The isothermal compressibility of seawater near one atmosphere

Deep-Sea Research, 1971, Vol. 18, pp. 1233 to 1254. Pergamon Press. Printed in Great Britain.

The isothermal compressibility of seawater near one atmosphere* F. K. LEPPLE~ and F. J. M~LLERO (Received 6 May 1971; in revised form 6 July 1971; accepted 14 July 1971)

Abstract--The isothermal compressibility of artificial seawater has been measured by a piezometric technique from 0 to 40%0 S in 5%0 intervals and from 0 to 40°C in 5 ° intervals. The measurements

were made at 17 bar increments to 34 bars and the data extrapolated to one atmosphere. Compressibility determinations on a Copenhagen seawater sample (,~35%oS) over the same temperature and pressure range yielded results that agreed with the artificial seawater results (within our experimental error of 4- 0.05 × 10-6 bar-l). The isothermal compressibility results at one atmosphere and 35700o are in excellent agreement with the values calculated from WILSON'S(1960) sound velocity data; however, our results disagree with the P - V - T data of E~MAN(I 908), NEWTONand KENNEDY(1965) and WILSONand BRADLEY(1968). The normalized compressibilities of Ekman show excellent agreement with Wilson's and our results. A theoretical equation for the compressibility of seawater as a function of chlorinity has been developed in terms of the apparent equivalent compressibility of the major ionic components of seawater. The theoretically calculated isothermal compressibilities of seawater at 25 ° agree very well with the experimental results (to within 4-0.09 × 10 -6 bar-l).

INTRODUCTION

HISTORICALLY, the agreement of the compressibility of seawater determined by various workers has not been satisfactory. The present-day tables of the specific gravity and volume of seawater are based on KNUDSEN'S(1901) tabulations of density at atmospheric pressure and EI(MAN'S (1908) determination of the mean compressibility of seawater. Ekman measured the compressibility of seawater at two salinities (31.13 and 38"83%0 salinity) at 200, 400 and 600 bars pressure and 0, 5, 10, 15 and 20°C. Ekman calculated the pressure in his studies using AS~AGAT'S(1893) results for the compressibility of pure water at 0°C. In 1958, Eckart questioned the precision of Ekman's compressibility results; due to the possibility of a 0-2 % systematic error in the pressure measurements (DEL GROSSO, 1959). Eckart estimated errors of 4-2 x 10- 4 cm3/g in the specific volume measurements of Ekman. LI (1967), however, has pointed out that Eckart made an error in pressure conversion and subsequently reached a pessimistic conclusion concerning Ekman's data. CREASE (1962) has calculated the specific volume of seawater using WILSON'S (1960) sound velocity measurements and Cox and SMITH'S (1959) heat capacity data. Crease's study has confirmed that Ekman's compression data between 200 to 600 bars are in agreement with his own calculations; however, the results near 1 arm disagree by 0.7% (Li, 1967). NEWTON and KENNEDY (1965) have determined the specific volume of seawater from 1 to 1300 bars (100 bar intervals) and from 0 to 25 ° (5 ° intervals). Li's calculations of the compressibility from their results show reasonable agreement with Ekman below 10 °, but Newton and Kennedy's compressibility values from 10 to 25 ° all appear to be too high. *Contribution N u m b e r 1370 from the University of Miami. tRosenstiel School of Marine and Atmospheric Science, Miami, Florida 33149.

1233

1234

F . K . LEPPLE and F. J. MILL~RO

WILSON and BRADLEY(1966, 1968) measured the specific volume of seawater for salinities between 0 to 40%0, from 0 to 40°C and from 1 to 1000 bars. Wilson and Bradley's specific volume data at high pressures agree with Newton and Kennedy's results to within 4-2 x 10 -4 cc/g. In summary, the tables (or equation of state) presently being used to determine the specific volumes of seawater yield results that are quite accurate at atmospheric pressure (better than 10ppm--Cox, MCCARTNEV and CULgIN, 1970); while the results for the specific volume at high pressures are not very accurate (4-200 ppm). Such errors in specific volume, although unimportant for geostrophic flow calculations, can be very important for the evaluation of hydrostatic stability in deep ocean waters. Recent advances in observational techniques allow the determination of temperature and salinity fields to a precision equal to or greater than the accuracy with which these properties can be related to the specific volume. Thus, there is a need for reliable specific volumes for seawater at high pressures. Some of the difficulties encountered in attempting to analyze the existing P - V - T data arise from the choice of various equations of state which the investigators have used to represent the data (FOFONOFF, 1962). The derived properties from these equations of state such as the thermal expansion (BRADSHAW and SCriLEXCI-mR, 1970; CALDWELLand TUCKER, 1970; and STURGES, 1970) and the compressibility (LI, 1967; MILLEROand LEPPLE,in preparation) are in doubt. Most previous workers have not demonstrated by calibrations with distilled water or other salt solutions that their experimental methods are adequately precise or accurate. Therefore, it is quite difficult to determine which data is reliable. In an attempt to resolve these problems, we have initiated a study of the P - V - T properties of seawater. In this preliminary work, we will report on our determinations of the isothermal compressibility of seawater near one atmosphere. We have also derived a semi-empirical formulation for the isothermal compressibility of seawater which is based on the summation of the (weighted) apparent equivalent volumes and compressibilities of the major ionic components in seawater. By using this approach, the volume properties (as well as other physical--chemical properties) of seawater are equal to the volume property of pure water and two components due to ionwater and ion-ion interactions of the weighted major ionic components of seawater.

EXPERIMENTAL

Methods

The isothermal compressibility apparatus used in this study was originally described by MILLERO, CURRY and DROST-HANSEN(1969). The apparatus consists of three basic units: a piezometer, a pressure cell (Fig. 1) and a temperature bath with regulating and monitoring equipment. The piezometer, C, is a cylindrical vessel, made of Coming type 7740 borosilicate glass whose total volume is approximately 410 ml. A precision bore capillary, E, (2 mm i.d. and 56 cm length) is fitted to the bottom of the piezometer. Calibration of the capillary is done by weighing various lengths of mercury (lengths determined with a cathetometer). The average value of the cross-sectional area of the capillary was found to be 0.03246 4- 0.00001 cmL Pressure cell, H, is constructed entirely of nickel-plated brass except for a glass

The isothermal compressibility of seawater near one atmosphere

1235

boiler tube which enables viewing of the upper capillary stem. Opening, D, which is fitted with a stainless steel Swagelok tee, serves as both the pressure inlet and the mercury exchange port. The chamber between the capillary and the boiler tube is open to the main pressure cell and thus the pressure inside and outside the piezometer is equalized during an experiment. Due to the presence of the glass boiler tube, measurements on this apparatus are restricted to a maximum of 35 bars.

