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?
10% w/w solution of glucose in water means that 10 g of glucose in present in 100 g of the solution i.e., 10 g of glucose is present in (100 - 10) g = 90 g of water.
Molar mass of glucose (C6H12O6) = 6 × 12 + 12 × 1 + 6 × 16 = 180 g mol-1
Then, number of moles of glucose = \(\frac{10}{180}\)mol
= 0.056 mol
∴ Molality of solution = \(\frac{0.056\;mol}{0.09 kg}\)
= 0.62 m
Number of moles of water = \(\frac{90g}{18g\;mol^{-1}}\)
= 5 mol
(xg) = \(\frac{0.056}{0.056 + 5}\)
Mole fraction of glucose = 0.011
And, mole fraction of water xw = 1 - xg
= 1 - 0.011 = 0.989
If the density of the solution is 1.2 g mL-1, then the volume of the 100 g solution can be given as
= \(\frac{100g}{1.2mL^{-1}}\)
= 83.33 mL
= 83.33 x 10-3 L
∴ Molarity of the solution = \(\frac{0.056\;mol}{83.33 \times 10^{-3}L}\)
= 0.67 M