Normality and Molality -The
Expendables
Both nomnalitv and molalitv receive aDpreciable attention in both introductory a i d advanced courses. Normality is considered, principally, in relation to volumetric analysis and molality in regard to colligative properties and thermodynamic relationships. It is submitted that neither of these expressions is necessary or useful and that attention should, instead, be directed to more fundamental corresponding concentration expressions, molarity and mole fraction. There are two objections which may be raised in common against normality and molality. The first is that these additional definitions, rather than simplifying and unifying their respective topics, tend to distract and confuse. A second criticism is that they are particularly susceptible to misuse. A third objection may be leveled against the molality function-that i t is inconsistent with the Law which it is nurnorted to serve. Normality and Molarity
What can be done with normality that cannot be done as well or better with molarity? The principal liiitation in the assignment of a value of normality is that the value is not unique; rather, it depends on conditions. As an illustratiou, the following questions from a prominent text in quantitative analysis are quite relevant: "Why is the term '1 N H,POn' ambiguous? Modify the term to make it meaningful." but, on the following page, "How many grams of solute are there i n . . . 37.5 ml of 0.109 N HaPOa?" The ambiguity referred to in the first question concerns the fact that under the usual conditions for titration of phosphoric acid two distinct end points and a very poor third end point can be found. Thus, the "normality" of 1 M phosphoric acid might be either 1 or 2, depending on the end point detection, but would not usually be 3; yet experience leads us to believe t,hat the expected answer for the second question presupposes complete neutralization. Similarly, the "normality" of diprotonic bases usually depends on the particular conditions. I n all such situations, however, sufficient information is available to use the invarient (and pedagogically sounder) molarities of reactants. A similar situation exists for redox titrations. The number of electrons gained or lost frequently is not unique for the reagent, but depends on the other reactant(~)and the end point detection. The variability in the "normality" of a permanganate solution under acidic, basic, and neutral conditions exemplifies this case.' It is noteworthy that several presentations have already omit,ted or advocated against continued use of " n ~ r m a l i t y " ~it; is proposed that such advocacy and omission be made universal.
provocative opinion Molalitv and Mole Fraction
Molality, formulated to provide a concentration expression with temperature independence, is usually defined as the number of moles of solute per kilogram of solvent. The student is commonly introduced to this expression through freezing point depression or boiling point elevation. A linear relationship between changes in such colligative properties and the molality of the solute in an ideal solution is assumed, often based on a presumed linear relationship between mole fraction and the property in question. However, such proportionality does not exist and significant error may result in the interpretation of solution data unless this theoretical error is recognized. The fundamental relationships for colligative propert,ies are based on Raoult's Law: where pi is the vapor pressure of a species over a solution, piois the vapor pressure of the pure sample, andX, is the mole fraction of this component. Classical thermodynamic considerations of a solute in solution in equilibrium with a second phase allow formulation of the fundamental relationship between concentration and temperature?
where T is the temperature at which the solvent, A, of mole fraction XA undergoes the phase change; Tois the temperature at which pure solvent undergoes the change; AH is the enthalpy change for the process at the temperature T; and R is the ideal gas constant. Equation (3) provides an exact temperature change against which approximations can be tested. The more common approximations are: (1) XB is very small, hence, for a binary solution (XA = 1 - Xa), in (1 - XB) = - XB, hence Taken in part from a paper presented to the Division of Chemical Education a t the l52nd h.Ieet,ing of the American Chemical Saciet,~,New York, N. Y., September, 1966. ' The author is grat,efnl t,o a reviewer for pointingont a relevant lab ex~erimentbased on t,his m i n t : see SIENKO.M. J.. AND PLANE: R. A.. "Exoerimental dhemikt,rv." ~ 2 . 1 .~ c k r a w " , (%d , Hill Book ~ o .l ;n c . , ' ~ .Y., 1961, p. 173. * See, e.K., KIEFFER,W. F., "The Mole Concept in Chemistry," Ch. 6, Reinhold Publishing Corp., 1962. The author is grateful to Dr. K&er for also pointing ant that neither CHEMS nor CBA uses normality. The subject has also been dropped in syllabus for high schools in the State of New York. a See, e.g., CASTELLAN, G. W., "Physical Chemistry," AddisonWesley Puhl. Co., Ino., 1964, Ch. 13. Volume 45, Number 3, March
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(2) XB = n ~ / n * hence ,
which gives rise to the usual molality expression, AT = Kma
(6)
The predicted temperature changes are therefore:
Some values of the two approximations and the reference temperature change are giveniu the table and the figure. Predicted Tem~erature Changes (Units of RTToIAH) Comparison of vLues predicted from mole fraction leqn..(4')1 and malality [eqn. (591 versus theoretical change [eqn. (3')l
mole fraction fc
MOLE FWCTIM SOLUTE.XB
Eqvotion Error. Deviation from theoretical temperature change encountered on using mole fraction opproxirnotion [eqn. (4'11 w moldity opproximotion [eqn. (5'11 instead of the exact relotionship of [eqn. 13'11.
- a)
with mole fraction [eqn. (4')l should offerno m o r e a n d probably less--diiculty than the use of molality [eqn. (6)], hence simplification of equ. (3) could be done in terms of the former. Molalily and Thermodynamic Standard States
One should not expect proportionality between either mole fraction or molality and boiling point elevation or freezing point depression, hence discussions of deviations from linearity (e.g., with reference to calculation of activities) should always distinguish those deviations which are inherent in the approximations from those due to the system involved. A full consideration of the derivation of eqn. (3) is no more essential to its use in an introductory course than the normally ignored (and less correct) derivation of eqn. (6). Since the mole concept has become an essential part of most introductory chemistry comes, an approximate proportionality of temperature change
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LATIMER. W. H.. "Oxidation Potentials" (2nd Ed.), PrentieeHell, Inc., 1952. See, e. g., HILDEBRAND, J. H., AND SCOTT, R. L., "The Solubility of Non-electrolytes,'' (3rd Ed.), Dover Publ. Ino., N. Y., 1964, p. 4. The author is indebted to Prof. E. H. Swift for providing helpful information concerning thin question.
The student's second encounter with molality is f r e quently through the Nernst Equation. Latimore used a 1 molal solution as the standard state for sol~tions,~ but his usage corresponds to a dual meaning of the term "molal" by chemists of the G. N. Lewis scientific family, viz. that of weight molal, corresponding to current usage of molal, and volumemolal, correspondingto what is now called molar.5 Thus, current use of molality in connection with standard states reflects confusion in usage; there is no physical basis for its use. Neither normality nor molality is necessary to describe chemical systems. Both lead to confusion and erroueous conclusions concerning the processes to which they refer. Therefore, it is proposed that both functions be deemphasized to the point of final omission from the teaching of chemistry. 1. J. Sacks State University College at Buffalo, New York 14222
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