I,.~OTNERMAL COMPRESSIBILITY APPARATUS

ZrE

I

Fig. 1. Diagram of isothermal compressibility apparatus. (A) Quartz crystal thermometer probe; (]3) piezometer support; (C) glass piezometer; (D) pressure inlet; (E) piezometer capillary; (F) magnetic stirring bar; (G) leveling feet; (H) nickel-plated brass pressure cell; (I) glass boiler tube. The interior of the pressure vessel, boiler tube not included, is filled with ethylene glycol which serves a threefold purpose: first, as a conducting medium for thermal transfer; second, as a hydrostatic pressurizing medium; and finally as a safety precaution to minimize the explosive effect if the pressure cell should fail. The entire compressibility vessel is submerged in a constant temperature bath (leveled by 3 bolts labeled G). Mixing inside the cell is accomplished by means of a magnetic stirring bar, F. The temperature of the bath containing the compressibility apparatus was regulated to -I-0.001°C with a Hallikainen thermoregulator. Temperature inside the cell is monitored on a strip chart recorder with a Hewlett Packard quartz crystal thermometer in order to determine when thermal equilibrium was reached before and after compression. The quartz crystal thermometer as supplied is capable of detecting temperature charges to 4-0.0001°C with an accuracy of -4-0"02°C. However, in this work the Hewlett Packard unit was calibrated against a platinum resistance thermometer (calibrated at the National Bureau of Standards)

1236

F.K. LEPPLEand F. J. MILLERO

and a G-2 Mueller Bridge, thereby yielding accuracies of :[z0-001°C. Typically, for a 17 bar increase in pressure, it takes 90 min to dissipate the heat of compression which corresponds to approximately 0.05°C. After this time, the temperature inside the pressure cell varies less than 4-0.0002°C, and it is expected that the fluctuations within the piezometer are smaller than this value. After thermal equilibrium has been established and the mercury level has been adjusted to be within one or two centimeters from the top of the capillary stem, an initial reading of the mercury meniscus and of the reference mark scribed near the top of the capillary stem is taken. Then approximately 17 bars of pressure is applied to the system using compressed argon. When thermal equilibrium is again reached, the new position of the mercury meniscus from the reference mark is recorded. The pressure change, AP, is measured with a Texas Instruments fused quartz precision pressure gauge and the change in the position of the mercury column, Ah, is measured with a Gaertner cathetometer to 4-0.0l mm or approximately 4-0.01%. The precision of any pressure measurement is 4-0.001 bar while the accuracy is reported to be about 0.015% of the reading, traceable to the National Bureau of Standards. This uncertainty would yield an absolute error of 4-0.005 bars at the highest pressure measured; however, since we are only concerned with pressure differences, the accuracy of the instrument is not a limiting factor. The densities of the various seawater solutions were measured by means of a magnetic float densimeter described in detail elsewhere (MILLERO,1967). These densities will be published elsewhere (L~I'PLEand MILLERO,in preparation).

Pr&ciples of operation The isothermal compressibility, r, of a liquid is defined by the equation fl = - - V - 1(~ V/~P)~

(1)

where V, P, and T are the volume, pressure and temperature. The total volume of the interior of the glass piezometer, Vg, is given by Vg = Vnq + Vng + Ah

(2)

in which Vl~q is the volume of the test solution and (VHg + Ah) is the volume of mercury. The cross-sectional area of the capillary is designated A and h represents the height of the mercury in the capillary measured from the reference mark. Differentiating equation (2) with respect to pressure, one obtains

OVg/OP = --OVnq/OP -- OVi~g/OP + hOA/DP + Aah/~P

(3)

where the negative sign indicates a decrease in volume. From the theory of elasticity, assuming the glass to be homogeneous and isotropic (DIAz-PE~A and MCGLASHAN, 1959), we have OA/OP = --2Aflg/3 (4a) and 0 Vg/OP = -- V~flg (4b) where fig is the isothermal compressibility of glass. Substituting equation (I) for mercury and the test liquid and equations (4a) and (4b) for glass into equation (3), one obtains fl the compressibility of the test liquid upon rearranging:

fl = -fla~(Vag/VHq) + fl~[1 + (Vng/Vnq) + AAh/3VHq] + (A/V,,,)(Ah/AP)

(5)

The isothermal compressibility of seawater near one atmosphere

1237

in which rug is the isothermal compressibility of mercury, Ah is the change in the height of the mercury meniscus, and Ap is the change in the pressure. The pressure differential is corrected for the change in height of the mercury and the volume of the liquid at the measured pressure is adjusted using the calculated compressibility.

Calibration The water used in the calibration of the isothermal compressibility apparatus was prepared by passing tap water through an Illinois Water Treatment Duplex De-Ionizer which consists of two ion exchange cartridges in series. Water treated in this manner is reported by the manufacturer to have a resistivity of 15 megohm with less than 0.04 ppm solids. In evaluating equation (5), the volume of water, VH2o, was calculated from the weight of the water divided by the appropriate density as tabulated by KEEL (1967). Mercury for the compressibility determinations was Fisher Certified ACS grade (triple distilled) which was air dried and filtered before each experiment. Volumes of mercury, VHg, at any temperature were obtained from the initial weight of mercury at the start of the experiment and from subsequent additions or removals of mercury at each temperature. Densities of mercury were obtained from WEAST (1968). Previously, the system has been shown (MILLERO, CURRY and DROST-HANSEN, 1969) to yield results for the compressibility of water that agree with the very careful measurements of KEEL and WHALLEY (1965) to within 4-0"l x 10 -6 bar -1 from 0 ° to 55°C. In this study and our recent work (MILEEROand LEPPEE,1971) using the flHg taken from BRIDGMAN(1911) and the fig given by DIAz-PE~A and MCGEASItAN (1959), we found agreement with Kell and Whalley's results to within 4- 0"07 x l0 -6 bar-1 from 0 ° to 65°C. This slight increase in accuracy is most likely due to the use of larger pressure intervals in this study (17 bars compared to 5 bars in the previous work). Table 1 lists our calibration results for water at 16.8 bars and those obtained by KEEL and WHAEEEY (1965) and KEEL (1970). Comparisons at other pressures are given elsewhere (LEPPLE, 1971). Our results for the compressibility of water are, on the average, higher by 0.07 x 10 -6 b a r - L Since the compressibility of glass is known to vary with glass type and configuration, this nearly constant deviation can be attributed to our piezometer having a correspondingly lower glass compressibility. For this reason, the fig has been redetermined from the calibration run using equation (5), the fla2o from KEEL and WHAEEEY and the ring from BRIDGMAN'S work. The resulting fig's were found to vary linearly with temperature by the equation fig = 2.86 x 10 -8 q- 1'3 x 10-at (bar-l).

(6)

This value is approximately 0.07 X 10 -6 bar -1 lower than the fig given by Diaz-Pefia and McGlashan. Table 1 also compares the isothermal compressibility at 16.8 bars applied pressure obtained by Kell with the results of this study after subtracting 0.07 x 10 -6 bar -~ over the entire temperature range. The last column shows the excellent agreement between our adjusted values and those of Kell (4- 0.02 x 10 -~ bar-a).

