Heat of Concentration and Boiling Point Elevation of Sea Water R. L. CLARK, K. J . NABAVIAN, and L A. BROMLEY
Downloaded by MIT on July 1, 2013 | http://pubs.acs.org Publication Date: January 1, 1960 | doi: 10.1021/ba-1960-0027.ch004
Department of Chemical Engineering, University of California, Berkeley, Calif.
Values of the heat of concentration and heat capacity of sea water near room temperature have been measured experimentally. The heat of con centration values compare favorably with those calculated from the vapor pressure data given by Arons and Kientzler by use of the Clapeyron equa tion. The heat capacity agrees with the values re ported by Cox and Smith. Calculated values for the heat of concentration and boiling point eleva tion from 77° to 302° F. at salinities up to 9% are presented in both tabular and graphical form.
A k n o w l e d g e of t h e t h e r m o d y n a m i c a n d p h y s i c a l p r o p e r t i e s o f s e a w a t e r i s n e e d e d i n t h e a n a l y s i s of a n y process f o r c o n v e r t i n g sea w a t e r t o f r e s h w a t e r . C h a m b e r s (8) has s u m m a r i z e d [ m a i n l y f r o m S v e r d r u p et al. (6) ] m a n y o f t h e p h y s i c a l p r o p e r t i e s of sea w a t e r . N o d a t a were a v a i l a b l e o n t h e h e a t o f c o n c e n t r a t i o n of s e a w a t e r . A s i m p l e c a l o r i m e t e r w a s b u i l t f o r t h e m e a s u r e m e n t o f t h i s h e a t effect n e a r r o o m t e m p e r a t u r e , a n d l a t e r w a s u s e d t o m e a s u r e h e a t c a p a c i t i e s o f sea s a l t s o l u t i o n s . T h e h e a t effect m e a s u r e d w a s f o r t h e reverse o f c o n c e n t r a t i o n — i . e . , m i x i n g : y
2
p o u n d H 0 - f V2 p o u n d concentrated sea water —• 1 p o u n d n o r m a l sea water ( 3 . 5 % s a l i n i t y ) (1) 2
ΔΗ84.9 F . = 0.0416 ± 0.004 B . t . u . / p o u n d n o r m a l sea w a t e r — i . e . , solution cools o n m i x i n g 0
T h e sea w a t e r w a s o b t a i n e d f r o m L a J o l l a a n d w a s c o n c e n t r a t e d t o h a l f i t s o r i g i n a l w e i g h t before d i l u t i o n . J u s t e n o u g h s u l f u r i c a c i d w a s a d d e d t o p r e v e n t t h e p r e c i p i t a t i o n o f solids d u r i n g t h e c o n c e n t r a t i o n . T h i s p r o c e d u r e m a y a l t e r t h e salt c o m p o s i t i o n s o m e w h a t , b u t i t is r e p r e s e n t a t i v e o f m o s t e v a p o r a t i o n processes. T h e measured heat capacities a t 2 3 ° C . (73.4° F . ) w e r e : N o r m a l sea water ( 3 . 5 % s a l i n i t y ) .
C , = 0.964 ± 0.01 B . t . u . / l b . / ° F .
C o n c e n t r a t e d sea water ( 7 . 0 % s a l i n i t y ) .
C = 0.995 ± 0.01 B . t . u . / l b . / ° F . p
T h e s e v a l u e s differ c o n s i d e r a b l y f r o m e a r l y m e a s u r e m e n t s (2, 3). R e c e n t d a t a of C o x a n d S m i t h g a v e C = 0.954 B . t . u . / l b . / ° F . f o r n o r m a l s e a w a t e r a t 2 3 ° C . (4). F r o m o u r v a l u e s a n d those f o r w a t e r , t h e r a t e o f change o f AH w i t h t e m p e r a t u r e (for R e a c t i o n 1) is c a l c u l a t e d t o b e : p
21
In SALINE WATER CONVERSION; Advances in Chemistry; American Chemical Society: Washington, DC, 1960.
22
ADVANCES IN CHEMISTRY SERIES
(ίΕγ) · ° ' 73
4
F
=
ACp
~
=
0
0
3
=*=
3
0
0
1
B
t
-/
u
l
b
-
s
e
a
water/
0
F.
