Calculate the mole fraction of ethanol and water in a solution containing 46 g ethanol and 54 g water.

📘 Complete Step-by-Step Solution

📌 Given Data

Mass of ethanol = 46 g

Mass of water = 54 g

Molar mass of ethanol = 46 g mol⁻¹

Molar mass of water = 18 g mol⁻¹

🔵 Step 1: Calculate Moles of Ethanol

Moles = Mass ÷ Molar Mass

Moles of ethanol = 46 ÷ 46

= 1 mol

✅ Ethanol = 1 mol

🟢 Step 2: Calculate Moles of Water

Moles of water = 54 ÷ 18

= 3 mol

✅ Water = 3 mol

🟠 Step 3: Calculate Total Number of Moles

Total moles = Moles of ethanol + Moles of water

= 1 + 3

= 4 mol

🟣 Step 4: Mole Fraction of Ethanol

The mole fraction of a component is:

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χ_ethanol = Moles of ethanol ÷ Total moles

= 1 ÷ 4

= 0.25

✅ Mole fraction of ethanol = 0.25

🔴 Step 5: Mole Fraction of Water

χ_water = Moles of water ÷ Total moles

= 3 ÷ 4

= 0.75

✅ Mole fraction of water = 0.75

🎬 3D-Style Mole Fraction Animation

The solution contains 1 mole of ethanol and 3 moles of water.

EtOH H₂O H₂O H₂O

1 mol ethanol + 3 mol water

Total = 4 mol

χ_ethanol = 1/4 = 0.25
χ_water = 3/4 = 0.75

🟢 Step 6: Verify the Answer

χ_ethanol + χ_water

= 0.25 + 0.75

= 1

✅ Sum of mole fractions = 1

✅ Final Answer

Mole fraction of ethanol = 0.25

Mole fraction of water = 0.75

🎯 Quick Revision

46 g ethanol ÷ 46 = 1 mol
54 g water ÷ 18 = 3 mol
Total moles = 4 mol
χ_ethanol = 1/4 = 0.25
χ_water = 3/4 = 0.75