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Question
A solution of glucose in water is labelled as 10% w/w, what would be the molality and mole fraction of each component in the solution? If the density of solution is 1.2 g mL−1, then what shall be the molarity of the solution?
Solution
Let mass of solution = 100 g
∴ Mass of glucose = 10 g
Mass of water = 100 – 10 = 90 g = 0.09 kg
No. of moles in 10 g glucose = `10/180`
= 0.0555 mol
No. of moles in 90 g H2O = `90/18`
= 5 moles
Volume of solution = `(100 "g")/(1.2 "g mL"^(-1))`
= 83.33 mL
= 0.0833 L
Molality = `"Number of moles of solute"/"Mass of solvent in kg"`
= `(0.0555 "mol")/(0.09 "kg")`
= 0.617 m
x (Glucose) = `"Number of moles of solute"/"Number of moles of solution"`
= `0.0555/5.0555`
= 0.01
∴ x (H2O) = 1 − 0.01 = 0.99
Molarity = `"Number of moles of solute"/"Volume of solution in L"`
= `0.0555/0.0833`
= 0.67 M
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