Relative Weights of Phases Present in a Heterogeneous System at Equilibrium W. M. SPICER and J. S. METCALF Georgia School o j Technology, Atlanta, Georgia
w
HEN the temperature and composition of a system are such that two phases are present a t equilibrium, both the composition and relative weights of the bases can be obtained from the tie lines. For example, consider the system of two components, B and C, as represented in the figure. A system a t temperature TI composed of D per cent B consists a t equilibrium of two phases; the "C" phase containing A per cent B and the UBW phase containing A ' per cent B. Furthermore, Weight of "B" Phase - Length A D Weight of "C" Phase Length DA'
(1)
Only one of the more familiar textbooks of physical chemistry1 gives a proof of this relation and this one for the special case where one phase is a pure component. Some books state, "It can be shown . . ," some say, "It is easy to show . . . ," and others simply state the relation as a fact. The proof of this proposition is neither so obvious nor so difficult that i t should be omitted. A proof follows. Notice that
Multiplying (2) by lOOD and (3)by 100 (100 - D) yields (100 - A')Dy (100
+ (100 - A)Dz = (100 - D)Dw
- D)A1y + (100 - D)Az
=
(100
- D)Dw
(100
- A W Y + (100 - AIDS = (100 - DM'Y + (100 -
(100 - A)Dz
- (100 - D)Az = (100 - D)A1y - (100 - A')Dy
(7)
lOODz - ADS A'Dy
- lO0Az + DAz = IWA'y
- DA'y - IOODy
or Weight of "B" layer - Length AD Weight of "C" layer Length DA'
Assume u = Total weight of mixture y = The weight of "B" layer z = The weight of "C" layer
Then
+ wt. of C i n "C"
layer = total weight Temp
and similarily wt. of B in "B" layer of B
+ wt. of B in "C"
layer
=
total weight
I MILLARD, "Physical~hemi~try for colleges." 5th ed., McGrawHill Book Co., New York, 1941, p. 382.
(6)
on rearranging
= Percent B in "B" layer = Per cent B in "C" layer = Per cent B in total mixture
wt. of C i n "B" layer of C
(5)
Then, from (4) and (5)
.
A' A D
(4)
+ (8)
