I,VDUSTRIAL A N D ENGINEERIiVG CHEMISTRY
July, 1931
803
A Weight Per Cent-Mol Per Cent Nomograph' Herbert Waterman 20 S E A X CAvB., ~ NEWYORK,N.
H E calculations incidental to the construction of thermal diagrams in metallography and phase-rule work are laborious. The experimental work is done on the basis of proportioning the components by weight. The results are usually represented on the basis of mol relation, the formation of compounds and variation in physical properties being shown best on such a diagram. It is the aim of the nomograph presented herewith (Figure 1) t o facilitate the transformation mol per cent-weight per cent for any binary system. This nomograph may also be used for similar transformations in ternary systems. The nomograph is based on the relation
T
a 100 ';i
x =
a
100
(1)
-a
;?+B where A = molecular weight of substance A B = molecular weight of substance B a = weight per cent of A x = mol per cent of A, corresponding to a Equation 1 may be transformed into 100
-x
X -A= B 100 - a
a
which is used for the construction of the nomograph. 1
Received March 7, 1931.
WEIGHT PERCENT
Y.
Given any binary system, with A and B the molecular weights of the components, a pivot point may be obtained, unique for this system, a t the intersection of the center line of the nomograph with a straight line joining the values of A and B, laid off on their respective scales. Any straight line drawn through this point will join equivalent mol and weight per cent of A, as indicated in Figure 1. Thus, after the pivot point is located, the drawing of the one line only is required to transform mol per cent to weight per cent or vice versa-a much simpler procedure than arithmetic calculation. For a given ternary system, the components being of molecular weights A , B, and C, two pairs of components are taken, and their respective pivot points located. For example, A-B and A-C may be taken. Given a point e (Figure 2) located on a ternary weight per cent diagram, draw two straight lines from the vertices B and C through e, The ratio of A and B is constant along eC, the point f indicating the relative weight per cent. This may be transformed into the corresponding mol per cent by the nomograph, point k. Similarly, point g, representing the weight, per cent relation of A-C may be transformed into point n,. The intersection of kC and mB, the point h, will represent the composition in mol per cent corresponding to e in weight per cent, The accuracy desired determines the size of the nomograph, which may be constructed to fit the needs of any one on the basis or Equation 2. The component scales are logarithmic, while the per cent scales are plotted as log (100 - z/z).
MOL PERCENT
NOMOGRAPH
1.4
-- ee
6
20 3 84 90
-
-- 80
4000 0'3-1 3000 a4--: 2000
1- 75
a6 --
14.0 -_ 40
20.01-
3o
6
zoo0 - .- 0.4
3Ooo 1- a3
4000
-
9 1 1
Figure 1
1.0
Mol Per Cent Figure.2
