A mixture contains 4.4 g of CO2​ and 3.2 g of O2​. Calculate the total number of molecules and the mole fraction of CO2​.

📘 Complete Step-by-Step Solution

📌 Given Data

Mass of CO₂ = 4.4 g

Mass of O₂ = 3.2 g

N_A = 6.022 × 10²³ mol⁻¹

🔵 Step 1: Calculate Moles of CO₂

First calculate the molar mass of CO₂:

Molar Mass of CO₂

= 12 + (2 × 16)

= 44 g mol⁻¹

Now calculate the moles:

Moles of CO₂ = Mass ÷ Molar Mass

= 4.4 ÷ 44

= 0.10 mol

🟢 Step 2: Calculate Moles of O₂

Molar Mass of O₂

= 2 × 16

= 32 g mol⁻¹

Moles of O₂ = 3.2 ÷ 32

= 0.10 mol

CO₂ = 0.10 mol    |    O₂ = 0.10 mol

🟠 Step 3: Calculate Total Number of Molecules

Number of molecules is calculated using:

Number of Molecules = Number of Moles × N_A

CO₂ Molecules

= 0.10 × 6.022 × 10²³

= 6.022 × 10²² molecules

O₂ Molecules

= 0.10 × 6.022 × 10²³

= 6.022 × 10²² molecules

🟣 Step 4: Calculate Total Number of Molecules

Total Molecules = CO₂ molecules + O₂ molecules

= 6.022 × 10²² + 6.022 × 10²²

= 12.044 × 10²²

= 1.2044 × 10²³ molecules

✅ Total number of molecules = 1.2044 × 10²³

🔴 Step 5: Calculate Mole Fraction of CO₂

Mole fraction is given by:

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χ_CO₂ = Moles of CO₂ ÷ Total Moles

Total moles:

Total Moles = 0.10 + 0.10

= 0.20 mol

Therefore:

χ_CO₂ = 0.10 ÷ 0.20

= 0.5

✅ Mole fraction of CO₂ = 0.5

🎬 3D-Style Molecular Animation

The mixture contains equal numbers of moles of CO₂ and O₂.

O C O + O O

0.10 mol CO₂ + 0.10 mol O₂

↓
Equal moles → Mole fraction of CO₂ = 0.5

⚡ Quick Shortcut

4.4 g CO₂ ÷ 44 = 0.10 mol

3.2 g O₂ ÷ 32 = 0.10 mol

Total moles = 0.20 mol

Total molecules = 1.2044 × 10²³

χ_CO₂ = 0.10 ÷ 0.20 = 0.5

✅ Final Answer

Total Number of Molecules = 1.2044 × 10²³

Mole Fraction of CO₂ = 0.5

🎯 Formula Revision

Moles = Mass ÷ Molar Mass
Molecules = Moles × N_A
Total Molecules = Sum of Molecules
χ_CO₂ = Moles of CO₂ ÷ Total Moles