A 40.0 gram-sample of methanol, CH4O is mixed with 60.0 grams of ethanol, C2H6O. What is the mole fraction of the methanol?
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A 40.0 gram-sample of methanol, CH4O is mixed with 60.0 grams of ethanol, C2H6O. What is the mole fraction of the methanol?
Given:
mass of solute = 40.0 g
mass of solvent = 60.0 g
solute: methanol (CH₄O)
solvent: ethanol (C₂H₆O)
Required:
mole fraction of solute
Solution:
Step 1: Calculate the molar mass of solute and solvent.
For solute
molar mass of solute = (12.01 g/mol × 1) + (1.008 g/mol × 4) + (16.00 g/mol × 1)
molar mass of solute = 32.042 g/mol
For solvent
molar mass of solvent = (12.01 g/mol × 2) + (1.008 g/mol × 6) + (16.00 g/mol × 1)
molar mass of solvent = 46.068 g/mol
Step 2: Calculate the number of moles of solute and solvent.
For solute
[tex]\text{moles of solute} = \frac{\text{mass of solute}}{\text{molar mass of solute}}[/tex]
[tex]\text{moles of solute} = \frac{\text{40.0 g}}{\text{32.042 g/mol}}[/tex]
moles of solute = 1.2483615 mol
For solvent
[tex]\text{moles of solvent} = \frac{\text{mass of solvent}}{\text{molar mass of solvent}}[/tex]
[tex]\text{moles of solvent} = \frac{\text{60.0 g}}{\text{46.068 g/mol}}[/tex]
moles of solvent = 1.3024225 mol
Step 3: Calculate the mole fraction of solute.
[tex]\text{mole fraction of solute} = \frac{\text{moles of solute}}{\text{moles of solute + moles of solvent}}[/tex]
[tex]\text{mole fraction of solute} = \frac{\text{1.2483615 mol}}{\text{1.2483615 mol + 1.3024225 mol}}[/tex]
[tex]\boxed{\text{mole fraction of solute} = 0.489}[/tex]
[tex]\\[/tex]
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