with temperature, which points to a very wide compositional range. This is
indeed the case, also because simple hydrogenation not only saturates
double bonds but also induces shifts in double bond position and cis–trans
isomerization. More directed hydrogenation is also possible, and an
example is the margarine fat in the figure. Here the aim is to have the
proportion solid at a constant level of about 0.4 in the range of 5–25 8 C, this
to keep the firmness constant. It is seen that this is indeed better the case
than for the shortening or the milk fat.
Interesterificationleads to a (more) random distribution of fatty acid
residues over and in the triglyceride molecules. Depending on the natural
configuration of triglycerides, it can lead to a higher or to a lower fraction
solid at room temperature.
Fractionationcan be achieved by letting a fat partly crystallize at a
given temperature and then separating the crystals from the remaining oil.
Of course, the opposite is also applied, i.e., the blending (mixing) of various
fats and/or oils.
Question
What would be the molar entropy of fusion of tristearate in its most stable form? Try
to derive this value in two completely different ways.
Answer
- At the temperature of fusion (melting), the difference in free energy
between the molten and the crystalline state is zero. Hence we can readily derive that
DSf¼DHf/Tm. From Table 15.2 we obtainTm¼ 738 C andDHf¼212 J?g^1. The
chemical formula of SSS is C 57 O 6 H 110 , leading to a molar mass of 891 Da. Hence
DHf¼189 kJ?mol^1 ;Tm¼346 K. We thus obtainDSf¼546 J?mol^1 ?K^1. - Equation (2.1) states thatS¼kBlnO, whereOis the number of ways in
which a system can be arranged. For a triglyceride this includes the number of
conformations that the molecule can assume, which causes virtually the only
difference in entropy between the crystalline and the molten state. From the formula
of SSS we derive that there are 59 C 22 C and C 22 O bonds. Assuming that for every
bond three different conformations can occur, we arrive at O¼ 359 possible
conformations. For the entropy per mole we have to takeR(¼8.314 J?mol^1 ) rather
thankB, and we calculate thatDSf¼521 J?mol^1. This comes quite close to the
precise value derived above from measurable parameters, although the value derived
forOis a crude approximation.