T h e same q u a n t i t y d e t e r m i n e d f r o m v a p o r p r e s s u r e d a t a c a l c u l a t i o n s is : AC
-0.023
=
P
I n v i e w o f t h e e x p e r i m e n t a l difficulties t h a t arise i n m e a s u r i n g heats of m i x i n g above room temperature, no further experimental w o r k was a t t e m p t e d . H i g h t e m p e r a t u r e heats o f m i x i n g w e r e c a l c u l a t e d f r o m t h e v a p o r p r e s s u r e of A r o n s a n d K i e n t z l e r ( i ) as f o l l o w s :
data
N e g l e c t i n g l i q u i d v o l u m e a n d a s s u m i n g i d e a l gas b e h a v i o r f o r t h e v a p o r , t h e C l a p e y r o n e q u a t i o n f o r p u r e w a t e r a n d f o r sea s a l t s o l u t i o n s b e c o m e s
Downloaded by MIT on July 1, 2013 | http://pubs.acs.org Publication Date: January 1, 1960 | doi: 10.1021/ba-1960-0027.ch004
dPi dT
Ριλι RT
=
(2)
2
dP dT
_ P^2 ~ RT
2
(3)
2
S u b t r a c t i n g E q u a t i o n 3 f r o m E q u a t i o n 2 (at t h e same t e m p e r a t u r e )
^
V
^
-
è
i
^
-
^
(
4
)
defining ΔΡ = Λ -
P
(5)
Δλ = λ -
^
(6
2
2
di^n dT D i v i d i n g b y Δ Ρ and rearranging d In AP a
A p l o t o f I n AP vs. ^
,_1 RT
.
ΓΑΡ RT
2
(7)
L
-λι
X l
λι J
Γ
1 "
1
Ρ Δλ~ λ,ΔΡ 2
(8)
w i l l h a v e a slope of — λ ^ Ι —
f r o m w h i c h Δλ m a y b e d e t e r m i n e d . T h e v a l u e s of Δ λ w h i c h were o b t a i n e d a r e :
77 Chlorinity, % 10 20 30 40 50
Temp., ° F . 167 212
122
257
302
Water Evaporated at Constant Composition, B . t . u . / L b .
0
-0.09 -0.18 -0.27 -0.39 -0.51
0.52 1.10 1.80 2.60 3.50
0.63 1.36 2.20 3.24 4.40
0.65 1.46 2.37 3.38 4.52
0.42 0.92 1.50 2.19 2.98
0.18 0.41 0.66 0.96 1.31
T o c a l c u l a t e t h e heats of m i x i n g i t i s necessary t o k n o w t h e r e l a t i v e p a r t i a l m o l a l e n t h a l p i e s of t h e s a l t a n d t h e w a t e r i n t h e sea s a l t s o l u t i o n s . water, L
ly
This quantity for the
is a r r i v e d a t as f o l l o w s :
F o r pure w a t e r b o i l i n g a t s a t u r a t i o n t e m p e r a t u r e , T a n d pressure P t h e heat of v a p o r i z a t i o n i s t h e difference b e t w e e n t h e e n t h a l p y o f t h e v a p o r p e r p o u n d , H , a n d the enthalpy of the l i q u i d water per p o u n d , H , o r s
1}
V1
L1
λι = Hvi — HLI
In SALINE WATER CONVERSION; Advances in Chemistry; American Chemical Society: Washington, DC, 1960.
(9)
CLARK ET AL—HEAT OF CONCENTRATION AND BOILING POINT ELEVATION
23
T h e h e a t o f v a p o r i z a t i o n f o r a sea s a l t s o l u t i o n b o i l i n g a t t h e same t e m p e r a t u r e a n d a t i t s o w n s a t u r a t i o n v a p o r p r e s s u r e , P , i s t h e difference b e t w e e n t h e e n t h a l p y of 2
the v a p o r per pound, H , V2
a n d t h e e n t h a l p y p e r p o u n d of t h e w a t e r i n t h e salt s o l u
tion,^. λ
2
= Ηγ2 — HL2
(10)
C o m b i n i n g E q u a t i o n s 6, 9, a n d 10 a n d f r o m t h e d e f i n i t i o n of L
ly
U
= (H
L2
-
H ) = (Hv2 L1
Hvi) -
one o b t a i n s
Δλ
(11)
T h e q u a n t i t y (H — H ) is t h e n e g a t i v e o f t h e e n t h a l p y change o n c o m p r e s s i n g ( i s o t h e r m a l l y ) t h e v a p o r a b o v e t h e sea s a l t s o l u t i o n f r o m p r e s s u r e P t o p r e s s u r e P : V2
vl
2
x
P
Downloaded by MIT on July 1, 2013 | http://pubs.acs.org Publication Date: January 1, 1960 | doi: 10.1021/ba-1960-0027.ch004
2
H -H V2
= f
V1
( ^ )
T
(12)
d P
Pi But
U s i n g a v i r i a l e q u a t i o n o f state f o r t h e v a p o r V =
+ Β
(14)
T h e s i m p l e e q u a t i o n of C a l l e n d a r (S) f o r t h e s e c o n d v i r i a l coefficient w a s u s e d . Β = 0.01602
-
26.3
^^y° ]cu. / 3
ft./lb.
