### Application of phase rule to three component systems

Coming to my exams point of view,they are over. But I’d forgot to share a cardinal question which has been asked in the physical chemistry paper.It was about the application of phase rule to a three component system.
Well, apart from the one and two-component systems, this can be analysed through equilateral triangle method of Stokes and Roozeboom.In order to show the phase behaviour of a three component system on a two-dimensional diagram, it is necessary to consider both pressure and temperature as fixed.The phases of a system as a function of the composition can shown on a plane diagram.Whether there is a single phase or two phases will depend upon the composition of the components of the system.For this ternary system, the phase rule equation is:
F=C-P+2
where, C=3 so the equation becomes,
F=3-P+2
(or) F=5-P
If pressure and temperature are kept constant, two degrees of freedom are reduced so that we can write as,
F=3-P(reduced phase rule equation)
If three phases are presenti.e.,P=3 then,
F=3-3=0
When two phases are present,
F=3-2=1 (monovariant)
When there is only one phase,
F=3-1=2(bivariant)
Although, many types of three-component systems are possible, most of them are quite complicated.But, we can discuss a simple one containing water,chloroform and acetic acid in which all the components are liquids.In this system, water and acetic acid, and acetic acid and chloroform are miscible with each other.But at ordinary temperature, water and chloroform are only slightly soluble in each other.Thus, this system involves only a single pair of partially miscible liquids namely ater-chloroform.The equilibrium diagram of this system can be visualised and the system is at 291K.

Please click the above image to enlarge.
If we add very small amount of water to chloroform, a homogeneous solution is obtained because water and chloroform are partly miscible.But if we increase the amount of water, the mixture separates into two layers:
1.containing a solution of chloroform in water
2.containing a solution of water in chloroform
Suppose, now we add acetic acid to this mixture, the acid distributes itself b/w the two layers and it increases the miscibility of water and chlorofom.If sufficient acetic acid is added, the two layers change into clear solution containing all the three liquids.
The changes in the miscibility of water and chloroform on adding acetic acid can be seen in the figure above.The points ‘a’ and ‘b’ represent the compositions of two layers when water and chloroform are mixed.On adding acetic acid to this mixture, the compositions of these layers changefrom a,b to a1,b1.The line joining a1 and b1 is called a tie line.As more amount of acetic acid added increases, the tie lines a1,b1;a2,b2;a3,b3 etc become smaller and ultimately reduced to ‘D’.The point ‘c’ represents the overall composition of the mixture when sufficient acetic acid has been added and we have a single phase containing all the three liquids.The area above adb shows a single phase and the area enlosed within adb shows two phases.