T H E APPARENT VOLUMES AND APPARENT COMPRESSIBILITIES OF SOLUTES IN SOLUTION. I1 CONCENTRATED SOLUTIONSOF LITHIUMCHLORIDEAND BROMIDE ARTHUR F. SCOTT
AND
G. L. BRIDGER
Deparlment of Chemistry, The Rice Institute, Uouston, Texas Received April 11, 1955
In the first paper (11) of this series it was shown that, from the standpoint of the apparent molal volume and compressibility, concentrated solutions of lithium chloride and bromide differ significantly from solutions of other strong electrolytes. It was impossible, however, with the limited data a t hand to determine a t what concentration these solutions become abnormal or to study the nature of the irregularity. The object of this paper is to report new measurements of the density and compressibility coefficient of concentrated solutions of these salts and to present a more complete picture of the anomalous properties of these solutes. The results of seven new experiments are summarized in table 1. No detailed description of these experiments will be given here, because the procedure followed throughout was the same as that described fully in a previous communication (10). It should be noted, however, that new stock solutions of both lithium chloride and lithium bromide were prepared for these experiments, and that all other solutions investigated were prepared by dilution of weighed portions of these stock solutions. From these data have been calculated the apparent molal volumc 9, thc apparent molal compressibility ( E + f), and the volume, concentration of the solute in the several solutions. Values of these calculated quantities are given in table 2, which may be regarded as a supplement to table 2 given in paper I. With the exception of some of the f values, the method of calculating these quantities is the same as that already described (11). The modification in the method for calculating f may be outlined briefly. I t will be recalled that by definition 9 =
v - ThVr
and
-
H = I . . ! ! ?=
dP
vp - ?21vlp,
1031
1032
ARTHTJR F.
sco'ni
AND
c.
L. BRIDGER
where 'v = volume of solution containing 1 gram-mole of solute, V I = volume of 1 gram-mole of pure water a t the temperature of thc s o htion, nl = number of moles of water present in the solution, and P, = compressibility coefficients of solution and water, respectively. 6, however, is a function of two independent variables, pressure and concentration, 9 =
w,c)
and n e can write for the total differential
Dividing through by dP, we get
The quantity f is the last term of this expression
whence
B+f
=
-($)
C
The method,of calculatingf, given in paper I, was for thc spcciul ca.sc whew 4 is a linear function of ci a t constant pressure (Masson's rule). For the concentrated solutions of the lithium halides where this relationship is not valid, it has been necessary to proceed as follows. The numerical value a4 of the slopc -was found graphically from a plot of 4 against c. Further, ac
since c = lOOO/V it follows that
dc = -1000dV dP p-p
= 1000 P =
7
CP
The product cp affords a simple means of getting the numerical value of the second term necessary for the evaluation off. It, should perhaps be noted here again that the calculated values of derived from our data refer t o solutions under a pressure of 200 metric atmospheres, and that therefore
1033
VOLLThI&S OF' SALTS: IN SOLUTION
the f values must bc calculated for the same condition. This requirement was met in the calculation of the f values gilren in table 2. The graphical method of computingf just described has also been applied to the calcalation of thefvalues omitted from table 1of the first paper (11). For the sake of completeness these new values as well as some recalculated
SOLUTION N O ,
1
PER 'IDNT
OF SALT
I
TABLE 1 Table of results DENSITY AT
35°C.
I
px
108
A V E R A G E DEVIATION
Lithium chloride solutions
I
1 2 3
41 ,020 37.003 27.450
1
1,25597 1.22536 1.15772
20.44
i::
~
0.01
