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?

Given:

10% w/w solution means that if solution is of 100g then 10g of glucose is present in it [[10 × 100]/100] and the amount of water present in it is [100-10], M_w = 90g.

Density, d = 1.2g/ml

To find: Molality and Mole Fraction of Each component

Formula:

Density, d

Molality

Mole Fraction of component

Molarity, M_o

Solution:

Calculation of Molality:

⇒ Molecular mass of Glucose, [C₆H₁₂O₆] = [6 × 12] + [12 × 1] + [6 × 16]

= 72 + 12 + 96

= 180g

⇒ Number of moles of Glucose, N_g = [10/180]

= 0.0556 moles

⇒ Molality

⇒ Molality

= 0.6177 m

≈ 0.62 m

Calculation of Mole Fraction:

⇒ Molecular Mass of Water, [H₂O] = [2 × 1] + [16 × 1]

= 2 + 16

= 18g

⇒ Number of moles of water, N_w = [90/18]

= 5 moles

⇒ Mole Fraction of Glucose,

= 0.011

⇒ Mole Fraction of Water,

= 1 – 0.011

= 0.989

Calculation of Molarity:

From density we can find out volume.

⇒ Volume, V = [100/1.2]

= 83.33 ml

⇒ Molarity

Molarity, M = 0.667 M

≈ 0.67 M

Therefore the answers obtained in the numerical can be summarized in following table: