any gas occupies 24.0 dm³ at 25 °C and 100 kPa.
- COne mole of any gas occupies 22.4 dm³ at 0 °C and 101.3 kPa.
- DOne mole of any gas occupies 22.7 dm³ at 25 °C and 100 kPa.
23.What is the empirical formula of a compound containing 85.7% carbon and 14.3% hydrogen by mass? (Ar: C = 12.01, H = 1.01)
Medium
- ACH₂
- BCH₃
- CC₂H₄
- DC₂H₆
24.A compound has the empirical formula CH₂O and a relative molecular mass of 180.16. What is its molecular formula?
Medium
- AC₆H₁₂O₆
- BC₅H₁₀O₅
- CC₄H₈O₄
- DC₃H₆O₃
25.What is the concentration in mol dm⁻³ of a solution containing 0.500 mol of solute in 250 cm³ of solution?
Easy
- A2.00 mol dm⁻³
- B0.125 mol dm⁻³
- C0.500 mol dm⁻³
- D4.00 mol dm⁻³
26.What volume of 0.100 mol dm⁻³ HCl is needed to react completely with 25.0 cm³ of 0.200 mol dm⁻³ NaOH? (HCl + NaOH → NaCl + H₂O)
Medium
- A50.0 cm³
- B25.0 cm³
- C12.5 cm³
- D100.0 cm³
27.Which statement about the empirical formula is correct?
Medium
- AIt gives the simplest whole-number ratio of atoms in a compound.
- BIt gives the actual number of atoms in a molecule.
- CIt is always the same as the molecular formula.
- DIt is only used for ionic compounds.
28.What is the relative formula mass of calcium hydroxide, Ca(OH)₂? (Ar: Ca = 40.08, O = 16.00, H = 1.01)
Medium
- A74.10
- B57.08
- C58.09
- D90.10
29.Which of the following statements about the mole are correct? (select all that apply)
Medium
- AOne mole of any substance contains 6.02 × 10²³ particles.
- BThe molar mass of a substance is its relative atomic or formula mass in grams.
- COne mole of any gas occupies 22.7 dm³ at STP.
- DThe mole is a unit of mass.
- EThe number of moles can be calculated using n = m / M.
30.One mole of any gas occupies the same volume at the same temperature and pressure.
Easy
True or false?
31.What is the total volume of gases remaining when 70 cm³ of ammonia is combusted completely with 50 cm³ of oxygen according to: 4NH₃(g) + 5O₂(g) → 4NO(g) + 6H₂O(l)?
Hard
- A70 cm³
- B40 cm³
- C30 cm³
- D90 cm³
32.What is the concentration in ppm of a solution containing 0.005 g of solute in 1 dm³ of water?
Medium
- A5 ppm
- B0.5 ppm
- C50 ppm
- D0.005 ppm
33.The Avogadro constant applies to atoms, molecules and ions.
Easy
True or false?
34.Which of the following is the relative molecular mass of K₂CO₃? (Ar: K = 39.10, C = 12.01, O = 16.00)
Easy
- A138.21
- B106.10
- C122.11
- D67.10
35.Which of the following is the relative formula mass of Ca(OH)₂? (Ar: Ca = 40.08, O = 16.00, H = 1.01)
Easy
- A74.10
- B57.09
- C58.09
- D76.10
36.Which of the following is the relative formula mass of (NH₄)₂SO₄? (Ar: N = 14.01, H = 1.01, S = 32.07, O = 16.00)
Medium
- A132.17
- B114.11
- C130.15
- D66.09
37.The relative formula mass (Mr) is used for compounds containing ions and is calculated in the same way as relative molecular mass.
Easy
True or false?
38.Which of the following is the molar mass of H₂O? (Ar: H = 1.01, O = 16.00)
Medium
- A18.02 g mol⁻¹
- B17.01 g mol⁻¹
- C18.02 g
- D18.02 mol g⁻¹
39.Which of the following is the molar mass of H₂? (Ar: H = 1.01)
Medium
- A2.02 g mol⁻¹
- B1.01 g mol⁻¹
- C4.04 g mol⁻¹
- D2.02 g
40.Which of the following is the molar mass of NaCl? (Ar: Na = 22.99, Cl = 35.45)
Medium
- A58.44 g mol⁻¹
- B58.44 g
- C22.99 g mol⁻¹
- D35.45 g mol⁻¹
41.Calculate the molar mass of urea, CO(NH₂)₂, in g mol⁻¹. (Ar: C=12.01, O=16.00, N=14.01, H=1.01)
Medium
42.Complete the definition of relative atomic mass.
Easy
The relative atomic mass (Ar) of an element is the weighted average mass of one atom compared to one ____ the mass of a carbon-12 atom.
43.Calculate the mass of 0.250 moles of zinc. (Ar: Zn = 65.38)
Medium
44.How many moles of hydrogen atoms are in 3.612 × 10²³ molecules of H₂O₂? (Avogadro constant = 6.02 × 10²³ mol⁻¹)
Medium
45.How many atoms are in 4.00 g of hydrogen gas? (Ar: H = 1.01, Avogadro constant = 6.02 × 10²³ mol⁻¹)
Medium
46.Complete the definition of the mole.
Medium
One mole is the amount of substance that contains ____ fundamental units, which is the number of atoms in exactly ____ g of carbon-12.
47.Complete the statement about Avogadro's Law.
Easy
At standard temperature and pressure (STP), one mole of any gas occupies ____ dm³. STP is defined as 0 °C and ____ kPa.
48.Urea, CO(NH₂)₂, is an animal waste product used as a fertiliser. Calculate the percentage by mass of nitrogen in urea. Give your answer to two decimal places. (Ar: C = 12.01, O = 16.00, N = 14.01, H = 1.01)
Medium
49.A compound with Mr = 104.07 contains 34.62% carbon, 3.88% hydrogen and 61.50% oxygen by mass. Calculate its empirical formula. Enter the formula using the format CxHyOz (e.g. C3H4O3).
Medium
50.An unknown compound contains carbon, hydrogen and oxygen only. A sample contains 3.20 g carbon, 0.54 g hydrogen and 4.26 g oxygen. Calculate the empirical formula of the compound. Enter the formula using the format CxHyOz (e.g. C3H4O3).
Medium
51.How many atoms are present in 0.200 mol of P₂O₅? (Avogadro constant = 6.02 × 10²³ mol⁻¹)
Medium
52.How many moles are in 2.35 × 10²⁴ molecules of oxygen gas? (Avogadro constant = 6.02 × 10²³ mol⁻¹)
Medium
53.Define the term one mole in chemistry.
Hard
54.Explain why the actual number of doses delivered by a nasal spray pump may be less than the calculated number.
Hard
55.Describe the changes of state and the energy changes that take place when a nasal spray pump is used.
Medium
56.Suggest one reason why it is better to use ethylene glycol in a car's cooling system rather than calcium chloride.
Medium
57.Suggest why repeating the decomposition of a sample of mercury oxide may give a higher mass of mercury than was obtained in the first attempt.
Hard
58.Calculate the molar mass of urea, CO(NH₂)₂, in g mol⁻¹. (Ar: C=12.01, O=16.00, N=14.01, H=1.01)
Medium
- A72.08 g mol⁻¹
- B54.05 g mol⁻¹
- C60.06 g mol⁻¹
- D66.07 g mol⁻¹
59.Calculate the mass of 0.250 moles of zinc. (Ar: Zn = 65.38)
Medium
- A18.3 g
- B17.3 g
- C15.3 g
- D16.3 g
60.How many moles of hydrogen atoms are in 3.612 × 10²³ molecules of H₂O₂? (Avogadro constant = 6.02 × 10²³ mol⁻¹)
Medium
- A1.2 mol
- B0.2 mol
- C3.2 mol
- D2.2 mol
61.How many atoms are in 4.00 g of hydrogen gas? (Ar: H = 1.01, Avogadro constant = 6.02 × 10²³ mol⁻¹)
Medium
- A4.38 × 10²⁴
- B3.38 × 10²⁴
- C1.38 × 10²⁴
- D2.38 × 10²⁴
62.Urea, CO(NH₂)₂, is an animal waste product used as a fertiliser. Calculate the percentage by mass of nitrogen in urea. Give your answer to two decimal places. (Ar: C = 12.01, O = 16.00, N = 14.01, H = 1.01)
Medium
- A55.94 %
- B46.62 %
- C41.96 %
- D51.28 %
63.A compound with Mr = 104.07 contains 34.62% carbon, 3.88% hydrogen and 61.50% oxygen by mass. Calculate its empirical formula. Enter the formula using the format CxHyOz (e.g. C3H4O3).
Medium
- A0
- B-1
- C1
- D2
64.An unknown compound contains carbon, hydrogen and oxygen only. A sample contains 3.20 g carbon, 0.54 g hydrogen and 4.26 g oxygen. Calculate the empirical formula of the compound. Enter the formula using the format CxHyOz (e.g. C3H4O3).
Medium
- A1
- B2
- C-1
- D0
65.How many atoms are present in 0.200 mol of P₂O₅? (Avogadro constant = 6.02 × 10²³ mol⁻¹)
Medium
- A7.587e+23 atoms
- B1.0115999999999999e+24 atoms
- C9.273e+23 atoms
- D8.43e+23 atoms
66.How many moles are in 2.35 × 10²⁴ molecules of oxygen gas? (Avogadro constant = 6.02 × 10²³ mol⁻¹)
Medium
- A5.9 mol
- B4.9 mol
- C2.9 mol
- D3.9 mol

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