The Mole And The Avogadro Constant

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The Mole and Avogadro Constant

The mole (mol) is the SI unit for amount of substance.
One mole of any substance contains 6.02 × 10²³ particles (Avogadro constant).
Particles can be atoms, molecules, ions, or formula units.
Example: 1 mol Na = 6.02 × 10²³ Na atoms; 1 mol H₂ = 6.02 × 10²³ H₂ molecules.
Molar mass is the mass of one mole of a substance (g/mol).
For elements, molar mass = relative atomic mass in grams.
For compounds, molar mass = relative molecular/formula mass in grams.

Mole–Mass–Mr Relationship

Use the formula triangle: moles = mass / Mr.
Mass = moles × Mr; Mr = mass / moles.
Always show working to avoid errors and gain credit.
Example: 0.250 mol Zn has mass = 0.250 × 65 = 16.25 g.
Example: 2.64 g sucrose (Mr = 342) gives moles = 2.64 / 342 = 7.72 × 10⁻³ mol.

Formula triangle for moles, mass and molar mass

Mole and Volume of Gas

Avogadro's Law: equal moles of any gas occupy equal volume at same T and P.
At RTP (20 °C, 1 atm), molar gas volume = 24 dm³ (24 000 cm³).
Volume = moles × 24 dm³ (or × 24 000 cm³).
Moles = volume (dm³) / 24 (or volume (cm³) / 24 000).
Example: 3 mol H₂ occupies 3 × 24 = 72 dm³.
Example: 1200 cm³ O₂ gives moles = 1200 / 24 000 = 0.05 mol.

Molar gas volume (dm³) formula triangle

Calculating Number of Particles

Number of particles = moles × Avogadro constant (6.02 × 10²³).
For compounds, count atoms per formula unit.
Example: 1 mol MgCl₂ contains 6.02 × 10²³ molecules, 3 × 6.02 × 10²³ atoms.
Example: 15.7 g H₂O (Mr = 18) → moles = 15.7/18 = 0.872 mol → molecules = 0.872 × 6.02 × 10²³ = 5.25 × 10²³.

Reacting Masses

Use balanced equation to find mole ratio between reactants/products.
Convert given mass to moles using moles = mass / Mr.
Use ratio to find moles of required substance.
Convert back to mass using mass = moles × Mr.
Example: 6.0 g Mg (Mr = 24) → 0.25 mol Mg → 1:1 ratio → 0.25 mol MgO → mass = 0.25 × 40 = 10 g.

Limiting Reactant

Limiting reactant is used up first and determines amount of product.
Excess reactant remains after reaction stops.
To find limiting reactant: calculate moles of each, compare with balanced equation ratio.
Example: 9.2 g Na (0.40 mol) + 8.0 g S (0.25 mol); equation 2Na + S → Na₂S requires 0.40 mol Na to react with 0.20 mol S; S (0.25 mol) is excess, Na is limiting.

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1.What is the Avogadro constant?
Easy
- A6.02 × 10²³
- B6.02 × 10²²
- C6.02 × 10²⁴
- D6.02 × 10²¹
2.How many moles are there in 2.64 g of sucrose (C12H22O11, Mr = 342)? Give your answer in standard form to 3 significant figures.
Medium
- A7.72 × 10⁻³
- B7.72 × 10⁻²
- C1.30 × 10²
- D2.72 × 10⁻³
3.State the volume, in dm³, occupied by one mole of any gas at room temperature and pressure.
Easy
4.One mole of any substance contains 6.02 × 10²³ particles.
Easy
True or false?
5.Complete the sentence.
Easy
The mass of one mole of a substance is called its ____ mass.
6.How many moles of carbon dioxide gas are present in 960 dm³ at RTP? (Molar volume = 24 dm³/mol)
Easy
- A40
- B36
- C48
- D44
7.Match each quantity to its correct value.
Medium
- Number of atoms in 1 mole of MgCl2
- Number of chloride ions in 1 mole of MgCl2
- Number of molecules in 1 mole of MgCl2
- 6.02 × 10²³
- 1.204 × 10²⁴
- 1.806 × 10²⁴
8.Arrange the following steps in the correct order to calculate the mass of product from a given mass of reactant in a chemical reaction.
Medium
- Calculate moles of reactant using mass ÷ Mr
- Use the balanced equation to find the mole ratio
- Calculate mass of product using moles × Mr

Thêm câu hỏi

9.Calculate the mass, in grams, of oxygen gas (O2) that contains 1.204 × 10²⁴ molecules. (Ar O = 16, Avogadro constant = 6.02 × 10²³)
Medium
- A70
- B76
- C58
- D64
10.In a reaction, 9.2 g of sodium reacts with 8.0 g of sulfur to produce Na2S. Which reactant is the limiting reactant? (Ar: Na = 23, S = 32)
Hard
11.What is the maximum mass of magnesium oxide (MgO) produced when 6.0 g of magnesium is completely burned in oxygen? (Ar: Mg = 24, O = 16)
Medium
- A12
- B11
- C9
- D10
12.What is the SI unit for amount of substance?
Easy
- Agram
- Bmole
- Clitre
- Dcoulomb
13.One mole of any substance contains how many particles?
Easy
- A6.02 × 10²³
- B6.02 × 10²²
- C6.02 × 10²⁴
- D6.02 × 10²¹
14.The mass of one mole of a substance is called its molar mass.
Easy
True or false?
15.What is the mass of 0.500 moles of calcium carbonate (CaCO₃)? (Ar: Ca = 40, C = 12, O = 16)
Easy
- A50.0 g
- B100 g
- C25.0 g
- D75.0 g
16.At room temperature and pressure (RTP), what volume does one mole of any gas occupy?
Easy
- A22.4 dm³
- B24 dm³
- C24 000 dm³
- D24 cm³
17.How many atoms are there in 0.25 moles of methane (CH₄)? (Avogadro constant = 6.02 × 10²³)
Medium
- A1.505 × 10²³
- B7.525 × 10²³
- C6.02 × 10²³
- D1.204 × 10²⁴
18.In the reaction 2Mg + O₂ → 2MgO, what mass of magnesium oxide is produced from 4.8 g of magnesium? (Ar: Mg = 24, O = 16)
Medium
- A8.0 g
- B4.0 g
- C10.0 g
- D6.0 g
19.In a reaction, 6.0 g of carbon reacts with 16.0 g of oxygen to produce CO₂. Which is the limiting reactant? (Ar: C = 12, O = 16)
Medium
- Acarbon
- Boxygen
- Cboth are exactly used up
- Dcannot be determined
20.Match each term on the left with its correct description on the right.
Medium
- Mole
- Avogadro constant
- Molar mass
- Molar gas volume at RTP
- 6.02 × 10²³ particles
- 24 dm³
- mass of one mole of a substance
- SI unit of amount of substance
21.Arrange the following steps in the correct order to calculate the number of atoms in a given mass of a compound.
Medium
- Calculate the number of moles using mass ÷ Mr
- Multiply by the Avogadro constant to find number of molecules
- Multiply by the number of atoms per molecule
- Determine the molar mass of the compound
22.Which of the following statements about the mole and Avogadro constant are correct? (Select all that apply)
Medium
- AOne mole of any substance contains 6.02 × 10²³ particles.
- BThe Avogadro constant is the number of particles in one mole of a substance.
- COne mole of oxygen gas (O2) contains 6.02 × 10²³ oxygen atoms.
- DThe molar mass of a compound is its relative formula mass in grams.
23.One mole of any gas at room temperature and pressure occupies a volume of 24 dm³.
Easy
True or false?
24.In a reaction, 9.2 g of sodium reacts with 8.0 g of sulfur to produce Na₂S. Which reactant is the limiting reactant? (Ar: Na = 23, S = 32)
Medium
- ASodium
- BSulfur
- CBoth are limiting
- DNeither
25.A student measures 48 dm³ of carbon dioxide gas at RTP. How many moles of carbon dioxide does this represent? (Molar volume = 24 dm³/mol)
Easy
- A2.0 mol
- B0.5 mol
- C1.0 mol
- D0.25 mol
26.What is the mass of 0.200 moles of calcium carbonate (CaCO₃)? (Ar: Ca = 40, C = 12, O = 16)
Easy
- A20.0 g
- B10.0 g
- C40.0 g
- D5.0 g
27.A sample of ethane (C₂H₆) contains 1.204 × 10²⁴ hydrogen atoms. How many molecules of ethane are present? (Avogadro constant = 6.02 × 10²³)
Medium
- A1.00 × 10²³ molecules
- B2.00 × 10²³ molecules
- C1.00 × 10²⁴ molecules
- D2.00 × 10²⁴ molecules
28.In the reaction 2H₂ + O₂ → 2H₂O, what mass of water is formed when 4.0 g of hydrogen reacts completely with excess oxygen? (Ar: H = 1, O = 16)
Medium
- A18 g
- B36 g
- C9.0 g
- D72 g
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 mass of one mole of a compound is equal to its relative formula mass in grams.
- COne mole of any gas at RTP occupies a volume of 24 dm³.
- DOne mole of sodium chloride contains 6.02 × 10²³ atoms.
- EThe Avogadro constant is the number of particles in one mole of a substance.
30.Match each quantity on the left with the correct value on the right.
Easy
- Mass of 1 mole of calcium (Ar = 40)
- Volume of 1 mole of gas at RTP
- Number of particles in 1 mole
- 24 dm³
- 6.02 × 10²³
- 40 g
31.In an experiment, 0.020 mol of magnesium reacts with excess hydrochloric acid to produce hydrogen gas. What volume of hydrogen gas, in cm³, is produced at RTP? (Molar volume = 24,000 cm³/mol)
Medium
- A480 cm³
- B240 cm³
- C960 cm³
- D120 cm³
32.Which of the following statements about the mole are correct? (Select all that apply.)
Medium
- AOne mole of a substance contains 6.02 × 10²³ particles.
- BThe mass of one mole of a substance is called its molar mass.
