T H E PARTIAL MOLAL T'OLUNES O F WATER A S D SALT I S SOLUTIOXS O F T H E -4LKdLI HALIDES* BY VICTOR K . LANER AND T . H. GRONWALL
I n the course of a research on the extension of the Debye-Huckel theory of strong electrclytes to concentrated solutions, it was found necessary t o establish empirical formulas in terms of the molality nz for t,he partial molal volumes a\-, an, of water, and aV, a n of salt, for the solutions of the alkali halides, the calculations being based on the density measurements of Baster and Wallace.' The empirical formulas2 are water: aV/dn, = a. salt: aY,'dn = bo
+ a? m2 + a3 m3 + a4 m4, + bl m + r n 2 + b3 mJ, 1i2
(1)
and Tables I and I1 give the coefficients in these formulas for the fifteen alkali halides. each at the temperatures oo, 25' and 5 0 . 0 4 ~ . The third column in the tables gives the value of v i a t the highest experimental point used in computing the coefficients. and extrapolation by means of the formulas lieyond this value of 712 is not advisable. Fig. I gives the graphs of the partial molal volume of the salt a t z j 3 , computed from Table 11. The formulas are derived as folloiTs: Let, T' be the volume of the solution containing no mols of water and 71 mols of salt; then the molality t n is given hy 111 = 5 5 . j o 8 1 n nor (2) anti the volume y of solution containing one mol of water by y = V/no (3) From ( 2 ) it follo~vsthat
am _ -an, and from (3) and
m a m - ;.;.5081, no' a n no
(4)
(4)
Kow 7 7 ~anti y may lie computed directly from the volume 1- of mlution and nciphts of n a t e r and salt iiieaiured by Raxter and 1Vallace. .I curve of the fouith degiee y = -Lo AI in - A? ni? 1A, 1113 A 4 in* 16)
+
+
"('ontrilution from the ('heniical Laboratories oi C01uml~i:iI-nivercity, S o . jz:. C;. I-'. Uayter a n d C. C. TVallace: J. Ani. ('lieni. $or,, 3 9 , i o 1916). 1.en.i; atid I~andall1 "Tliermodvnamica," 1 1y2,a give i~ nunilier of inqmious graphical mcthodi for calculating partial mohl volumes an(1 discuss their thermodynamic utility. I
~
394
VICTOR K . LAVER A S D T. H. GROSWALL
3
.= 0
X
0 0
C
0 C
"103
N
0 0
0 0
O h ? + ex h * v. W v, * e 0 0
. 0. 0.
0 0
.
.
.
- K T -K$ m
- h a N
-
r
? ? ? 0
0
0
I
l
l
s x c: -i= 0 0
.
.
c: CI
.
- .m . x-
s
- x i =
0
3
h
- 5 )
.
0 0
.
O
0
.
0
0
.
:%
.
C
h
N N
13
N
-
e
CI -
3c
0 9 0
6
.
CI
N
0
.
0
0 0 0
.
0
0
0
0
O
X
-
0
0
0
0
0
0
I
l
l
+++ +++ +++ O
6
N
N X -
0
0
0
0
0 0 0
* ? + " 1 3 -
,
.
.
I
l
l
I
l
l
-
I
-.
-
- - o c,
tc
.
.
0" e
-
0 0
0 0
6 0
0
v, 0
.
.
N
.-
I
c
.
V'
% .0:
0
0
s13x
0 0
0
0
r:
0 0
.
0
;.$ :. .
0 0
.
0
3 3 X
COW,*
.
0
i
2
O
- 0 0 0 0 0
6
-
0
*
I
0
l
0
l
.=--
PARTIAL MOLAL VOLUMES O F WATER AND SALT
'
V 2 - h 6
W
-
a
- 6 h N
;
W
W
0
0
0
0
0
0
I
l
2
-
0 0
I
l
" ; - h
W - V ,
N
b r n W X - om00 w e n 0 0
l
0 0
0 0 0
0
.
53 C
" i W
c
N
u R N 0 0 . .
N
0
0
0
I
l
l
w,
03m
- u
0
.
" ;
"i
. O. N.
O
oc_mm c
-
0
tc 0
h
Z 3 " i - O W
G 6 f b
0 - 0
e
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
l
I
l
l
l + l
O
h
'4.2"
iCOj vi b
I
53"
0
N vi 3 N
N
m u 0
- o m 0
0
I
0
0
++ 0
l
I
m * e + L o . -
n
v, h
m m
X
' c o o
0 0 0
l
- C " .t
- 0
oc
r n 6
- N P -
6u
3 - 3
* - m
cow
"i N e 6
0 0
6
h
-
N
v. 6 e
-
N
h
v?
