Question

How do you calculate the molar fraction of glucose C₆H₁₂O₆ in a solution of water if the vapor pressure of water is 700mmHg in 100 degree celsius?

Answer 1

At 100 ^oC,(Boiling point of water) Vapor pressure of water is 760 mm of Hg (i.e. 1atm). By definition of boiling point.

Hence Vapor pressure of pure water (solvent) = P^o = 760 mm of Hg

On addition of solute Glucose (C6H12O6) vapor pressure of solution = P = 700 mm of Hg.

Say X be the mole fraction of water (solvet).

The partial pressure of solution (P), Vapor pressure of solvent (P^o) and mole fraction of solvent (X) are related as,

P = (X) x P^o

Let us put all known values and solve it for X

700 = (X) x 760

X = 700/760

X = 0.9211

Mole fraction of solvent = 0.9211

In a solution of single solute,

Mole fraction of solute + Mole fraction of solvent = 1 (unity)

Hence,

Mole fraction of solute (Glucose) = 1 - Mole fraction of solvent (water)

Mole fraction of solute (Glucose) = 1 - 0.9211

Mole fraction of solute (Glucose) = 0.0789.

Mole fraction of glucose is 0.0789.

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