Start by reviewing the key formulas, then work through the practice questions in this worksheet. Finally, assess your progress with the included quiz.
The Mole Concept
Definition: The mole (symbol: mol) is the SI unit of the amount of substance. One mole contains exactly 6.022 x 10²³ elementary entities (atoms, molecules, ions, electrons, or other specified particles). This number is known as Avogadro’s constant (Nₐ).
Significance: The mole bridges the microscopic world of atoms and molecules and the macroscopic world of grams and kilograms, which we can measure in the lab.
Key Relationships & Formulas
1. Moles, Mass, and Molar Mass
n = m / M- where:
- n = number of moles (mol)
- m = mass of substance (g)
- M = molar mass of substance (g/mol) (Molar mass is the mass of one mole of a substance. It’s numerically equal to the sum of the atomic masses of the constituent atoms in the formula.)
Example 1 (Mass to Moles): What is the number of moles in 10.0 g of sodium chloride (NaCl)?
- Calculate Molar Mass: M(NaCl) = 23 g/mol + 35.5 g/mol = 58.5 g/mol
- Use Formula: n = m / M = 10.0 g / 58.5 g/mol = 0.171 mol
Example 2 (Moles to Mass): What is the mass of 0.500 moles of carbon dioxide (CO₂)?
- Calculate Molar Mass: M(CO₂) = 12.01 g/mol + (2 * 16.00 g/mol) = 44.01 g/mol
- Use Formula: m = n * M = 0.500 mol * 44.01 g/mol = 22.0 g
2. Moles, Number of Particles, and Avogadro’s Constant
n = N / Nₐ- where:
- n = number of moles (mol)
- N = number of particles
- Nₐ = Avogadro’s constant (6.022 x 10²³ particles/mol)
Example 3 (Number of Particles to Moles): How many moles are present in 3.011 x 10²³ atoms of iron (Fe)?
Solution: Use Formula: n = N / Nₐ = (3.011 x 10²³ atoms) / (6.022 x 10²³ atoms/mol) = 0.500 mol
Example 4 (Moles to Number of Particles): How many molecules are there in 2.00 moles of oxygen gas (O₂)?
Solution: Use Formula: N = n * Nₐ = 2.00 mol * (6.022 x 10²³ molecules/mol) = 1.204 x 10²⁴ molecules
3. Moles, Volume (for Gases), and Molar Volume
n = V / Vₘ(Applicable only to gases)- where:
- n = number of moles (mol)
- V = volume of gas (dm³ or L)
- Vₘ = molar volume of gas (dm³/mol or L/mol) (At standard temperature and pressure (STP: 0°C or 273 K and 1 atm or 101.3 kPa), Vₘ = 22.4 dm³/mol. At room temperature and pressure (RTP: 25°C or 298 K and 1 atm or 101.3 kPa), Vₘ = 24.0 dm³/mol.) Always check the conditions given in the question.
Example 5 (Volume to Moles): What is the number of moles in 11.2 dm³ of hydrogen gas (H₂) at STP?
Use Formula: n = V / Vₘ = 11.2 dm³ / 22.4 dm³/mol = 0.500 mol
Example 6 (Moles to Volume): What is the volume of 0.250 moles of nitrogen gas (N₂) at RTP?
Use Formula: V = n * Vₘ = 0.250 mol * 24.0 dm³/mol = 6.00 dm³
4. Calculations involving solutions and concentration
n=cV where:
- n = number of moles (mol)
- c = concentration (mol/dm³ or M)
- V = volume (dm³)
Example 7: What is the number of moles in 500 cm³ of a 0.1 mol/dm³ solution of sodium hydroxide (NaOH)?
Convert volume to dm³: 500 cm³ = 0.5 dm³
Use Formula: n = cV = 0.1 mol/dm³ * 0.5 dm³ = 0.05 mol
Multi-step Calculations (Stoichiometry)
General Steps:
1. Balance the Chemical Equation: This is the foundation. A balanced equation ensures the conservation of mass. The coefficients in front of each chemical species represent the relative number of moles of that species involved in the reaction.
2. Convert Given Quantities to Moles: You’ll usually be given the mass, volume (of a gas), or concentration (of a solution) of a reactant or product. Use the appropriate formulas (n = m/M, n = V/Vₘ, or n = cV) to convert these quantities into moles.
3. Use Mole Ratios: This is the heart of stoichiometry. The coefficients in the balanced equation give you the mole ratios. Set up a proportion to find the number of moles of the desired substance.
4. Convert Moles to Desired Quantities: Once you’ve calculated the moles of the desired substance, you might need to convert it back to mass, volume, or concentration using the same formulas as in step 2, but rearranged.
Example 8: Mass-to-Mass Problem
Problem: What mass of carbon dioxide (CO₂) is produced when 10.0 g of propane (C₃H₈) is burned completely?