- COne mole of any gas at RTP occupies 22.4 dm³.
- DThe mole is the SI unit for amount of substance.
33.Arrange the following steps in the correct order to calculate the mass of product formed from a given mass of reactant in a chemical reaction.
Medium
- Convert the mass of reactant to moles using its molar mass.
- Use the balanced equation to find the mole ratio between reactant and product.
- Calculate the moles of product formed from the mole ratio.
- Convert the moles of product to mass using its molar mass.
34.A student heats 2.00 g of hydrated copper(II) sulfate (CuSO₄·5H₂O, Mr = 249.5) to constant mass. The residue is anhydrous copper(II) sulfate (CuSO₄, Mr = 159.5). What is the mass of the residue?
Hard
- A1.28 g
- B1.60 g
- C0.80 g
- D1.92 g
35.One mole of hydrogen gas (H₂) contains 6.02 × 10²³ hydrogen atoms.
Easy
True or false?
36.A student reacts 2.0 g of magnesium (Ar = 24) with excess hydrochloric acid. The balanced equation is Mg + 2HCl → MgCl₂ + H₂. What mass of hydrogen gas is produced?
Medium
- A0.083 g
- B0.17 g
- C0.33 g
- D1.0 g
37.A sample of a hydrocarbon contains 85.7% carbon by mass. Its molar mass is 84 g/mol. What is the molecular formula of the hydrocarbon? (Ar: C = 12, H = 1)
Hard
- ACH₂
- BC₃H₆
- CC₆H₁₂
- DC₆H₁₄
38.One mole of methane (CH₄) contains 6.02 × 10²³ atoms.
Easy
True or false?
39.A student heats a sample of hydrated copper(II) sulfate (CuSO₄·5H₂O) to constant mass. The mass of the residue is 1.60 g. What is the mass of water lost if the original sample mass was 2.50 g? (Mr: CuSO₄ = 159.5, CuSO₄·5H₂O = 249.5)
Medium
- A0.90 g
- B1.60 g
- C2.50 g
- D0.64 g
40.A student performs an experiment to determine the number of moles of water of crystallisation in a hydrated salt. Which of the following steps are necessary to obtain an accurate result? (Select all that apply)
Medium
- AWeigh the hydrated salt before heating
- BHeat the salt until no further mass change occurs
- CRecord the volume of gas produced
- DAllow the residue to cool in a desiccator before weighing
- EUse a balance that measures to the nearest 0.001 g
41.One mole of any gas at room temperature and pressure occupies a volume of 24.0 dm³.
Easy
True or false?
42.How many moles are present in 36.0 g of water (H₂O)? (Ar: H = 1, O = 16)
Easy
43.How many moles of carbon dioxide gas are present in 480 cm³ at RTP? (Molar volume = 24 000 cm³/mol)
Medium
44.State the meaning of the term 'molar gas volume'.
Easy
45.What is the mass, in grams, of 0.250 moles of zinc? (Ar Zn = 65)
Easy
46.State the volume, in cm³, occupied by one mole of any gas at room temperature and pressure.
Easy
47.Calculate the number of moles in 88 g of carbon dioxide (CO₂). (Ar: C = 12, O = 16)
Easy
48.What volume, in dm³, is occupied by 0.500 moles of chlorine gas at RTP? (Molar volume = 24 dm³/mol)
Easy
49.Complete the sentence:
Easy
In a chemical reaction, the reactant that is used up first is called the ____ reactant.
50.State the value of the Avogadro constant.
Easy
51.Explain why the limiting reactant determines the amount of product formed in a chemical reaction.
Medium
52.In a reaction, 9.2 g of sodium reacts with 8.0 g of sulfur to produce sodium sulfide (Na₂S). Determine which reactant is the limiting reactant. (Ar: Na = 23, S = 32)
Medium
53.In a titration experiment, 25.0 cm³ of 0.100 mol/dm³ hydrochloric acid neutralises 20.0 cm³ of sodium hydroxide solution. Calculate the concentration of the sodium hydroxide solution in mol/dm³. The equation is: HCl + NaOH → NaCl + H₂O.
Medium
54.In a reaction, 6.0 g of magnesium reacts with 16.0 g of oxygen to produce magnesium oxide (MgO). Determine which reactant is the limiting reactant and calculate the maximum mass of magnesium oxide formed. (Ar: Mg = 24, O = 16)
Hard
55.In an experiment, 0.020 mol of magnesium reacts with excess hydrochloric acid. The hydrogen gas produced is collected over water. The volume of hydrogen collected is 480 cm³ at RTP. Calculate the percentage yield of hydrogen gas. (Molar volume at RTP = 24 dm³/mol)
Hard
56.How many moles are present in 36.0 g of water (H₂O)? (Ar: H = 1, O = 16)
Easy
- A1 mol
- B4 mol
- C2 mol
- D3 mol
57.How many moles of carbon dioxide gas are present in 480 cm³ at RTP? (Molar volume = 24 000 cm³/mol)
Medium
- A2.02 mol
- B-0.98 mol
- C0.02 mol
- D1.02 mol
58.What is the mass, in grams, of 0.250 moles of zinc? (Ar Zn = 65)
Easy
- A15.25 g
- B17.25 g
- C18.25 g
- D16.25 g
59.Calculate the number of moles in 88 g of carbon dioxide (CO₂). (Ar: C = 12, O = 16)
Easy
- A2 mol
- B4 mol
- C1 mol
- D3 mol
60.What volume, in dm³, is occupied by 0.500 moles of chlorine gas at RTP? (Molar volume = 24 dm³/mol)
Easy
- A14 dm³
- B12 dm³
- C13 dm³
- D11 dm³

