The mole fractions of glucose and water in aqueous glucose solution are 0.0244 and 0.9756 respectively. What is the weight percentage (w/w) of glucose in this solution?
Show Hint
- 40
- 25
- 20
- 10
The Correct Option is C
Solution and Explanation
Step 1: Let total moles = 1 mole. Given:
- Mole fraction of glucose = 0.0244
- Mole fraction of water = 0.9756 So, moles of glucose = 0.0244 mol, and moles of water = 0.9756 mol.
Step 2: Use molar masses.
- Molar mass of glucose (C$_6$H$_{12}$O$_6$) = 180 g/mol
- Molar mass of water (H$_2$O) = 18 g/mol Mass of glucose = \( 0.0244 \times 180 = 4.392 \) g
Mass of water = \( 0.9756 \times 18 = 17.5608 \) g
Step 3: Calculate weight percentage of glucose. \[ w/w % of glucose} = \frac{4.392}{4.392 + 17.5608} \times 100 \approx \frac{4.392}{21.9528} \times 100 \approx 20% \]
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