Heat of Concentration and Boiling Point Elevation of Sea Water

pound H 2 0 -f V2 pound concentrated sea water —• 1 pound normal sea water .... 160. 180. 200. 220. TEMPERATURE - °F. Figure I. Heat of concentra...
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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...