1238

F.K. LEPPL~and F. J. MILL~RO

Table 1. Isothermal compressibility o f water at 16.8 bars Temp (*C)

Our results*

K & W~

0 5 10 15 20 25 30 35 40 45 50 55 60 65

50"74 49.08 47"71 46"66 45.81 45.17 44"66 44"36 44"16 44.04 44"07 44"17 44"38 44"68

50.72 49"06 46"69 46"59 45"72 45.06 44"57 44"24 44.04 43"96 43"99 44"11 44.32 44"61

~r × 106 bar -1 A(*-t) Our results adj. +0.02 +0-02 +0.02 +0"07 +0-09 +fill +0.09 +0.12 +0.12 +0.08 +0"08 +0.06 +0.06 +0-07

50.67 49"01 47.64 46-59 45-74 45"10 44"59 44"29 44"09 43-97 44.00 44"10 44"31 44"61

Kell§

A(t-§)

a(++-§)

50.63 48.95 47-61 46.55 45.70 45.07 44"59 44.26 44-06 43-97 44.00 44.12 44.32 44.62

+0"09 +0.I1 +0.08 +0"04 +0.02 --0.01 --0-02 --0.02 --0-01 --0.01 --0.01 --0.01 0.00 --0.01

+0.04 +0.06 +0.03 +0.04 +0"04 +0.03 0.00 +0.03 +0.03 0.00 0.00 --0.02 --0.01 --0-01

4-0.03

4-0.02

Av. +0.07

*Calculated using fin, from B~VGMAN(1911) and t , from DIAZ-PEI~IAand McGLASHAN(1959). ~'Calculated from KELLand WHALLEY'S(1965) results. SOur results subtracting 0.07 × 10-6 bar-1 over the entire temperature range. §Calculated from I~LL and WHALLEY'Swork as a function of pressure and KELL'S(1970) results at one atmosphere. Such an approach, however, is still limited by uncertainty of the absolute values of the compressibilities o f mercury and glass. This problem can be overcome by analyzing differential measurements, that is by examining the quantity ( f l - fl°) which is developed by subtracting equation (5) for water from equation (5) for the test liquid. In this manner, we obtain

fl -- t ° = (AAh/VAP)IIq -- (AAh/VAP)H2O

(7)

when (V~)n2o----(Va,)llq and V~ao = Vllq, provided (Ah/Ae)l~q and (Ah/AP)H2O are compared at the same pressure. This approach effectively eliminates the fig and fla~ terms since the compressibility measurements on all of the samples reported in this work were performed in the same piezometer, with approximately the same volumes of liquid and mercury. The pressure changes were also approximately equal. Since the precision of the term (A/Vxiq)(Ah/AP) is approximately 4- 0.025 x 10 -6 bar -x, the precision of(fl -- fl°) is 4- 0'05 x 10 -6 bar -x.

Preparation o f artificial seawater In m a n y physicochemical studies, it is advantageous to use artificial rather than natural seawater in order to minimize biological effects and to provide a reproducible solution of known composition. The recipe used in the preparation of the artificial seawater was that o f K.~TER, DUEDALL, CONNO~ and PYTKOWICZ (1967) which is basically an updated version of the LYMAN and FLEMING(1940) formula. The formula of K~TBR, Dtr~OALL, CONNOgS and PYTKOWICZis based on CULr,X~'S (1965) analysis of natural seawater. The salts are added in two groups: gravimetric and volumetric. The gravimetric salts are dried and weighed in anhydrous form (NaC1, NaaSO4, KCI, NaHCOa, KBr, H3BOa and NaF). Direct weighings of MgC12, CaCIs and

The isothermal compressibility of seawater near one atmosphere

1239

SrC12 are unsatisfactory due to hydration. These three salts are added volumetrically f r o m concentrated solutions. One m o l a r solutions o f M g C I 2 , 6 H 2 0 and C a C I 2 . 2 H 2 0 and 0.1 molar SrC12.6H20 are prepared and their chloride concentrations determined by titration (BLAEOEL and MELOCrm, 1957). Mallinckrodt Analytical Reagent Grade salts (without further purification) were used in the preparation o f the artificial mix. The same source o f water mentioned in the compressibility calibration section was used t h r o u g h o u t this study. A n initial batch o f 40Yoo salinity was prepared and dilutions o f this original quantity provided all o f the artificial seawater samples used in this study. Table 2 lists the ratios o f the grammes (gdCl), equivalents (ndCl) and ionic strength [(nJmOZ~Z/C1] to chlorinity for the species present in the artificial seawater used in these studies. Also given in this table are the equivalent fraction o f each species, E i = nJnr.

Table 2. Ratios of species present in artificial seawater mixture. Species

gdCl*

n,/Cl f

(n,/mOZ,2/Cl*

Na ÷ Mg2+ Ca 2+ K+ Sr2+ CISO42HCOaBrHaBOa F-

0.55539 0-06739 0.02072 0.02033 0"00039 0-99892 0"14023 1.00734 0.00340 0"00137 0.00008

0.0241579 0.0055456 0.0010340 0.0005200 0.0000088 0"0281759 0.0029196 0.0001204 0.0000426 -0.0000042

0.0241579 0.0110912 0.0020680 0.0005200 0"0000176 0"0281759 0"0058392 0.0001204 0"0000426 -0.0000042

Z = 1"81556

~ = 0-0625290

Y, = 0"0720370

E~§ 0.772694 0.177377 0.033073 0.016632 0.000281 0"901211 0.093384 0.003851 0.001363 -0-000134

* gdCl is the grammes of species i/chlorinity, the total grammes gr = (r,g~/C1) × C1 = 1.81556 × C1.

tn~/Cl is the equivalents of species i/chlorinity, the total equivalents nr = [l/2~n~/C1] × C1 = k × CI = 0"0312645 × C1. (ndm~)Z~2/C1is the ionic strength fraction of species i, the total ionic strength Ir = [1/2X(ndmO Z~~] CI x CI = k' × C! = 0.0360185 × C1 (where m~ is the number of equivalents of species i; m = 1 for Na +, 2 for Mgz+ , etc.). § E, is the equivalent ion fraction of species i, E~ = n,/1/2Zn~ = ndnr. The Copenhagen seawater (35"00~oo) vials were obtained f r o m G. M. M a n u facturing C o m p a n y , N e w York.

Analysis of seawater samples D u e to the necessity o f degassing the samples and to the possible concentration changes that can occur while falling the piezometer, the seawater samples were analyzed at the end o f each experiment. The solutions were analyzed by a chloride titration (BLA~DEL and MELOCrm, 1957) which was chosen rather than the standard oceanographic m e t h o d using K n u d s e n burettes and hydrographic tables since this study involved both dilute and concentrated seawater samples. In these analyses, the silver nitrate solution was standardized against pure N a C I and the chloride equivalent in the artificial seawater samples was converted to chlorinity by using the factor o f 1.00043 (Cox, 1965). The precision o f the chloride

1240

F . K . LEPPLE and F. J. MILLERO

titrations was a p p r o x i m a t e l y -4-0"01~o C1. Salinities o f the various samples were calculated f r o m the relationship ( U N E S C O , 1966) S~o = 1.80655 C1%o.

(8)

RESULTS The differences between the i s o t h e r m a l compressibility o f seawater c o m p a r e d to p u r e w a t e r as a function o f salinity, t e m p e r a t u r e a n d pressure are given in T a b l e 3. These values for ( t 3 - / 3 °) have been calculated f r o m e q u a t i o n (7); thus, they are i n d e p e n d e n t o f the values selected for the compressibility o f m e r c u r y o r glass. The pressures listed are the average a p p l i e d pressures at which the m e a s u r e m e n t s were m a d e ( P = 0 at 1 atm). Since (,8 - - / 3 °) does n o t v a r y c o n s i d e r a b l y with pressure (i.e., within o u r e x p e r i m e n t a l e r r o r o f 4- 0.05 x 10 -6 b a r -z) we have e q u a t e d the average values to the e x t r a p o l a t e d 1 a t m values. W e are thus assuming t h a t the c o m p r e s s i b i l i t y o f seawater has the same pressure d e p e n d e n c e as that o f water. This a s s u m p t i o n is justified because for this range o f pressure, t h e / 3 --/30 q u a n t i t y varies f r o m a m a x i m u m o f 0"06 x 10 -6 b a r -1 at 0 ° to 0.03 x 10 -6 b a r -1 at 40°C at the highest salinity (WILSOn a n d BRADLEY, 1968). To convert these ( f l - t3°) values to/3, we m u s t a d d selected/3o values for the compressibility o f water to/3 --/3o.

Table 3. The difference between the isothermal compressibility of seawater and pure water (fl --/3°) as a function of temperature, pressure and salinity. T (°C) 0.028

S = 6-14%o P - - ( f l - - f l ° ) × 108 (bars) (bar-a ) 8.926 16'726 25'688

0-81 0'82 0"82

T (*C) 0.009

P (bars) 8'945 16'809 25.754

Av. = 0.82 5.031

8.907 16"754 25'661

10.048

8"903 16-770 25.673

0"76 0.75 0'74

5"012

9.004 16'810 25'814

10"027

8.928 16"793 25.722

8'910 16"686 25-596

0.66 0.65 0'64

8"905 16-785 25-690

0"65 0'59 0'54 Av. = 0.59

1"46 1.38 1-30 Av. = 1.38

15.031

8'939 16.804 25"743

Av. = 0-65 20.027

1-22 1.49 1.71 Av. = 1.47

Av. = 0"71 15.028

1-69 1-64 1"59 Av. = 1-64

Av. = 0"75 0.72 0'71 0.71

S = 11"80%o --(/3--/30)× 106 (bar-a )

1-41 1.33 1.23 Av, = 1-33

20.031

8"963 16"796 25"758

1.27 1"22 1.19 Av. = 1-23

T h e i s o t h e r m a l compressibility o f seawater n e a r o n e a t m o s p h e r e

1241

Table 3. Continued T (°C) 25.008

p (bars)

s = 6.14~o _~_/~o) X 10' (bar -1)

8"926 16"753 25"679

0"58

T (°C) 25"019

0"55 0.50

P (bars) 8"932 16.716 25.648

Av. = 0"54 30.019

8"897 16-038 24'935

8-909 16"763 25"672

0.56 0.50 0"47

30.000

8.936 16.837 25.774

8.904 16"750 25"654

0"53 0-53 0"51

35"000

8-930 16"799 25.729

0.52 0"48 0"46

0"013

S = 14"75~o P --(13--fl')X (bars) ( b a r - 1) 8"920 16"776 25"696

2" 11 2'05 1"99

1.16 I. 10 1.03 Av. = 1.10

40'006

8.923 16" 794 25.717

Av. = 0.49

T (°C)

1.14 1 "09 1.05 Av. = 1.09

Av. = 0"52 40.002

1.20 1.13 1"04 Av. = 1.12

Av. = 0"51 34.999

s = 11.80~o _ ~ _/~o) X 10" (bar -1)

1.12 1.05 0.97 Av. = 1"05

106

T (°C) 0"012

P (bars) 16'800 25"762

S = 21"01~o -- (3 -- /~*) X 106 ( b a r - 1) 2-70 2"79 Av. = 2-75

Av. = 2"05 5'018

8.925 16"774 25"699

1'92 1 "87 1"81

5"013

16"820 25 "806

2"38 2"54 Av. = 2"46

Av. = 1"87 10"024

8-926 16"788 25.714

1"77 1"71 1"63

10"026

16"890 25-814

2-17 2-27 Av. -- 2-22

Av. = 1-70 15"008

8-932 16"781 25.713

1"73 1"60 1"45

15"033

16"814 25"786

2"05 2"17 Av. = 2"11

Av. = 1"59 20"012

8"923 16.787 25.710

1 "53 1"52 1"51

20"029

16"800 25"741

1 "88 2"07 Av.----- 1"98

A v . = 1"52

1242

F.K.

LEVPLE a n d F. J. MILLERO

Table 3. Continued 7" (°C) 24.994

S = 14"75~o e -(~-/~°)xlo (bars) (bar -1) 8"935 16.789 25-724

°

1 "45 1.42 1 "38

7" (°C) 25.006

e (bars) 16"809 25-755

S = 21'01~o -~-8 °) x l o (bar -I)

4

1"78 1 '82 Av. = 1.80

Av. = 1.42 30.006

8-911 16.771 25.682

1.40 1.34 1.28

30.016

16.824 25.783

1.73 1.89 A v . = 1.81

Av. ----- 1.34 35.000

8-916 16.782 25.698

1.34 1.32 1-28

35.001

16.808 25.749

1-66 1.80 Av. = 1.73

Av, = 1.31 39.989

8.928 16.801 25.729

1-27 1.23 1-20

40.008

16.799 25.782

1.53 1.68 Av. = 1.61

Av. = 1.23

zr (*C)

0.027

S = 24"52~o e - ( f l - 8 °) z lO ~ (bars) (bar -1) 8"936 16"819 25.755

3.33 3"26 3"19

T (*C)

0"030

e (bars)

8"966 16"771 25-737

Av. -----3.26 5.030

8.905 16.785 25"690

2-94 2.92 2.91

8-932 16.808 25.740

2.64 2.64 2.64

5"027

8.941 16.773 25.714

8"929 16.778 25.707

2.50 2.45 2-40

10"033

8.913 16.806 25.719

8"953 16-786 25.739

2.40 2.29 2.19 Av, = 2-29

3.22 3"19 3"15 Av. = 3"19

15'019

8"927 16.805 25.732

Av. -----2.45 20.023

3"59 3"55 3.52 Av. = 3"55

Av. ~ 2"64 15.022

3"93 3'88 3"83 Av. = 3"88

Av. = 2"92 10.039

S = 29-38~o - ( f l --/~0) x 10 ° (bar -1)

3-06 3.00 2"94 Av. = 3.00

20.021

8.938 16"777 25.715

2.79 2.73 2.67 Av. = 2.73

The isothermal compressibility of seawater near one atmosphere

1243

Table 3. Continued S=24.52~

T

e

(°C)

(bars)

25-008

8-920 16.762 25.682

S=29"38Yoo

- - ( 3 - - 3 °) x l 0 ~ (bar -1) 2.28 2.26 2.28

r

P

(°C)

(bars)

25.004

8.923 16.094 25.017

Av.=2.27 30.021

8.931 16.653 25.584

8.933 16.778 25.711

2.15 2-09 2.04

30.016

8.914 16.792 25.683

8.887 16.706 25.593

2.18 2.12 2.04

35.006

8.908 16-792 25.700

0"012

e (bars)

2.00 2.00 2-02

8"911 16"768 25.679

S = 34"25~o --(fl--fl°)× (bar -~) 4.45 4.40 4-35

40.007

8.907 16-768 25.675

8.929 16"760 25"689

4.05 4.00 3.96

10 6

T (°C)

8"933 16"798 25"731

3"73 3"66 3'59

0"017

8.966 16"801 25.767

8'945 16"793 25"738

3.50 3"42 3"33

5.017

8-980 16.770 25.750

8"917 16"793 25"710

3"26 3.21 3"17 Av. -----3"21

4.20 4"14 4"07 Av. = 4"14

10.026

8.924 16.797 25.721

3.86 3.80 3.72 Av. ---- 3"79

15.007

8.923 16.772 25.695

Av. -----3.42 20"023

4"63 4-57 4-50 Av. = 4.57

Av. ---- 3"66 15'025

2.44 2-37 2.32

S = 35"00~oo (Copenhagen) P - - ( f l - - f l ° ) × 10a (bars) (bar -~)

Av. = 4.00 10"026

2.50 2.48 2.45

Av.=2.38

Av. -----4.40 5.008

2.54 2.52 2.52

Av. ----2.48

Av.=2.01

T (°C)

2.74 2.70 2.64

Av.-----2.53

Av. = 2-11 40.001

6

(bar -1)

Av.=2.69

Av.=2.09 35.005

--(3--# °)×1o

3"62 3"55 3"47 Av. = 3"55

20.009

8-919 16-762 25.681

3.38 3"32 3"25 Av. ~ 3-32

1244

F.K.

LEPPLE a n d F. J. MILLERO

Table 3. Continued T (°C) 25-010

p (bars)

s = 34-25%0 _q~_~o) × 1o~ (bar -1)

8"926 16-797 25.723

3"09 3"08 3-05

T (°C) 24.997

s = 35.00~o ( C o p e n h a g e n ) P -@-8 °) × l O ~ (barO (bar -1) 8"913 16"810 25-723

Av. = 3"07 30'019

8-922 16"782 25.704

Av. = 3.14

2.89 2.88 2.89

30.001

8"929 16"777 25"706

Av. = 2.89 34"995

8.921 16.720 25"641

8.955 16-786 25.731

2.87 2.76 2.63

35-015

8"916 16"745 25"661

0"009

P (bars)

2"73 2.69 2.66

8"842 16.832 25"674

S = 39"00~o --(/3--fl°)× (bar - a ) 5-11 5"05 4"99

39"987

8"954 16"738 25"692

8.788 16"815 25.603

4.59 4"55 4"50

106

T (°C) 20"028

P (bars) 8,890 16,795 25.685

8"869 16-749 25"618

4-26 4.18 4'09

24"987

8,919 16.773 25.692

8"832 16-760 25"618

4"03 3"94 3-85

3.64 3.60 3.55

3-59 3.53 3.45 Av. = 3.52

30"024

8-929 16"549 25.478

Av. = 4"18 15-028

- - ( f l - - / 3 °) × (bar - a )

Av. = 3.60

Av. = 4"55 10"014

2.82 2,76 2.71 Av. = 2.76

Av. = 5.05 5-011

2.99 2,95 2,90 Av. = 2.95

Av. -----2"69

T (*C)

3-05 2"99 2-93 Av. = 2"99

Av. = 2.75 40.009

3"•8 3"15 3-09

3"35 3.24 3.13 Av. = 3.24

35"002

8.784 16.800 25.584

Av. = 3'94

3.27 3.21 3.15 Av. = 3-21

40.006

8.929 16.736 25-665

3.17 3.09 3-02 Av. = 3-09

106

The isothermal compressibility of seawater near one atmosphere

1245

KELL (1970) has recently analyzed the compressibility data for water determined directly from P - V - T studies and from sound velocity. He found the t3° could be represented by the equation /3° × 106 = (50.88630 + 0.7171582t + 0.7819867 × 10-3t 2 + 31.62214 × 10-6t 3 -- 0-1323594 x 10-6t ~ + 0.6345750 × 10-°ts)/(1 + 21.65928 x 10-30 (9) from 0 to I I 0 ° C (with a standard error of 0.002 × 10 -6 bar-l). We have chosen values for t3° determined from equation (9) to convert the/3 --/30 results to the/3 for seawater. The results for/3 are given in Table 4.

Table 4. The isothermal compressibility of seawater at 1 atm as a function of salinity and temperature. 10*C

15"C

(bar-1) 20"C

25*C

30"C

35"C

47.811 47.10 46.43 46.11 45.59 45.17 44.62 44.15 44.02 43-63

46.736 46-09 45.41 45.15 44.63 44.29 43.74 43.32 43.19 42.80

45.895 45-31 44.66 44.38 43.92 43.61 43.17 42.69 42.58 42-30

45.250 44.71 44.13 43.83 43.45 42.98 42.56 42.18 42.11 41.73

44.774 44-26 43.68 43.43 42.96 42.68 42-24 41.88 41.78 41.53

44.444 44.243 43.92 43-75 43.34 43-19 43.13 43.01 42.71 42.63 42.33 42.23 41.96 41-86 41.69 41-55 41.49 41.48 41.23 41.15

/3 × 10 - 6

S(~o) 0 6-14 11.80 14.75 21.01 24.52 29.38 34.25 35.00 39.00

0*C 50.886 50.07 49.25 48.84 48.14 47-63 47.01 46.49 46.32 45-84

5"C 49.171 48.42 47.70 47.30 46.71 46-25 45.62 45.17 45.03 44-62

40"C

Comparisons of our compressibility results at 35-0%0 S with those obtained by other workers (WILSON, 1960; EKMAN, 1908; WILSON and BRADLEY, 1968; and NEWTON and KENNEDY, 1965) are given in Table 5. The/3 for seawater obtained by other workers has been normalized by using the Tait-Gibson equation (LI, 1967 and MILLERO and LzPPeE--in preparation). There is excellent agreement between our results and those obtained from Wlesoy's (1960) sound velocity measurements. The/3 results calculated from the P - V - T data of Ekman, Wilson and Bradley and Newton and Kennedy do not agree with our results (as well as Wilson's results). Ekman's/3's are about 0.6 ~o higher than our results over the entire temperature range; Wilson and Bradley's results are higher than our results from 0 to 15°C and lower than our results above 15°; Newton and Kennedy's results are higher than ours over the entire temperature range (0.3 ~ at 0 ° to 1.7 ~ at 25°). In an attempt to minimize any systematic errors in the P - V - T measurements made by other workers, we have recalculated their results as differences between the/3 of seawater and the/30 of water. These differences are listed in Table 6. By examining the data in this manner, we can see that E k m a n ' s results for/3 --/3o are in excellent agreement with our results and those of Wilson. Wilson and Bradley's and Newton and Kennedy's values still show large deviations from our results. It is quite apparent from this comparison that although Ekman's absolute values for the/3 of seawater were in error, his internal precision was very good. This comparison also indicates that the P - V - T results obtained by Wilson and Bradley and Newton and Kennedy are probably less precise than E k m a n ' s original work.

