Minimum molecular weight approach for determining empirical

Describes the determination of empirical formulas from "minimum molecular weight," the molecular weight divided by the number of atoms of an element p...
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H. James Harwood University of Akron Akron, Ohio


Minimum Molecular Weight Approach for Determining Empirical Formulas


corresponding minimum molecular weight (MMW)' can be calculated for each element. present in a molecule. This quantity is simply the molecular weight divided by the number of atoms (n) of the element present in the molecule. The minimum molecular weight can also be calculated from the weight percentage of the element (%E) in the compound by using equation (Z), where MW and A W refer to molecular weight and atomic weight, respectively. E q u a tion (2) results from rearranging equation (I), which is commonly used t o calculate the weight percentage of an element, %E: in a compound.

formula is then given by the factor required to obtain the empirical formula weight from the minimum molecular weight, i.e., EFW/MMW. 4) A final comparison of calculated and an* lytically determined compositions is recommended as a check. Examples

The first example is based on analytical results obtained by Liebig for gallic acid. Fieser and Fieser4 have described the application of the conventional method to these same results. Examination of the MMW multiple table in Example 1shows instantly that Example 1

The minimum molecular weight is the smallest molecular weight consistent with a given analytical result and both the empirical formula weight (EFW) and the molecular weight should be integral multiples of this quantity. This is illustrated by equations (3) and (4), which are derived from equations (1) and (2). These relationships form the basis of the method proposed in this paper.




46.08 ( d i l l . )




1hpil.irill Iurrnula weight: "



l f " I :

3 4 6 f i 7 S 7 2 . 4 ! K G 121 145m1!)3 X'2.i I l l 13X(IGD)l!U . . . 63.6 I l l 3 l:ii a 2 0 0 . . . . . . 2 .. . . .



CiIf6Oi ( 17111

Example 2

I n using minimum molecular weights to determine empirical formulas, the following procedure is followed: 1) Minimum molecular weights are calculated for each element present using formula (Z).3 2) Multiples of the various minimum molecular weights are then calculated and recorded in tabular form. These calculations can be done rapidly mith a slide rule if the index is set on the minimum molecular weight. (This setting is obtained in step 1.) 3) The empirical formula weight is obtained by examining the table for approximately constant numbers. If reliable analytical results are being considered, these numbers should agree within a few per cent. The number of atoms of each element in the empirical Minimum molecular weights are commonly employed in protein chemistry, hut their use in general or organic chemistry is not usually encountered. 1 The symbol 7 represents the ratio of molecular weight to empirical formula weight (MWIEFW). The ratio, n/r, thus is equivalent to the number of atoms of the element in the empirical foimula. Except for the fsctor of 100 involved, this quantity is the reciprocal of the quantity calculated a t the start of the conventional &pproach.



Journal of Chemical Education





P 0

16.62 44.22 (diff.)

187 36.2

Saponification equivalent MW ( R a t ) Empirical formula weight: 181-188 Empirical formula: CsHlrPOs (184) Moleculrtr formula: CrHlaPOs

MMW Multides

187(1)' 181 (5) 217 (6) 183 187

CIHBOsis a better choice than CnH,03,hut that CeHsOl and C3H,06 cannot be dismissed casually. The best agreement is obtained with C?HeOs, however, particularly if the empirical formula weights based on carbon and oxygen are considered more reliable than those based on h y d r ~ g e n . ~One of the advantages of this 4 FIESER, L. F., AND FIESER,M., "Advanced Organic Chemistry," Reinhold Publishing Company, New York, N. Y., 1961, pp. 5-8. This is also discussed in other Fieser texts. 6 This consideration is not universally valid, hut it is reliable in this situation, where the molecule has a high oxygen content and a low hydrogen content. An error of 0.3% (absolute) in the hydrogen analysis would cause MMW and MMW multiples to change by 10% (relative), but a similar error in the estimation of the oxygen content (by difference) would cause MMW multiples to change by only about 1%.

method is that it provides an indication of the reliability of the empirical formula selected. As experience is gained with this method, certain shortcuts will become obvious. For example, the M M W multiple table need not be filled out entirely; if multiples of the highest M M W are first calculated, then M M W multiples obtained from other analytical results must be in the vicinity of these values to be of interest. The slide rule can be employed very effec-

tively in these calculations. The reader will appreciate this if he repeats Example 2, taken from the writer's research records. The alternate method for determining empirical formulas proposed in this article has been used by the writer for over five years in preference to the couventional procedure. The most important feature of the proposed method is that it simplifies the determination of complex empirical formulas.

Volume 42, Number 4, April 1965