[Rutherford]

Of course.
xCHOH(CH₂OH)₂ 2xHCHO+xHCOOH
yCH₂(OH)-CH(OH)-C₂H₅ yHCHO+ yC₂H₅CHO
Now it is said that, that only aldehyde groups reacted with KMnO₄, so HCOOH won't react.
5C₂H₅CHO+2MnO₄^-+6H⁺ 5C₂H₅COOH+2Mn²⁺+3H₂O
5HCHO+4MnO₄^-+12H⁺ 5CO₂+4Mn²⁺+9H₂O
From the 1st reaction, 0.4y of the permanganate reacted and from the 2nd one, 1.6x+0.8y reacted, so it is:
1.6x+1.2y=0.028
92x+90y=1.64
x=1.536·10^-2
y=2.53·10^-3
Molar share of glycerol is therefore is 85.86%. Did I do this correct?

[Dan]

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 CO₂ 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 CO₂, 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 CO₂), because formaldehyde is oxidised to CO₂ in two steps via formic acid:

Formaldehyde + oxidant Formic acid        (eq 1)
Formic acid + oxidant CO₂                     (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 CO₂, then it follows that any formic acid in the system will also affect the titration.

[Rutherford]

Yes, it is unrealistic, but as I see ambiguities are the main part of IChO problems. Your way seems much more appropriate. Thanks for the help.