1246

F . K . LEPPLE and F. J. MILLERO

Table 5. The isothermal compressibility o f 35%0 S seawater at one atmosphere as a function o f temperature. /~T × 106 bar -1

Temp (*C) 0 5 10 15 20 25 30 35 40

Our results*

a

b

c

d

46-33 45.05 44-04 43-21 42-63 42"10 41.82 41.54 41.45

46"33 45"06 44.04 43"23 42"60 42"13 41.79 ---

46.60 45.34 44"32 43"49 42.85 -----

46"66 45-35 44"25 43.35 42"62 42-05 41.65 41.37 41.22

46.49 45.30 44.43 43.81 43.20 42-81 ----

*(8 -- 8*) × 10-6 at 35~o S given inTable 6 + fl" tabulated by KELL(1970). a. Calculated from velocity of sound data of WXLSON(1960). b. Calculated from EKMAN'S(1908) P-V-Tresults. c. Calculated from WilSON and BRADLEY'S(1968) P - V - T data. d. Calculated from NEWTONand KENNEOY'S(1965) P-V-T data. As discussed by others (ECKART, 1958; CREASE, 1962) E k m a n ' s absolute fl's for seawater are in error due to the fact that he used AMAGAT'S (1893) compressibility results for pure water to calculate the pressure. A m a g a t ' s results for pure water are a b o u t 0.8 % higher t h a n KELL'S (1970) values from 0 to 40°C. It is quite clear from the T a b l e 6 that it is i m p o r t a n t to use pure water as calibrating fluid for seawater P - V - T work since the results can be n o r m a l i z e d at a later date when more reliable values b e c o m e available for the P - V - T properties o f pure water. D u e to the similarity of the isothermal compressibilities of d e u t e r i u m oxide a n d water (MILLERO a n d LEPPLE, 1971), a n y variations o f this isotope in n a t u r a l water systems can be ignored in compressibility considerations. I n the next section, we will a t t e m p t to show that the P - V - T properties o f seawater can be analyzed by considering c o m p o n e n t s due to pure water, i o n - w a t e r interactions a n d i o n - i o n interactions. This concept is n o t novel; WroTH (1940) d e m o n s t r a t e d that the density o f seawater at one atmosphere could be adequately

Table 6. The difference between the compressibility o f 35%o salinity seawater and pure water at various temperatures. - -

Temp (*C) 0 5 10 15 20 25 30 35 40

(8 -- fl*)r × 10-6 bar-x

Our results*

a

b

c

d

4"56 4"12 3.77 3"53 3.27 3"15 2.95 2.90 2.79

4"53 4.07 3.73 3.47 3.26 3-09 2.95 ---

4"59 4.15 3-77 3"51 3.28 -----

4"35 4"13 3"96 3"82 3.70 3"61 3"53 3"48 3"44

4"71 4"49 4"31 3.76 3"54 3.26 ----

*Calculated from experimental coefficients given in Table 7. a. Calculated from the velocity of sound data of WILSON(1960). b. Calculated from EKUnN'S(1908) P-V-T data. c. Calculated from WrLSONand BgADLEV'S(1968) 1"--V-T data. d. Calculated from NEWTONand I(mrCrqF.DY's(1965) P - V - T data.

The isothermal compressibility of seawater near one atmosphere

1247

represented as a function of volume chlorinity with two constants (related to ionwater and ion-ion interactions) that are only functions of temperature. A similar semi-empirical relationship for the compressibility of seawater will be derived in the next section. COMPRESSIBILITY RELATIONS The development of either a semi-empirical or a theoretical compressibility relation requires an understanding of the concepts of the apparent equivalent volume (~bv) and the apparent equivalent compressibility (~K). These relationships will be derived for binary mixtures (water and an electrolyte) and will then be extended to multi-component (seawater) electrolyte solutions.

Binary solutions

The volume properties of electrolyte solutions containing various charge types are normally (WIRTH and MILLS, 1968) expressed in terms of equivalents. The apparent equivalent volume, ~v, of an electrolyte in aqueous solution is defined by ~v = (Vsoln -- Va2o)/nz

(10)

where Vsol, is the volume of the solution, VH~Ois the volume of water in the solution (Vn2o = nl V°~; 17o is the partial molar volume of water at infinite dilution and nl is the number of moles of water) and n2 is the number of equivalents of electrolyte. When Vsol, = 1000 ml, n2 is equal to N (N is the normality of the solution in equivalents/liter) and the volume of water can be expressed as

VH.~O = ( 1 0 0 0 d - M')/d °

(11)

in which dis the density of the solution, d ° is the density of water and M' is the equivalent molecular weight of the electrolyte (M' = M/m2; m is the number of equivalents-e.g., for NaC1, m = 1 ; for MgC12, m = 2). Combining equations (10) and (11), one obtains ~v

=

M'/d°---lO00( d -- d°)/Nd °.

(12)

MASSON (1929) found that ~v varies linearly with N IIs.Thus (gv = d?v ° Jr Sv*N ~'2

(13)

where q~v° is the apparent equivalent volume at infinite dilution and Sv* is the experimental slope that varies with electrolyte type. Many other workers (see MILLERO 1971 a, b for review) have also examined the q~vof electrolytes using the above equation and have found that it adequately represents ~bv over a wide temperature and concentration range. The apparent equivalent volume at infinite dilution is related to ionwater interactions and Sv* is related to ion-ion interactions (MILLERO, 1971a). Combining equations (12) and (13) and rearranging, we obtain the ROOT (1933) equation. 1000(d -- d °) = A N Jr B N s/~ (14) in which A = [ M ' - - ~ v ° d °] and B = - - S v * d °. Equation (14) essentially states that the density of a solution can be represented by the density of water plus a perturbation term, A, due to ion-water interactions plus another perturbation term, B, due to ion-ion interactions.

1248

F.K. LEPPLEand F. J. MILLERO The apparent equivalent compressibility of an electrolyte is defined by --d?~ = (&fiv/OP)r.

(15)

Differentiating equation (10) with respect to pressure and substituting fl = --1/V(aV/~P)T where fl is the compressibility of the solution (t3° is compressibility of water), we obtain ~K = [flVso~, -- fl°Va2o]/n2. (16) Setting the same conditions as in the derivation of equation (11), the above relationship for ~b~ becomes ~ : = 1000(/3 -- ~3°)IN + fl°~v. (17) As in the case of~v, it has been found (SCOTT and WILSON, 1934) that the concentration dependence of ~ follows the simple form c~: = efiK° -t- SK* N 1/2

(18)

because differentiation of equation (13) with respect to pressure leads to ~ : = (~x° -- [(OSv*/aP)r + flSv*/2]NI/L

(19)

Furthermore, s~* = - [ ( ~ s ~ * / o P ) r +

~°s~*/2]

(20)

since fl can be replaced by flo in equation (19) without causing a large error below I = 1.0 (HARNED and OWEN, 1958). The combination of equations (13), (18) and (20) with equation (17), leads to an expression of the form 1000(/3 --/3 °) --= A ' N + B ' N 312 (21) in which A ' - - - q ~ o / 3 O ~ v o and B ' - - - - S ~ * - - f l ° S v °. In a manner similar to the density formulation, the compressibility of a solution can be represented by the compressibility of water plus a term due to the effect of pressure on ion-water interactions and a term due to the effect of pressure on ion-ion interactions. Multi-component solutions

The volume properties of multi-component electrolyte solutions can be treated in a manner similar to that developed in the previous section for binary solutions. For a multi-component electrolyte solution such as seawater, the mean apparent equivalent volume, ~v, is defined [analogously to equation (10)] by ~v = (Vsoln -- Vu2o)/nT

(22)

in which nr, the total number of equivalents = 1/2£n~, where n~ is the number of equivalents of ion i. Substituting the definitions of Vsoln and Va2o into equation (22) and noting that if Vsoln = 1000 ml, nT becomes Nr, the total number of equivalents• liter, we obtain ~ v = M r / d ° -- 1 0 0 0 ( d - d°)[d°Nr (23) where the mean molecular weight of the theoretical sea salt, Mr = Z E , M~ (E~ is the equivalent fraction of species i: E1 = nJnr; M~ is the equivalent molecular weight of the ion:: M~ = M(ion)/m).

