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Q.(a) What do you mean by elevation of boiling point ? Derive the relationship between elevation of boiling point and molecular mass of solute. [2+3=5]

(b) An aqueous solution of glucose (m = 180) containing 12 g of it dissolved in 100 g of water was found to boil at 100.34 degrees C, while the boiling point of pure water was 100 degrees C. Calculate the molal elevation constant for water. [2]
Odisha ChseOdisha CHSE +2 Science Board Exam 2024Subjective· 7mImportance★★★★★
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Elevation of boiling point is a colligative property (delta-Tb = Kb x molality); using the given glucose data, the molal elevation constant of water works out to Kb = 0.51 K kg/mol.

(a) Elevation of boiling point: When a non-volatile solute is dissolved in a volatile solvent, the vapour pressure of the solution is lowered, so a higher temperature is needed for the vapour pressure to equal atmospheric pressure (i.e. to boil). The boiling point of the solution (Tb) therefore becomes higher than that of the pure solvent (Tb-degree). This increase, delta-Tb = Tb - Tb-degree, is called the elevation of boiling point.

Derivation of the relation with molar mass: since delta-Tb is a colligative property, it is directly proportional to the molal concentration (molality, m) of the solute:

delta-Tb proportional-to m, i.e. delta-Tb = Kb x m

where Kb is the molal elevation constant (ebullioscopic constant) of the solvent, a constant characteristic of the solvent (its value when m = 1 molal). If w2 grams of solute of molar mass M2 are dissolved in w1 grams of solvent, the molality is:

m = (w2 x 1000) / (M2 x w1)

Substituting into delta-Tb = Kb x m:

delta-Tb = (Kb x w2 x 1000) / (M2 x w1)

Rearranging to isolate the molar mass of the solute:

M2 = (1000 x Kb x w2) / (delta-Tb x w1)

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