Density of a Binary Mixture:
A Classroom or Laboratory Exercise
dhether it be by volume or by mass.' As rs classroom exercise the following hypothetical problem can be used. However, it would be more desimhle if a variety of cylinders of two metals mch as aluminum (d = 2.70 g cm-9 and copper (d = 8.94 g cm-9 were available and an actual experiment performed to illustrate the procedure. and pore solid B (d = 9.00 g cm-') is Suppose that a. series of binary mixtures of pure solid A (d = 1.00 g prepared. Suppose further that, in order to simplify the calculations somewhat, each mixture has a total mass of 100 g. (Alternatively, a mixture of 100 cma total volume could also be used.) By varying the percentage of A by mass in steps of 10, the accompanying tableis constructed by the application of the following equat,ion Averaxe Densities of Mixtures of Two Pure Solids
where DA = density of pure A, DB = density of pure B, DT = average density of the mixture, M A = mass of A in the mixture, Me = mass of B in the mixture, MT = mass of the mixture, li\ = volume of A in the mixture, and VB = volume of B in the mixture.
Procedure
(a) Plot e. curve with density of the mixture on the Y axis and % of A by voltune on the X axis. ( b ) Determine the equation for the Curve. ( c ) Determine from the curve and from the equation the density of a mixture of A and B containing 35.0% of A by volume. (d) Using the same axes as those used for part (a) plot density versus % of A by mass. (e) Determine whether the following expression
is equal to the volume percentage or the mass percentage of the less dense or of the more dense component. It should be noted that the method cannot be applied to solutions, which are usually non-ideal hecsuse of contraction or expansion accompmying solution. Furthermore some solutions such as HBOcHzO at high HaSol concentrations give one density corresponding to two different. concentrations of HsSOd.
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W. R., A N D HEVESY,GEORGE, AND BERQLUND, VIGGO,J. Chem. Soe. (London), 125, 2372 (1924). SCAOELLER, POWELL, A. R. "The Analysis of Minerals and Ores of the Rarer Elements" (3rd ed.), Charles Griffin and Co. Ltd., London. 1955. D. 146. Drsn~.HARVEY."Quantitative A n ~ l l i E l e m e n t aPrincides and Practice," Oakland Street ~cience'p'ress,Ames, 10w& 1970, p. 44. "Handbook of Chemistry andPhysics" (48th ed.), The Chemical Rubber Co., Cleveland, Ohio, 1967, p. F-6.
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H. I. FEINSTEIN
Volume 49, Number 2, February 1972
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