The isothermal compressibility of seawater near one atmosphere

1249

Assuming that an additivity relationship holds for a multi-component electrolyte solution, Young's Rule (YouNo and SgITH, 1954) for Or, the estimated mean apparent equivalent volume is given by Ov = ZE~Ov(i). (24) In this equation, Ov(i) is the apparent equivalent volume of species i at the same ionic strength equivalent to NT. The ionic strength, I = N w / m (valence factor w = 1/2Ey~Z~2; y~ is the number of particles of charge Z). Since Or(i) for each component can be given by Or(i) = Ov°(i) q- Sv(i)I 1'2 (25) in which Sv(i) = Sv*ml12w - 1/2, equation (24) now becomes Ov = Ov ° + S v I *n

(26)

where Ov ° = EE~q~v°(i) and Sv = ZE~Sv(i). Combining equations (23) and (26) and rearranging the terms will yield 1000(d- d °) = [MT -- @v°d°]Nr -- [Svd°]NT I1/2.

(27)

At this point, we will express the concentration dependence of equation (27) in more familiar oceanographic terms, namely the volume chlorinity, Clv (Clv = C1%o x density). At 20°C, the volume chlorinity is identical to the chlorosity. If we assume that the major ions in seawater have constant ratios to chlorinity and that any changes in total concentration result from dilution (or evaporation) involving pure water, Nr and I can be represented by (see Table 2) N r = kClv = 0"0312645 Clv

(28)

I = k'Clv = 0-0360185 Clv.

(29)

and Substituting equations (28) and (29) into equation (27) in place of Nr and 11/2, we obtain 1000(d- d °) = AvClv + BvClv 3~2 (30) in which Av = [Mr --(~v°d°]k and By = [Svd°]k(k')l/L As in the binary solution section, Av is related to ion-water interactions and By is related to ion-ion interactions of the major (weighted) ionic components. A similar theoretical development can be made for OK, the mean apparent equivalent compressibility of a multi-component salt solution. By differentiating equations (22) and (24) and setting the same conditions as in the derivation of the @v, we obtain O~ = 1000(/3 -- fl°)/NT + fl°Ov. (31) Again assuming that an additivity relationship for the compressibility of a multi-component electrolyte solution can be given by Young's Rule, the mean apparent equivalent compressibility is given by OK = ZE,q~K(i)

(32)

where ~bK(i) is the apparent equivalent molal compressibility of species i at the ionic strength corresponding to Nr. Since ~ for each component i can be represented by ~x(i) = q~:°(i) + SK(i)P '2

(33)

1250

F . K . LEPPLE and F. J. MILLERO

where Sr(i) = S~:*w-ll2rn 112, equation (32) thus becomes

~ x = ~K ° + S:~1112

(34)

where dOK° = Y,E~r°(i) and S~: = ZEi SK(i). Substituting equation (34) into equation (31) and rearranging yields 1000(fl -- flo) = [qb~co_ flO~vO]Nr "-I- [SK -- fl°Sv]NrP/L

(35)

Substituting for NT and I using equation (28) and (29), we obtain 1000(fl --flo) = AKCIv + BKCIv 3/2

(36)

where AK = [~K ° -- fl°Ov°]k and BK = [S~. -- fl°Sv]k(k'/JL Equation (36) predicts that (fl -- fl°)/Clv plotted versus Clv 1/2 for seawater should be a straight line. The intercept AK is related to the weighted summation of the ion-water interactions of the major ionic components of seawater and the slope BK is related to the weighted summation of the ion-ion interactions of the major ionic components of seawater. In Fig. 2, the linearity of (fl -- fl°)/Clv versus Clv 1/~ at 0, 10, 20 and 30°C is demonstrated. Although the low chlorinity points shown on this graph appear to deviate from linear dependency, one must realize that an error of -4-0.05 x 10 -6 bar -~ in fl -- flo at these points yields an error of 4-0.015 units in (/3 -- fl°)/Clv which is within the linear representation given. Table 7 lists the constants A~: and BK determined by a leastsquares best fit from 0 to 40°C. The standard deviation of the fit was 4-0-04 x 10 -6 b a r - ~ over the entire temperature and chlorinity range. Since it is inconvenient to use volume chlorinity units and Clv ~ C1 (because d---~ 1.0), we have also determined the constants A r and BK using C1 (i.e., plotting fl -- fl°/C1 vs. CP/2). The results are given in brackets in Table 7. The standard deviation of this fit was also 4-0-04 × 10 -6 bar -1.

0.26 0.24 j

.

S

•

•

•

0.22 0.20

o 0.18 "i"

0"

~

30 °

0.16 0.1'I I I Fig. 2.

I 2

I 3

I 4

Plot o f --10°(fl -- fl*)/Clv 1'2 for seawater at 0, 10, 20 and 30"C.

The isothermal compressibility of seawater near one atmosphere

1251

Table 7. Experimental compressibility coefficients.* Temp(*C) 0 5 10 15 20 25 30 35 40

--A~: × 104

BK × 106

2-62[2-59] 2.4012"381 2-2212.19] 2.05[2"03] 1.9111-89] 1.8011.78] 1.7111.69] 1.6511.62] 1-6111-58]

7.415.41 7.415"71 7.315"51 6.114.7] 5.9[4-6] 4.8[3.3] 4.9[3.8] 3.9[2.8] 4.4[3.2]

*The values in brackets were determined expressing the compressibility differences as a function of chlorinity instead of volume chlorinity (Clv). In the least-squares fit of the experimental data, the AK coefficients were forced to be a smooth function of temperature. An error of -4-0.05 × 10-a bar -1 in fl --/3" is equivalent to a maximum uncertainty of 4-0-02 × 10-4 in A~ and 4-0.5 × 10-6 in BK. Besides p r e d i c t i n g the f u n c t i o n a l v a r i a t i o n o f f l - fl°, e q u a t i o n (36) can be used to p r e d i c t the c o m p r e s s i b i l i t y o f seawater f r o m the value for p u r e w a t e r a n d ~bK for electrolytes in p u r e water. U n f o r t u n a t e l y , at present e x p e r i m e n t a l ~K d a t a for electrolyte solutions are available only at 25°C. T h e ~K°'s a n d S~'s f o r the m a j o r ionic c o m p o n e n t s are given in T a b l e 8. T h e ionic values were d e t e r m i n e d b y using a d d i t i v i t y principles a n d the c o n v e n t i o n ~ ° ( K + ) = ~K°(F - ) a n d SK(K +) = S K ( F - ) .

