Alfred P. Mills University of Miami Coral Gables, Florida
Derivation of Equations for the Interconversion of Concentration Units
In line with the recent upgrading in the teaching of the principles of chemistry it would seem appropriate that the handling of concentration units and their interconversion be treated in a manner more like that encountered in physical chemistry. Several of the more recent general chemistry textbooks are using symbolic definitions of concentration units, but have not dealt with the derivation of the equations relating them. These derivations involve only the simplest algebra; thus they aren't open to criticism on the basis of the difficulty of the mathematics involved. Symbols in this area are not well standardized. Those chosen here are commonly nsed. The first step is to symbolically define the concentration units (the examples are for binary systems) : W%,
=
100W1
w, . + , W;-
1M)h =-.--
v
e
= - 10OOnzd~
m
=--
X*
= nr nn
w,+ w9 lOWn.
w, n1
+
W,
solvent (g) solute (K) nt = males solvent na moles solute MI = = mol. wt. solvent M n = mol. wt. solute Y = volume solution (ml) d = density solution (g/ml) or - wt. % solute molarity m = molality X 1 = mole fraction solute
W2
= wt. = wt.
Y' I
The equation relating any two concentration units may be obtained by a two-step process: 1) Solve each of the two symbolic definitions for a common term which contains all of either the solute or solvent. 2) Equate the parts equal to this term, cancel out the remaining extensive terms, and solve for the concentration unit desired. Example I-Derive a formula for converting weight % to molan'ty: From the definition of weight Ojo :
Presented before the Division of Chemicd Eduoation at the 148th Meeting of the American Chemical Society, Chicago, Illinois, August 1964.
314
/
Journol of Chemical Education
From the definition of molarity :
+
Note that the common term ( W , W J contains all of the solvent. Failure to remove all of one of the constituents a t this point may result in a much more difficultsolution. Equate the terms which are qua1 to W l Wp:
+
Cancel out the other constituent (it has to cancel), simplify, and solve for the concentration unit desired:
Example 2-Derive a formula for converting mole fraction to molality: The common term in this case is not so obvious, but nl or W ,will easily serve: From the definition of mole fraction:
From the definition of molality:
Equating:
The procedure described above has been nsed successfully with two honors sections of general chemistry. The total time required was no more than is usually spent on concentration units, and it is believed that the long-range gain is greater.
