finding molecular weight or formula from ionization of weak acid?

Question

A weak monoprotic acid (HA) solution consisting of 8.169 grams of the weak acid and 100ml of water has a freezing point of -0.384 degrees celsius. The acid was determined to ionize in the solution to 50%, meaning that 50% of the acid molecules ioniaed to H+ and A- anion. The acid was determined to consist of 14.70% carbon, 65.09% chlorine, 19.59% oxygen and 0.62% hydrogen. What is the molecular formula of this weak acid?

Answer 1

Trichlorethanioc acid, C2Cl3O2H, although to display the formula more structurally, would be CCl3COOH. Two carbons. With three chlorines on one carbon and an O-O-H group on the other.

How did I solve it? Set up a spreadsheet with those weight fractions, divided each by atomic weight (gives numbers proportional to mole fractions). And then trail&error plugged in multipliers of all those "weight fractions" until they were all whole numbers. The multiplier that worked was 163.34, the molecular weight of the compound.

Then I googled "C2Cl3O2H" and it popped up.

For my technique, the FP depression and extent of ionization was extraneous. The wt percentages lead to molecular formation, (using atomic weights).