Table 8. Calculations of the mean apparent equivalent compressibility of seawater at 25o. * 1on Na + Mg 2+ Ca 2+ K÷ Sr 2+ CISO~2HCO3BrF-

--dPK*(i)× 104 40.3 39.5 31.7 33-9 32.0 11.2 36-0 1.0 1.3 33.9

SK(i)

--EflgK*(i)× 10~

EtSr(i) × 104

6.2 11.6 11.6 7.2 11.6 5-2 9.6 4.0 4.0 7-2

31.1404 7.0049 1.0482 0.5639 0.0091 10-0937 3.3619 0.0039 0.0018 0.0045

4.7908 2.0571 0.3836 0-1198 0.0033 4.6863 0.8965 0.0154 0.0055 0.0010

~x*=Z=

--53"2323

SK=N=12"9593

*Derived from the data tabulated by MiUero (unpublished). The ionic values were determined by assuming SK*(K+) = SK*(F-) and SK(K +) = StdF-). Since $r* and Sx are evaluated from data at high concentration (0.1 to 1 m), they may differ from the correct infinite dilution value of ~b,c*and the theoretical Debye-Hiickel limiting slope St. WIRTH (1940) first p r o p o s e d this m e t h o d to divide the ~bv a n d Sv o f salts into their ionic c o m p o n e n t s since K + a n d F - have similar crystal radii. A s shown elsewhere, this m e t h o d yields results f o r 6v ° in p u r e w a t e r a n d seawater t h a t agree with o t h e r m e t h o d s (MILLERO, 1969a, b; MILLERO, 1971a, b, c). U s i n g ~bK° a n d SK f r o m T a b l e 8 with ~v ° = 13.88 a n d Sv = 2.03 (LEPPLE a n d MILLERO---in p r e p a r a t i o n ) we have c a l c u l a t e d A~: = - - 1 . 8 6 x 10 -4 a n d BK = 7"2 X 10 -6 c o m p a r e d to the e x p e r i m e n t a l values o f A~¢ = - - 1 . 8 0 x 10 -4 a n d BK = 4.8 x 10 -6. T h e theoretical values for

1252

F.K. LEPPLEand F. J. MILLERO

A~ and BK yield results for fl --/3 ° at 25 ° for seawater to within 4-0.09 x 10 -6 bar -1 (4-0.02 at S = 20%0 to 4-0.09 at S = 40%0). The agreement between the calculated and experimental fl -- flo at 25 ° is excellent considering the large number of assumptions made and also that until the present work, the fl of seawater derived from previous direct P-V-T measurement was known to only 4- 0.I × 10 -6 bar -1. Because the ~K° of many electrolytes varies similarly with temperature and SK appears to be independent of temperature (OWEN and KRONICK, 1961), we have attempted to estimate Ar and BK for seawater at 0 ° assuming the temperature dependence of O~ ° for sea salt equals that of NaCl and that SK at 0 ° equals SK at 25 °. The values of (I)v° (10.04) and Sv (3.17) for sea salt at 0 ° were taken from the work of LEPPLE and MILLERO (in preparation). We obtain AK = --2-72 X 10 -4 and BK = 6.7 X l0 -6. The calculated A~: and BK yield results for f l - flo at 0 ° to within 4-0.26 x 10 -6 bar -1 (4-0.13 x 10 -6 at S = 20%0 and 4-0-26 x 10 -6 at S = 40%0). Since the measured qb~°'s of sea salt (calculated from the AK's in Table 7) (Fig. 3) seem to have nearly the same temperature dependence as NaC1 (i.e. from 25 to 0°C), the disagreement of the calculated and experimental fl -- flo at 0 ° can be attributed to the error involved in assuming Br to be independent of temperature. This is supported by the fact that the measured Br's for seawater appear to decrease with increasing temperature. We are presently measuring the ~ : for sea salts from 0 ° to 45°C; thus, in future work we will be able to calculate the theoretical temperature dependence of AK and Br.

f

"¢"Sea sa/t

F , 400

, 10

.

, 20

30

40

l °C Fig. 3. Plot of ~ ° of sea salt and sodium chloride as a function of temperature.

The isothermal compressibility of seawater near one atmosphere

1253

Since the AK (i.e. ~I~ ° and qbv°) term is related to the infinite dilution properties (i.e. the ion-water interactions) of the major ionic components of seawater, errors involved in calculating the theoretical Ar cannot be attributed to non-additivity effects. However, the BK term (i.e. Sv and SK), although being additive for simple systems, can differ according to the choice of salts used to determine the ionic properties (MILLERO, 1971d). By selecting the proper salts, it is possible to eliminate cation-anion interactions; however, cation--cation and anion-anion interactions cannot be eliminated unless all the excess properties of the major ions in seawater are known (MILLERO, 1971d). At 25°C, the deviations from additivity appear to be small for the SK of sea salt as seen by the remarkable agreement between the estimated and the measured values. At present, we are extending the general model developed for/3 --/3o to other physical-chemical properties of seawater such as expansibility, heat capacity, enthalpy, etc. CONCLUSIONS

1. The compressibility of seawater near 1 atm has been measured from 0 to 40°C and 0 to 40%0 S with a precision of :t:0-05 x 10 -6 bar -1. The results agree very well with the values calculated from W1LSON'S (1960) sound velocity data and the compressibilities obtained by normalizing the P - V - T data of Ekman. 2. A semi-empirical equation is developed for the chlorinity dependence of the compressibility of seawater in terms of the apparent equivalent compressibility (¢~:) of the major ionic components of seawater. The semi-empirical equation yields results for the/3 of seawater at 25°C that agree with measured values to 4-0.09 x 10 -6 bar- 1. Acknowledgements--The authors would like to acknowledge the support of the Office of Naval Research ( N O N R 4008 (02)) and the Oceanographic Section of the National Science Foundation (GA 17386) for this study. REFERENCES AMAGAT E. H. (1893) Mrmoire sur l'61asticit6 et la dilatabilit6 des fluides jusqu'aux trrs hautes pressions. Annls Chim. Phys., 29, 68-136, 505-574. BLAEDEL W. J. and V. W. MELOCHE (1957) Elementary quantitative attalysis: theory and practice. Row, Peterson, 826 pp. BRADSHAW A. and K. E. SCHLEICHER (1970) Direct measurement of thermal expansion of seawater under pressure. Deep-Sea Res., 17, 691-706. BRIDGMAN P. W. (1911) Mercury, liquid and solid, under pressure. Proc. Am. Acad. Arts Sci., 47, 347~38. CALDWELL D. R. and B. E. TUCKER (1970) Determination of thermal expansion of seawater, by observing onset of convection. Deep-Sea Res., 17, 707-719. Cox R. A. (1965) Physical properties of seawater. In: Chemical oceanography, J. P. RILEY and G. SKIRROW,Editors, Academic Press, 1, 73-120. Cox R. A., M. J. MCCARTNEY and F. CULKIN (1970) The specific gravity/salinity/temperature relationship in natural seawater. Deep-Sea Res., 17, 679-689. Cox R. A. and N. D. SMITH (1959) The specific heat of seawater. Proc. R. Soc., (A) 252, 51-62. CREASE J. (1962) The specific volume of seawater under pressure as determined by recent measurements of sound velocity. Deep-Sea Res., 9, 209-213. CULKIN F. (1965) The major constituents of seawater, In: Chemical Oceanography, J. p. RILEY and G. SKIRROW,Editors, Academic Press, 1, 121-161. DEE GROSSO V. A. (1959 Speed of sound in pure water and seawater. Conf. on phy. and chem. properties of seawater, Publ. 500 Nat. Acad. Sci., Nat. Res. Council. DIAZ-PE~A M. and M. L. MCGLASHAN (1959) An apparatus for the measurement of the isothermal compressibility of liquids. The compressibility of mercury, carbon tetrachloride and water. Trans. Faraday Soc., 55, 2018-2024.

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