Solution:
- Balance the Equation: C₃H₈ + 5O₂ → 3CO₂ + 4H₂OConvert Mass of Propane to Moles:
- M(C₃H₈) = (3 * 12.01) + (8 * 1.01) = 44.11 g/moln(C₃H₈) = m/M = 10.0 g / 44.11 g/mol = 0.227 mol
- n(CO₂) = 3 * n(C₃H₈) = 3 * 0.227 mol = 0.681 mol
- M(CO₂) = 12.01 + (2 * 16.00) = 44.01 g/molm(CO₂) = n * M = 0.681 mol * 44.01 g/mol = 30.0 g
Answer: 30.0 g of CO₂ is produced.
Example 9: Mass-to-Volume Problem (Gas)
Problem: What volume of oxygen gas (O₂) at STP is required to completely react with 5.00 g of methane (CH₄)?
Solution:
- Balance the Equation: CH₄ + 2O₂ → CO₂ + 2H₂O
- Convert Mass of Methane to Moles:
- M(CH₄) = 12.01 + (4 * 1.01) = 16.05 g/mol
- n(CH₄) = m/M = 5.00 g / 16.05 g/mol = 0.312 mol
- Use Mole Ratio: From the balanced equation, 1 mole of CH₄ reacts with 2 moles of O₂.
- n(O₂) = 2 * n(CH₄) = 2 * 0.312 mol = 0.624 mol
- Convert Moles of O₂ to Volume (at STP):
- V(O₂) = n * Vₘ = 0.624 mol * 22.4 dm³/mol = 14.0 dm³
Answer: 14.0 dm³ of O₂ is required.
Mole Conversion Worksheet with Answers
The answers are included at the end. Total questions – 30
Section 1: Mass to Moles (5 Questions)
- What is the number of moles in 25.0 g of sodium hydroxide (NaOH)?
- How many moles are present in 100.0 g of calcium carbonate (CaCO₃)?
- Calculate the number of moles in 12.5 g of sulfuric acid (H₂SO₄).
- Determine the number of moles in 40.0 g of potassium chloride (KCl).
- Find the number of moles in 7.5 g of glucose (C₆H₁₂O₆).
Section 2: Moles to Mass (5 Questions)
- What is the mass of 0.250 moles of magnesium oxide (MgO)?
- Calculate the mass of 1.50 moles of ammonia (NH₃).
- What is the mass of 0.750 moles of nitric acid (HNO₃)?
- Determine the mass of 0.100 moles of copper(II) sulfate (CuSO₄).
- Find the mass of 2.00 moles of ethanol (C₂H₅OH).
Section 3: Number of Particles to Moles (5 Questions)
- How many moles are present in 6.022 x 10²⁴ atoms of gold (Au)?
- Calculate the number of moles in 3.011 x 10²² molecules of water (H₂O).
- How many moles are in 1.204 x 10²⁵ ions of sodium (Na⁺)?
- Determine the number of moles in 9.033 x 10²³ molecules of carbon dioxide (CO₂).
- Find the number of moles in 1.806 x 10²⁴ atoms of iron (Fe).
Section 4: Moles to Number of Particles (5 Questions)
- How many molecules are there in 0.500 moles of oxygen gas (O₂)?
- Calculate the number of atoms in 1.25 moles of aluminum (Al).
- How many ions are present in 0.750 moles of chloride ions (Cl⁻)?
- Determine the number of molecules in 0.200 moles of methane (CH₄).
- Find the number of atoms in 2.50 moles of hydrogen gas (H₂).
Section 5: Gas Volume to Moles (at STP) (5 Questions)
- How many moles are present in 22.4 dm³ of nitrogen gas (N₂) at STP?
- Calculate the number of moles in 11.2 dm³ of hydrogen chloride gas (HCl) at STP.
- How many moles are in 5.6 dm³ of ammonia gas (NH₃) at STP?
- Determine the number of moles in 33.6 dm³ of carbon monoxide gas (CO) at STP.
- Find the number of moles in 16.8 dm³ of sulfur dioxide gas (SO₂) at STP.
Section 6: Moles to Gas Volume (at STP) (5 Questions)
- What is the volume of 0.750 moles of argon gas (Ar) at STP?
- Calculate the volume of 1.20 moles of helium gas (He) at STP.
- What is the volume of 0.250 moles of oxygen gas (O₂) at STP?
- Determine the volume of 1.50 moles of carbon dioxide gas (CO₂) at STP.
- Find the volume of 0.90 moles of nitrogen gas (N₂) at STP.
Answer Key
Section 1:
- 0.625 mol
- 1.00 mol
- 0.127 mol
- 0.537 mol
- 0.0416 mol
Section 2:
- 10.1 g
- 25.5 g
- 47.3 g
- 16.0 g
- 92.1 g
Section 3:
- 1.00 mol
- 0.0500 mol
- 2.00 mol
- 1.50 mol
- 3.00 mol
Section 4:
- 3.011 x 10²³ molecules
- 7.528 x 10²³ atoms
- 4.517 x 10²³ ions
- 1.204 x 10²³ molecules
- 3.011 x 10²⁴ atoms
Section 5:
- 1.00 mol
- 0.500 mol
- 0.25 mol
- 1.50 mol
- 0.75 mol
Section 6:
- 16.8 dm³
- 26.9 dm³
- 6.0 dm³
- 33.6 dm³
- 20.2 dm³