I
b -
0 0
0
0
-
0
0
,
0
.
0
w
6
0
PI
0
rnc
0 0
0
0 0
e o 3 w o w
b
-
l
+ I 1
.
$7$ T T $ T $ $
0
w. b
l
e
3
0 0 0 0
I
2 -w,0x
-
m v, ".?om
W
03
++ 0
0
-,
00
- m
-
N
6
0
0
0
E:: 0 0 .
.
0
,
.
.
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
I
l
l
I
l
l
I
l
l
I
l
l
I
l
l
I
l
l
I
l
l
W
N
0 0 0
X x - w O
.
O
.
"i
rn N
.
m 0 3 5 m
-
h
3
. w.
"i
m
-
O
9 0 0
p m c O
.
N
03
.
0
0
6
0
v N, v 0,
0 9 0
O
.
r
c
N
6
..
;%
e .
r
.
",
0
6
o m 0 N
c
Y e
;t
r( v
v.
,"
.
.
6 b -
. e. -.
0
.
b e N
0 0 0
'xx - w 0
.
0
.
" ;
". N
.
3 -
,ex
0 9 9
cox "
O
.
O
.
N N " :
.
.
.
rc,
" ;
".
\=
0330
N
o. o . w. x x m
.
e
- - -
b e l t . w. m 10
"'
v, w,
-
0
0 0 0
c. w. c.. c.,
0
6
0 0
0 6 0 0
0
6
0 0
0
0
v. 0 N w.
0
v N. W 0
0 v N. v 0.
0
-
0
0
0 - - c
N X r, . . P .
0
0 0 0
- 0
m
N
w.
,
t.33 el ";ti 0 0 0
3
w
C
"=,5"02 5 2 "'-5
3
0 0 0
N
m m c
"i
e e e
-
L
v. h
x m m -
r-hh
c
c
h x
W N W
w.
*
6
0
.
-..e
-.om
W
0
0
TTT $$$
6 6 X t . 0
0
h - c c '
0
0 he, ? N O
.
6
n 3 m
N
e
0
O
0
N
N
0
N
o m h c o o
-
vie*
m bm m
0
N
2 %
0
G
0
"X N
-
0
+ l I
* w n
b";
~
0
l
m o v ?
m - 0 h " i r ow03
395
0. 0. 0.
N
6
0 0
P I
. . . m
e
0 0 A
6 0 0
N
LC
VICTOR K. LAMER A S D T. H. GROSWALL
3 96
.-.
V . X X
r , 0 0 0 0 0
0 0
L ? V *
c -3rc P , N N
0
0
0
In0
0
0
cc
w.v,
m o w ,
0
VIP-%
v.*
- h X - 0 0 0 0 0
*
W
0
3 N
0
0
+++ +++ +++ +++ +++ +++
N W
m
-
0
0
0
3 -3
x h c.
e x e. *.
0
0
* C
0 c
0
0
0
vi 3. "Lc
m
r-
0
0
0
0
0
0
c c S - N O x c x I C W c . . .
c C - ..
++S
m
.
.
.
0
0
0
0
0
0
0
0
0
0
0
0
ci
I
l
l
I
l
l
I
l
l
I
l
l
I
m.3
h
.
- -
cc h e
rt .r
:++ v,
.
cc'r0 v. S
3 . I e *SI.
- - -
.
.
.
01 N
d
S
N
c1
. e
.
I.
I.
+ + T
*.
0 0
h h
.
h h
* m r c
.
c,
,..
* c'
!P,
LT
r,
.
+++ I.
.
C
.
-
I.
.
v, e c c c N
+++ +++ -e\=
0
.
2
.
0
,
h b y 3
G
O
6
0
W,
0
CI
LT
0 0 9
- L
,
T
-
.
y
.
0"
c c .c
3 v. ri
C. o. d.
-
+++ e
CI
is: "1 * - 2 . . , 0
v, I.
-
h.3
X C .3
h
a. = ." .
P - L f
0 C m .G O 0
.
G
*.
l
-* .
L?
I-
I . "
M
-. l
c1 c, c
d CI
.
L.
.
r-rtc
Sft
ci
N
3
0
N
I.
-.
1
.
.
x
0
.
5
-x?
