When 70.4 g of benzamide (C,H,NO) are dissolved in 850. g of a certain mystery l

Question

When 70.4 g of benzamide (C,H,NO) are dissolved in 850. g of a certain mystery liquid X, the freezing point of the solution is 2.7 C lower than the freezing point of pure X. On the other hand, when 70.4 g of ammonium chloride (NH CI) are dissolved in the same mass of X, the freezing point of the solution is 9.9 °C lower than the freezing point of pure X. Calculate the van't Hoff factor for ammonium chloride in X. Be sure your answer has a unit symbol, if necessary, and round your answer to 2 significant digits.

Explanation / Answer

moles of benzamide = mass / Molar mass of it = 70.4g / ( 121.14g/mol) = 0.58 mol

Molality = moles of solute ( benzamide) / ( solvent mass in kg)   = 0.58 mol / ( 0.85kg) = 0.6837

we have formula dT = i x Kf x m , where dT = change in freezing point = 2.7C , i = vantoff factor = 1 for non dissociable solutes , Kf = freezing oint constant of solvent , m = 0.6837

hence 2.7C = 1 x Kf x 0.6837m

Kf = 3.949 C/m

we use this Kf value for calculating i for NH4Cl , where moles of NH4Cl = ( 70.4g/53.491g/mol) =1.316 mol

molality = ( 1.316mol) / ( 0.85kg) = 1.5484 , dT = 9.9

hence 9.9 = i x 3.949C/m x 1.5484 m

i = 1.62

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