4.1.5 Mole-Mass Calculations

This topic explains how to perform mole-mass calculations in stoichiometry. It shows how to convert between moles of one substance and mass of another using a balanced chemical equation.

Definition

Mole-Mass Calculation: A stoichiometric calculation in which the mass of a substance is determined from the number of moles of another substance (or vice versa) using the mole ratio from a balanced chemical equation.

Main Idea

In a balanced chemical equation, the coefficients give the mole ratio. Using this ratio, we can convert moles of one substance to moles of another, and then use the molar mass to convert moles to mass (or mass to moles). This allows us to calculate how much mass of a product is formed from a given mass of reactant, or how much mass of reactant is needed to produce a given mass of product.

Core Concept

The key steps in mole-mass calculations are:

1. Convert mass to moles (if starting with mass): Moles = MassMolar Mass

2. Use the mole ratio from the balanced equation: Moles of unknown = Moles of known × Coefficient of unknownCoefficient of known

3. Convert moles to mass (if ending with mass): Mass = Moles × Molar Mass

Detailed Explanation

Steps for Mole-Mass Calculations

• Write the balanced chemical equation.
• Convert the given mass to moles using molar mass.
• Use the mole ratio from the balanced equation to find moles of the required substance.
• Convert moles to mass using molar mass.

Example 4.6: Decomposition of Potassium Chlorate

Problem: Potassium chlorate is used in making matches and dyes. On decomposition, it produces KCl and oxygen gas. If 25 g KClO₃ is decomposed, calculate the quantities of the following:

a) How many moles of O₂ are produced. b) How much mass in grams of O₂ is produced.

Chemical Equation: 2KClO₃ → 2KCl + 3O₂

Solution:

• Mass of KClO₃ = 25 g
• Molar mass of KClO₃ = 39 + 35.5 + 16 × 3 = 122.5 g/mol

• Moles of O₂
• Mass of O₂

Step 1: Calculate moles of KClO₃ Moles of KClO₃ = 25122.5 = 0.204 moles

Step 2: Use mole ratio to find moles of O₂

From the equation: 2 moles of KClO₃ give oxygen = 3 moles

0.204 moles of KClO₃ give oxygen = 32 × 0.204 = 0.306 moles of O₂

Step 3: Calculate mass of O₂ Mass of O₂ = moles × molar mass = 0.306 × 32 = 9.796 grams

• Moles of O₂ produced = 0.306 moles
• Mass of O₂ produced = 9.796 grams

Formula Summary

Example 4.7: Ionization of H₂SO₄ (from textbook)

Problem: 20 g of H₂SO₄ on dissolving in water ionizes completely. Calculate:

a) Number of H₂SO₄ molecules b) Number of H⁺ and SO₄²⁻ ions c) Mass of individual ions

Solution:

• Mass of H₂SO₄ = 20 g
• Molar mass of H₂SO₄ = 98.016 g/mol

Part (a): Number of H₂SO₄ molecules Number of molecules = MassMolar Mass × 6.02 × 10²³ = 2098.016 × 6.02 × 10²³ = 1.228 × 10²³ molecules

Part (b): Number of H⁺ and SO₄²⁻ ions

The ionization equation: H₂SO₄ → 2H⁺ + SO₄^2-

According to the equation: 1 molecule of H₂SO₄ = 2 H⁺ ions 1.228 × 10²³ molecules of H₂SO₄ = 2 × 1.228 × 10²³ H⁺ ions = 2.456 × 10²³ H⁺ ions

As 1 molecule of H₂SO₄ = 1 SO₄²⁻ ion: 1.228 × 10²³ molecules of H₂SO₄ = 1.228 × 10²³ SO₄^2- ions

Part (c): Mass of individual ions

Mass of H⁺ ions: Mass = moles × molar mass Moles of H⁺ = 2.456 × 10²³6.02 × 10²³ = 0.408 mol Mass of H⁺ = 0.408 × 1 = 0.408 g

Mass of SO₄²⁻ ions: Moles of SO₄^2- = 1.228 × 10²³6.02 × 10²³ = 0.204 mol Mass of SO₄^2- = 0.204 × 96 = 19.584 g

Intermediate Level

Steps for Mole-Mass Calculations

Example 4.6

• Mass of KClO₃ = 25 g
• Molar mass of KClO₃ = 122.5 g/mol

• Moles of O₂
• Mass of O₂

Equation: 2KClO₃ → 2KCl + 3O₂

Solution: n_KClO3 = 25122.5 = 0.204 mol n_O2 = 0.204 × 32 = 0.306 mol m_O2 = 0.306 × 32 = 9.796 g

• Moles of O₂ = **0.306 mol**
• Mass of O₂ = **9.796 g**

Important Points

• 1. Convert mass to moles using molar mass.
• 2. Use mole ratio from balanced equation.
• 3. Convert moles to mass using molar mass.
• 4. Example: 25 g KClO₃ → 0.306 mol O₂ → 9.796 g O₂.
• 5. Example: 20 g H₂SO₄ → 1.228 × 10²³ molecules.

Remember

• - Mass to moles: n = mM
• - Mole ratio: Coefficient ratio
• - Moles to mass: m = n × M
• - Example: 2KClO₃ → 2KCl + 3O₂

Common Mistakes

• 1. Forgetting to balance the equation: Always balance first.
• 2. Using the wrong mole ratio: Use the correct coefficients.
• 3. Mixing up molar mass: Use the correct molar mass for each substance.
• 4. Forgetting to convert mass to moles: Always convert to moles first.

Quick Revision

• Convert mass to moles using molar mass.
• Use mole ratio from balanced equation.
• Convert moles to mass using molar mass.
• Example: 25 g KClO₃ → 0.306 mol O₂ → 9.796 g O₂.
• Example: 20 g H₂SO₄ → 1.228 × 10²³ molecules.

60-Second Revision

• Mass to moles: n = mM
• Mole ratio: Coefficient ratio
• Moles to mass: m = n × M
• Example: 2KClO₃ → 2KCl + 3O₂

QUALITY VALIDATION

• Topic: 4.1.5 Mole-Mass Calculations
• Chapter: 4 (Stoichiometry)

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