Page 116 - Elements of Chemical Reaction Engineering 3rd Edition

88 Rate Laws and Stoichiometry Chap. 3

In this reaction, 2 mol of reactant forms 2 mol of product. When the number
of reactant molecules forms an equal number of product molecules at the same
temperature and pressure, the volume of the reacting mixture will not change
if the conditions are such that the ideal gas law is applicable, or if the com-
pressibility factors of the products and reactants are approximately equal.
For liquid-phase reactions taking place in solution, the solvent usually
dominates the situation. As a result, changes in the density of the solute do not
affect the overall density of the solution significantly and therefore it is essen-
tially a constant-volume reaction process. Most liquid-phase organic reactions
do not change density during the reaction, and represent still another case to
which the constant-volume simplifications apply. An important exception to
this general rule exists for polymerization processes.
For the constant-volume systems described above, Equation (3-25) can
be simplified to give the following expressions relating concentration and con-
version:

v= vo

Concentration as a
function of
conversion when
no volume change
occurs with (3-26)
reaction

( 3
c, = c,, a,+-x

Example 3-4 Expressing = hj(X) for a Liquid-Phase Reaction

Soap consists of the sodium add potassium salts of various fatty acids such as oleic,
stearic, palmitic, lauric, and myristic acids. The saponification for the formation of
soap from aqueous caustic soda and glyceryl stearate is
3NaOH(aq) + (C,7H3SCOO)3C3 H, --+ 3C,, H3,C0ONa + C3 %(OW3

Letting X represent the conversion of sodium hydroxide (the moles of sodium
hydroxide reacted per mole of sodium hydroxide initially present), set up a stoichi-
ometric table expressing the concentration of each species in terms of its initial con-
centration and the conversion X.

Solution
Because we are taking sodium hydroxide as our basis, we divide through by the sto-
ichiometric coefficient of sodium hydroxide to put the reaction expression in the
form