200 
In neither case is the vapor saturated with the volatile acids of butter 
fat during the period of distillation and the liquids in the still are made 
up of water and the insoluble fatty acids. 
The vapor pressures of the volatile acids differ and their solubility in 
water and fatty acids influence the water of distillation. 
Of two acids having approximately the same vapor pressure, the one 
which is least soluble in the mixed liquid will distill the faster. 
Combining the factors, solubility in water and in the fatty acids, a 
mathematical expression for the rate of distillation becomes only ap- 
proximately true. 
Theoretically,’ if we do not keep the volume constant as is the case in 
the R.-M. process of distillation, that is by making no addition to the liquid 
in the still during distillation, 
; cl y 
The equation is pet = fie 
dx x 
Log y=a Log x+c or y= 
“ 
and integrating we get 
xe 
y equals amount of volatile acids left in solution and x amount of 
liquid left in still, the original amount being taken as 1. 
On the other hand, if the volume is kept constant as is the case in 
steam distillation x becomes constant. 
In this case we consider the quantity of water removed to the quantity 
of volatile acids left in the still. 
: ; ; dy : ; 
We then write equation — _——_ — ay. Integrating we get the equation 
dx 
—Log y=ax+c, or y= » 
ax 
y = amount of volatile acide left in solution, original amount being 
taken as 1; x = amount of water and volatile acids distilled. 
The above equations do not take into account the condensation in the 
still. 
1H. D. Richmond, Analyst, 1908. 
S. Young, fractional distillation. 