(16)
S u b s t i t u t i n g E q u a t i o n s 13 t o 16 i n t o E q u a t i o n 12 t o c a l c u l a t e {H
V2
—H ) a n d V1
t h e n s u b s t i t u t i n g i n t o E q u a t i o n 11, t h e v a l u e s of L o b t a i n e d a r e : 1
77 inity, % 10 20 30 40 50
Temp., ° F . 212 167
122
257
302
Water i n Solution, B . t . u . / L b .
0
+0.09 +0.18 +0.27 +0.40 +0.52
-0.52 -1.09 -1.79 -2.57 -3.47
-0.64 -1.44 -2.34 -3.33 -4.46
-0.61 -1.32 -2.14 -3.15 -4.29
-0.39 -0.86 -1.40 -2.05 -2.79
-0.14 -0.31 -0.51 -0.74 -1.01
T o c a l c u l a t e t h e r e l a t i v e p a r t i a l e n t h a l p y of t h e salts i n sea w a t e r i t w a s necessary to integrate the G i b b s - D u h e m equation g r a p h i c a l l y .
jdL
2
= -
fj^dt*
w h e r e ^ is t h e w e i g h t r a t i o o f w a t e r t o s a l t . iV2
In SALINE WATER CONVERSION; Advances in Chemistry; American Chemical Society: Washington, DC, 1960.
24
ADVANCES IN CHEMISTRY SERIES T h e c o m p o s i t i o n c o n v e r s i o n s u s e d are : Chlorinity, %o 10 20 30 40 50
N /N ,
Salinity,
X
2
Lb./Lb.
54.3 26.7 17.5 12.8 10.1
1.81 3.61 5.42 7.22 9.03
A s i t w a s i m p o s s i b l e t o i n t e g r a t e t h e G i b b s e q u a t i o n t o t h e zero of L
x
were a v a i l a b l e a t e x t r e m e l y l o w salt c o n t e n t s ) , lowest
data
available—i.e., 1 0 % chlorinity. 2
have a n y meaning.
With
2
(no data
are referred t o the state
only
I n t h e f o l l o w i n g c a l c u l a t i o n s o n l y differences
were
o
differences of L
a l l v a l u e s of L
t h i s n e w reference
Downloaded by MIT on July 1, 2013 | http://pubs.acs.org Publication Date: January 1, 1960 | doi: 10.1021/ba-1960-0027.ch004
used. T h e heat effect o n m i x i n g f o r t h e r e a c t i o n P u r e water + (sea water)« —• (sea w a t e r ) NIR l b . water}
_
\N
I P
lb. water/
(17)
p
1 l b . n o r m a l sea water
is g i v e n b y AH
= AL = N L 2p
N
2p
+ NipLip
-
NL 2R
2R
-
NL lR
lR
- 0
= N R — pounds of salt
2 P
(18) (19)
2
Rearranging, AH
= N (L 2P
2P
-
L ) 2R
+ iVipLip -
NIRLXR
(20
T h e heat of c o n c e n t r a t i o n — i . e . , n e g a t i v e of t h e heat of m i x i n g f o r R e a c t i o n 1, c a l c u l a t e d f r o m E q u a t i o n 2 0 — i s s h o w n i n F i g u r e 1.
^ 2.0 fO
N O T E : POSITIVE HEAT OF CONCENTRATION INDICATES ABSORPTION OF H E A T WHEN CONCENTRATING ISOTHERMALLY.
I...
