280 OUTLINES OF PHYSICAL CHEMISTRY
account of the number of equivalents of each substance in the medium in which the reaction is taking place. The volume of this medium does not then influence the values of the constants k and k x .
First Example. Equilibrium of Esterification and of Saponification. — When we bring together a equi- valents of acetic acid, b of alcohol, a x of ethyl acetate, and bi of water, stationary equilibrium is established after a few hours if the operation be performed at 100°C. (or after a few days if it take place at the ordinary temperature). A simple titration tells us • then what quantity of acetic acid is still free, and from this we can calculate the active masses of the other three substances.
From the equation of equilibrium :
k(a— x) (6— x) = kxfa+x) (b { +x)
we find :
k_ = ( flt+s) {b Y +x)
k x (a— #) (6— x)
k In order to find the value of the ratio ^- we first take the simplest case, in which a=&=l and a 1 =6 1 =0. The
equation then becomes :
k{l-xf=k l x' i ,
and
k x ~~ (1-xf
Now, when we allow one equivalent of acetic acid to act on one of alcohol, esterification takes place to the extent of 66 per cent. The value of x is therefore 0*66, and
If Guldberg and Waage's theory is true, this ratio must be constant. We can, therefore, calculate what the value of x (the degree of esterification) will be if the initial quantities (a, b 9 a u b u ) of the substances be varied. The
�� �
