130 Mr. J. A. Wanklyn on Fractional Distillation. 



heat received by A and B, must also express the relative quanti- 

 ties of A and B in the vapour evolved on boiling, and conse- 

 quently in the distillate. 



Now let us pass from the hypothetical case of liquids of equal 

 volatility to the actual cases of liquids of unequal volati- 

 lities. In such cases the composition of the vapour which 

 escapes when the mixture is boiled will be different from the 

 composition of the original mixture ; and putting v for the co- 

 efficient of volatility of A, and v' for the coefficient of volatility 

 of B, we have av and bv 1 for the relative quantities of A and B 

 which escape in the form of vapour on distilling the mixture. If 



we put 8 for an infinitely small first distillate, we have j~, 



7 J£ 



for the quantity of A in the first unit of distillate, and 5- 



^ J ' av + bv 



for the quantity of B in the first unit of distillate. Collecting 



the formulae, we have :• — 



a + b = relative quantities of A and B in the original mixture. 



av + bv' = relative quantities of A and B in the first unit of 

 distillate. 



■ j—, — quantity of A in first unit of distillate. 



av + bv ^ J 



7 /^ 



n = quantity of B in first unit of distillate. 



av + bv' ^ J 



After the escape of the first unit of distillate ( = $) the com- 

 position of the liquid left behind in the retort will have altered, 

 and the relative quantities of A and B will now be represented 

 not by a and b } but by the formulas 



and 



(avB \ 

 av + bv'/ 



\ av-\- bv'/ 



In order to find the values of A and B in ihe second unit of 

 distillate, these formulas must be substituted for a and b. It 

 will be obvious that as the distillation progresses, the composi- 

 tion of the successive units of distillate must progressively alter. 

 If v be greater than v 1 , then the quantity of A in the units of 

 distillate must progressively diminish ; if v be less than v' } the 

 quantity of A in the units of distillate must progressively increase. 

 Obviously, too, the greater the difference between v and v 1 , the 

 more rapid the alteration in the composition of successive units 

 of distillate, 



