How do I find the various formulae for something, given Freezing point depression information?

An unknown compound contains only carbon, hydrogen, and oxygen. Combustion analysis of the compound gives mass percents of 31.57% C and 5.30% H. The molar mass is determined by measuring the freezing point depression of an aqueous solution. A freezing point of -5.20°C is recorded for a solution made by dissolving 10.56 g of the compound in 25.0 g water. Determine the empirical formula, molar mass, and molecular formula of the compound. Assume that the compound is a nonelectrolyte. (Type your answer using the format CO2 for CO2.)

you have to use the formula for freezing point depression and some simple algebra to figure out the empirical formula of the compound (assume oxygen takes up the rest of the percentage).

assume 100 g of compound to begin with, and then use molar masses to find relative moles to each other–>the empirical formula

31.57 g C/12 g/mol = 2.63 mol C/2.63 = 1 mol
5.3 g H/1 g/mol = 5.3 mol H/2.63 = 2 mol
(100-31.57-5.3) g O/ 16 g/mol = 3.95 mol O/2.63 = 1.5 mol

empirical formula = CH2O1.5 = C2H4O3 (mw=76 g/mol)

t=kmi

kf of water= -1.86 C/m
i organic cpd = 1

-5.2 = -1.86 * m
2.8 m= x moles cpd/ 0.025 kg water
x=0.070 moles
10.56 g / x g/mol = 0.070 mol
molar mass = 151 g/mol

151 g/mol / 76 g/mol = 2

molecular formula * 2 = empirical formula
C4H8O6

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