I don't believe I have a correct answer, but I'll describe the process and you might spot the error. The equation for combustion isn't balanced, since we don't know the structure of the fatty acid. The problem is further complicated since we do not know how much of the oxygen is supplied by O2 and that which comes from the fatty acid. So we need to work with the facts we do have. I decided to calculate the moles of H and C that were formed from the H2O and CO2, since we have their masses and molar masses. We have to ignore the oxygen, since we don't know it's source. But if we have the moles, and masses of the C and H, we know they came from the fatty acid. The difference, in grams, is the oxygen that came from the fatty acid.
Moles CO2: 46.33g/44.01 g/mole = 1.053 moles CO2
Moles H2O: 16.3 g/18 g/mole = 0.9056 moles H2O
From these two we can obtain the grams of both C and H that came from the fatty acid.
- 1.053 moles CO2 = 1.053 moles C, at 12g/mole means 12.63 grams C was from the fatty acid
- 0.9056 moles H2O = 0.9056 moles H2 atoms from the fatty acid, at 2g/mole means 1.81 grams of H was from the fatty acid.
So now we know:
12.63 grams C
1.81 grams of H
Unknown g of O
16.71 g of the fatty acid
This means (16.71-(12.63+1.81)) = 2.27 grams O from the fatty acid.
Convert these masses from the fatty acid into moles:
(12.63 grams C) /12g/mole = 1.053 moles C
(1.81 grams H) / 1 g/mole = 1.81 moles H
(13.27 grams O) / 16 g/mole = 0.142 moles O
Now we need to find a ratio amoung these value to make them whole numbers. This is where I had a problem - I don't see an easy way to make them all whole. The closest I get is:
That gives a molar mass of 242, close, but not the reported value of 238 g/mole. However, I do find pentadecanoic acid, a long chain fatty acid with a molecular weight of 242, so I'll blame the discrepancy on my lab partner.
I hope this helps, and please let me know if you find an answer that works for the 238 g/mole number. We could kick out 4 hydrogens and replace them with double bonded carbons in two locations, but stll, the data doesn't support that.