Thẻ ghi nhớ

What is the SI unit for amount of substance?

The mole, symbol mol.

What is the Avogadro constant?

6.02 × 10²³ particles per mole.

How many atoms are in one mole of sodium (Na)?

6.02 × 10²³ atoms.

How many molecules are in one mole of hydrogen gas (H₂)?

6.02 × 10²³ molecules.

How many formula units are in one mole of sodium chloride (NaCl)?

6.02 × 10²³ formula units.

What is the molar mass of an element?

The relative atomic mass in grams.

What is the molar mass of a compound?

The relative molecular or formula mass in grams.

What is the molar gas volume at room temperature and pressure (RTP)?

24 dm³ or 24,000 cm³ per mole.

What conditions define RTP?

20 °C and 1 atmosphere (atm).

Write the formula linking moles, mass, and molar mass.

Moles = mass / molar mass (or Mr).

Calculate the mass of 0.250 moles of zinc (Ar = 65).

16.25 g (0.250 × 65).

How many moles are in 2.64 g of sucrose (Mr = 342)?

7.72 × 10⁻³ mol (2.64 / 342).

How many molecules are in 15.7 g of water (Mr = 18)?

5.25 × 10²³ molecules (15.7/18 × 6.02×10²³).

How many atoms are in 15.7 g of water?

1.58 × 10²⁴ atoms (3 × 5.25×10²³).

In MgCl₂, how many chloride ions are in 1 mole?

12.04 × 10²³ chloride ions (2 × 6.02×10²³).

What is the molar ratio in the reaction 2Mg + O₂ → 2MgO?

2 : 1 : 2 (Mg : O₂ : MgO).

Calculate the mass of MgO produced from 6.0 g Mg (Ar Mg=24, O=16).

10 g (0.25 mol Mg → 0.25 mol MgO → 0.25 × 40).

What is a limiting reactant?

The reactant that is used up first and limits the amount of product formed.

What is an excess reactant?

The reactant that remains after the reaction stops.

9.2 g Na reacts with 8.0 g S to form Na₂S. Which is limiting? (Ar Na=23, S=32)

Na is limiting (0.40 mol Na requires 0.20 mol S, but 0.25 mol S available).

Calculate the maximum mass of Al from 51 tonnes Al₂O₃ (Ar Al=27, O=16).

27 tonnes (500,000 mol Al₂O₃ → 1,000,000 mol Al → 27,000,000 g = 27 t).

What is Avogadro's Law?

At the same temperature and pressure, equal amounts of gases occupy the same volume.

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