6.5.1 Mole-Mass Calculations

This topic explains how to convert between moles and mass using molar mass — one of the most important calculations in chemistry.

Definition

Mole-mass calculations involve converting between the number of moles of a substance and its mass in grams using its molar mass.

Simple explanation: If you know how many moles you have, you can find the mass. If you know the mass, you can find the moles.

Main Idea

The key relationship is:

Number of moles = Mass of substance (g)Molar mass (g/mol)

Or rearranged:

Mass of substance (g) = Number of moles × Molar mass (g/mol)

Simple explanation: Mass = moles × molar mass. Moles = mass ÷ molar mass.

Core Concept

The Mole-Mass Triangle

n = mM

• **n** = number of moles
• **m** = mass in grams
• **M** = molar mass in g/mol

Simple explanation: Use this formula to convert between moles and mass.

Types of Problems

Detailed Explanation

Example 6.3: Calculating mass of one mole of a substance

Problem: Calculate the molar masses of (a) Na, (b) Nitrogen, (c) Sucrose C₁₂H₂₂O₁₁.

Problem Solving Strategy: If an element is a metal, its molar mass is its atomic mass expressed in grams (gram atomic mass). If an element exists as a molecule, its molar mass is its molecular mass expressed in grams (gram molecular mass).

Solution:

(a) Na (metal): 1 mole of Na = 23 g

• Molecular mass of N₂ = 14 × 2 = 28 amu
• Therefore, mass of 1 mole of N₂ = **28 g**

• Molecular mass = 12 × 12 + 1 × 22 + 16 × 11
• = 144 + 22 + 176
• = **342 amu**
• Therefore, mass of 1 mole of sucrose = 342 g

Simple explanation: Molar mass is the atomic/molecular/formula mass expressed in grams.

Example 6.4: Calculating the mass of a given number of moles of a substance

Problem: Oxygen is converted to ozone (O₃) during thunderstorms. Calculate the mass of ozone if 9.05 moles of ozone is formed in a storm.

Problem Solving Strategy: Ozone is a molecular substance. Determine its molar mass and use it to convert moles to mass in grams.

Solution:

Step 1: Find the molar mass of O₃. 1 mole of O₃ = 16 × 3 = 48 g

Step 2: Use the formula. Mass = Moles × Molar mass

Mass = 9.05 moles × 48 g/mol

Mass = 434.4 g of O₃

Final Answer: 9.05 moles of ozone has a mass of 434.4 g.

Simple explanation: Multiply the number of moles by the molar mass to get the mass.

Example: Moles from Mass (from page 106)

Problem: 100 g of H₂O = how many moles?

Solution:

Moles = MassMolar mass

Molar mass of H₂O = 2(1) + 16 = 18 g/mol

Moles = 10018.016 = 5.55 moles of H₂O

Final Answer: 100 g of water contains 5.55 moles.

Simple explanation: Divide the mass by the molar mass to get the number of moles.

Intermediate Level

Step-by-Step Approach

• Write the formula.
• Find the molar mass of the substance.
• Multiply moles × molar mass.
• Write the final answer with units.

• Write the formula.
• Find the molar mass of the substance.
• Divide mass by molar mass.
• Write the final answer with units.

Concept Assessment Exercise 6.5 (from the book)

1. Hydrogen peroxide (H₂O₂) — used for bleaching hair. Calculate: (a) Mass of H₂O₂ that would contain 2.5 moles.

• Molar mass of H₂O₂ = 2(1) + 2(16) = 2 + 32 = 34 g/mol
• Mass = 2.5 × 34 = **85 g**

(b) Number of moles of H₂O₂ that would exactly weigh 30 g.

**Solution:** - Moles = 3034 = **0.88 moles**

2. A spoon of table salt (NaCl) contains 12.5 grams. Calculate the number of moles it contains.

• Molar mass of NaCl = 23 + 35.5 = 58.5 g/mol
• Moles = 12.558.5 = **0.214 moles**

3. Barium sulphate (BaSO₄) — swallowed before X-rays. Calculate the mass of one mole of BaSO₄.

Solution: - Molar mass = 137 + 32 + 16 × 4 = 137 + 32 + 64 = 233 g/mol

Common Molar Masses

Important Points

• - Formula: n = m / M or m = n × M.
• - **n** = number of moles.
• - **m** = mass in grams.
• - **M** = molar mass in g/mol.
• - Moles to mass: multiply by molar mass.
• - Mass to moles: divide by molar mass.
• - Molar mass = atomic/molecular/formula mass in grams.
• - Examples:
• - 9.05 moles of O₃ = 434.4 g
• - 100 g of H₂O = 5.55 moles
• - 2.5 moles of H₂O₂ = 85 g
• - 30 g of H₂O₂ = 0.88 moles
• - 12.5 g of NaCl = 0.214 moles

Remember

• - Moles = Mass / Molar mass.
• - Mass = Moles × Molar mass.
• - Molar mass = atomic/molecular/formula mass in grams.
• - **H₂O** = 18 g/mol; **CO₂** = 44 g/mol.
• - **NaCl** = 58.5 g/mol; **O₃** = 48 g/mol.
• - **9.05 moles of O₃** = 434.4 g.
• - **100 g of H₂O** = 5.55 moles.

Common Mistakes

• 1. Forgetting to find the molar mass first. Always find M before using the formula.
• 2. Multiplying when you should divide. Moles to mass = multiply; mass to moles = divide.
• 3. Forgetting to multiply by subscripts in molar mass. For H₂O, molar mass = 2(1) + 16 = 18, not 1 + 16 = 17.
• 4. Forgetting units. Mass is in grams; moles are in mol; molar mass is in g/mol.
• 5. Confusing molar mass with molecular mass. Molar mass is in g/mol; molecular mass is in amu.
• 6. Thinking moles and mass are the same. They are different — moles count particles; mass measures how heavy.

Quick Revision

• Mole-mass calculations: converting between moles and mass using molar mass.
• Formula:
• n = m / M (moles from mass)
• m = n × M (mass from moles)
• n = number of moles; m = mass in grams; M = molar mass in g/mol.
• Examples:
• 9.05 moles of O₃ → 9.05 × 48 = 434.4 g
• 100 g of H₂O → 10018 = 5.55 moles
• 2.5 moles of H₂O₂ → 2.5 × 34 = 85 g
• 30 g of H₂O₂ → 3034 = 0.88 moles
• 12.5 g of NaCl → 12.558.5 = 0.214 moles
• Molar mass = atomic/molecular/formula mass in grams.
• Common molar masses: H₂O = 18, CO₂ = 44, O₂ = 32, O₃ = 48, NaCl = 58.5, H₂O₂ = 34, BaSO₄ = 233.

60-Second Revision

• Moles = Mass / Molar mass.
• Mass = Moles × Molar mass.
• **H₂O** = 18 g/mol; **CO₂** = 44 g/mol; **NaCl** = 58.5 g/mol.
• **9.05 moles of O₃** = 434.4 g.
• **100 g of H₂O** = 5.55 moles.
• Warning: moles to mass = multiply; mass to moles = divide.