Answer :
Mole fraction of sucrose = 0.1128 mol / 27.5718 mol = 0.0041 , the mole fraction of sucrose in the solution is approximately 0.0041.
To calculate the mole fraction of sucrose in the solution, we need to first calculate the number of moles of sucrose and water, and then use these values to determine the mole fraction.
Given:
Mass of sucrose (C₁₂H₂₂O₁₁) = 38.6 g
Mass of water = 495 g
Final volume of the solution = 508 mL
First, let's calculate the number of moles of sucrose (C₁₂H₂₂O₁₁):
Molar mass of sucrose (C₁₂H₂₂O₁₁) = (12 × 12.01 g/mol) + (22 × 1.01 g/mol) + (11 × 16.00 g/mol) = 342.34 g/mol
Number of moles of sucrose = Mass of sucrose / Molar mass of sucrose
Number of moles of sucrose = 38.6 g / 342.34 g/mol
Next, let's calculate the number of moles of water:
Molar mass of water (H₂O) = (2 × 1.01 g/mol) + (16.00 g/mol) = 18.02 g/mol
Number of moles of water = Mass of water / Molar mass of water
Number of moles of water = 495 g / 18.02 g/mol
Now, let's calculate the total moles of solute and solvent in the solution:
Total moles = Moles of sucrose + Moles of water
Next, we need to convert the final volume of the solution to liters:
Final volume of the solution = 508 mL = 508 mL × (1 L / 1000 mL) = 0.508 L
Now, let's calculate the mole fraction of sucrose:
Mole fraction of sucrose = Moles of sucrose / Total moles
Substituting the calculated values, we can now calculate the mole fraction of sucrose in the solution.
Moles of sucrose = 38.6 g / 342.34 g/mol = 0.1128 mol
Moles of water = 495 g / 18.02 g/mol = 27.459 mol
Total moles = 0.1128 mol + 27.459 mol = 27.5718 mol
Mole fraction of sucrose = 0.1128 mol / 27.5718 mol = 0.0041
Therefore, the mole fraction of sucrose in the solution is approximately 0.0041.
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