Question

Calculate the mole fraction of glycerol in 30% by weight of aqueous glycerol (C$_3$H$_8$O$_3$) solution.

Hint:

In weight percent solutions, always assume 100 g of solution to simplify calculations. Then convert masses to moles for mole fraction determination.

Answer 1

Step 1: Understanding the problem.
We are given a 30% by weight aqueous solution of glycerol. This means that in 100 g of solution, glycerol contributes 30 g and water contributes 70 g.
Step 2: Calculate moles of glycerol.
Molecular mass of glycerol (C$_3$H$_8$O$_3$) = (3 × 12) + (8 × 1) + (3 × 16)
= 36 + 8 + 48
= 92 g/mol.
Moles of glycerol = $\dfrac{30}{92} \approx 0.326$ mol.
Step 3: Calculate moles of water.
Molecular mass of water (H$_2$O) = 18 g/mol.
Mass of water = 70 g.
Moles of water = $\dfrac{70}{18} \approx 3.889$ mol.
Step 4: Calculate mole fraction of glycerol.
Total moles = 0.326 + 3.889 = 4.215 mol.
Mole fraction of glycerol = $\dfrac{0.326}{4.215} \approx 0.077$.
Conclusion:
The mole fraction of glycerol in 30% by weight aqueous glycerol solution is approximately: \[ \boxed{0.077} \]