My answer of 67% is wrong - I misread the question and thought it was butane-2,3-diol - sorry about that.

When I do the calculations for butane-1,2-diol

*and* assume that formic acid is oxidised to CO

_{2} by permanganate, I get 44% glycerol (mole ratio). The method is the same as yours, but I use 2x + 1.2y= 0.028 because I think the formic acid formed in the periodate cleavage of glycerol will react with permanganate.

*If* it is true that you can ignore the formic acid from the oxidative cleavage of glycerol

*and* that formaldehyde is oxidised to CO

_{2}, then your answer is correct. However, I do not think you can do that - my opinion is below if you are interested:

If you are assuming that formic acid does not react with permanganate, then you should work on the assumption that formaldehyde is oxidised to formic acid (not CO

_{2}), because formaldehyde is oxidised to CO

_{2} in two steps via formic acid:

Formaldehyde + oxidant

Formic acid (eq 1)

Formic acid + oxidant

CO

_{2} (eq 2)

If we can ignore the formic acid produced in the reaction of periodate with glycerol, then we are saying that eq 2 does not happen. Therefore any formaldehyde from the periodate step is oxidised only to the formic acid level based on the first assumption. If we do this, then the equation is 0.8x + 0.8y = 0.028. Solving the simultaneous equations gives a nonsense answer.

I admit that the question does say that the "aldehyde groups were titrated...", but I think this is unrealistic. If permanganate oxidises formaldehyde to CO

_{2}, then it follows that any formic acid in the system will also affect the titration.