The relative amount of unsaturation in a fat or oil is expressed as an iodine
number. Olive oil, for instance, is highly unsaturated and has an iodine
number of 172, while butter is much less unsaturated and has an iodine number
of \(37 .\) Defined as the number of grams of \(\mathrm{I}_{2}\) absorbed per 100
grams of fat, the iodine number is based on the fact that the carbon-carbon
double bonds in fats and oils undergo an addition reaction with
\(\mathrm{I}_{2}\). The larger the number of double bonds, the larger the amount
of \(\mathrm{I}_{2}\) that reacts.
To determine an iodine number, a known amount of fat is treated with a known
amount of \(\mathrm{I}_{2}\). When the addition reaction is complete, the amount
of excess \(\mathrm{I}_{2}\) remaining is determined by titration with
\(\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}\) according to the equation
$$
2 \mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}(a q)+\mathrm{I}_{2}(a q)
\rightarrow \mathrm{Na}_{2} \mathrm{~S}_{4} \mathrm{O}_{6}(a q)+2
\mathrm{NaI}(a q)
$$
Knowing both the amount of \(\mathrm{I}_{2}\) originally added and the amount
remaining after reaction, the iodine number can be calculated. Assume that
\(0.500 \mathrm{~g}\) of human milk fat is allowed to react with \(25.0
\mathrm{~mL}\) of \(0.200 \mathrm{M} \mathrm{I}_{2}\) solution and that \(81.99
\mathrm{~mL}\) of \(0.100\) \(\mathrm{M} \mathrm{Na}_{2} \mathrm{~S}_{2}
\mathrm{O}_{3}\) is required for complete reaction with the excess
\(\mathrm{I}_{2}\).
(a) What amount (in grams) of \(\mathrm{I}_{2}\) was added initially?
(b) How many grams of \(\mathrm{I}_{2}\) reacted with the milk fat, and how many
grams were in excess?
(c) What is the iodine number of human milk fat?
(d) Assuming a molecular weight of 800 , how many double bonds does an average
molecule of milk fat contain?
