Question

A solution contains 11.70 g of unknown compound (non-electrolyte) dissolved in 50.0 mL of water. (Assume...

A solution contains 11.70 g of unknown compound (non-electrolyte) dissolved in 50.0 mL of water. (Assume a density of 1.00 g/mL for water.) The freezing point of the solution is -7.01 ∘C. The mass percent composition of the compound is 38.70% C, 9.74% H, and the rest is O.

What is the molecular formula of the compound?

Express your answer as a molecular formula

So far I got CH3O as my empirical, but I can't seem to figure out how to find the molecular formula

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Answer #1

Let the molality of the solution be m

Given,

Freezing point = -7.01 degree C

=> Depression in freezing point = delta Tf = 7.01 degree C

Kf for water = 1.86

We know that,

delta Tf = Kf x m

=> 7.01 = 1.86 x m

=> m = 3.77

The molality of the solution is 3.77 m

Molality = Moles of solute / Mass of solvent (in kg)

Mass of water = 50 x 1 = 50 g = 0.05 kg

=> 3.77 = Moles of unknown compound / 0.05

=> Moles of unknown compound = 3.77 x 0.05 = 0.1884 moles

Mass of unknown compound = 11.7 g

=> Molar Mass of unknown compound = 11.7 / 0.1884 = 62.1 g / mol

Given,

The mass percent composition of the compound is 38.70% C, 9.74% H, and the rest is O.

Assuming 100 g of compound

Mass of C = 38.7 g

=> Moles of C = 38.7 / 12 = 3.225

Mass of H = 9.74

=> Moles of H = 9.74 / 1 = 9.74 moles

Mass of O = 51.56 g

=> Moles of O = 51.56 / 16 = 3.2225

Dividing each moles by 3.225, we get

Moles of C = 1

Moles of H = 3

Moles of O = 1

=> The emperical formula of the compound is CH3O

Emperical Mass = 12 + 3 + 16 = 31

n = Molar Mass / Emperical Mass = 62.1 / 31 = 2

=> Molecular Formula = C2H6O2

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