Nomographs for Determining Molecular Weights by the Freezing Point and Boiling Point Methods W. S . GILFOIL, Omega, La.
100 90
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15
600
500
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300
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200
4
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80
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50
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10
0.0005 0.0004
FIGURE2. MOLECULAR WEIGHTNOMOGRAPH
m = 1000- K X g / G AT
10
11
FIGURE1. NOMOGRAPH
In case a value falls off the chart, as in the case of I, for water, divide by 10 (for simplicity's sake); running the line from 53.9 through 100' C., we obtain a value on the & line which, when divided by the same number, 10, gives the proper value of I(, (Figure 1). In the formation of the second nomograph (Figure 2), as there are four variables, a turning line is necessary. Its use may be illustrated by the following example: Experimental data give a ratio g/G of 0.010, the difference in temperature between the freezing point of solvent and solution was l.OOOo C., and K/ was 10.0. Draw a straight line from 10 on the K line to 0.01 on the g/G line. From the point where this line intersects the turning line, draw a straight line through the m line and the point 1.000 on the AT line. The value of m is then read as 100, the proper value.
T
HE determination of molecular weights is a common step after the ultimate organic analysis of a compound. AS a
rule the data obtained are less accurate than the nomographs, which are satisfactory for all practical purposes. The method makes use of two sets of analogous equations, The boiling point equations are the same as those given here for the freezing point method, and the same charts are used for both. K,
=
To2 / 503 11
m = 1OOOKf X g / G X AT,
(1)
(2)
where Kj represents the molal depression of the freezing point To,the freezing point of the solvent in degrees Kelvin 1 , the latent heat of fusion in calories per gram the weight of solvent g, the weight of solute, expressed in the same units m, the molecular weight of the solute AT,, the observed freezing point depression
6,
RECEIVED June 19, 1935.
The correction of temperature to the Kelvin scale is taken care of in the charts, so that Centigrade temperature is used. 228
