Partial Molal Volumes of 16 Salts in Sea Water Ivet W. Duedall Marhe Lology Laboratory, Fisheries Research Board of Canada, Bedford Institute, Dartmouth, Nova Scotia
Dam for calculating the partial molal volumes, in sea water, of 16 salts over the salinity range of 30 to 40% and temperature range of 0" to 25" C. are reported. At 35.10% salinity and 25" C., the partial molal volumes, in ml. per mole, are: NaCl, 18.90 f 0.08; Na.$04, 21.03 f 0.14; NaHC03, 27.07 f 0.27; NaNOa, 30.46 f 0.17; KCl, 29.20 f 0.14; K&O4, 41.63 f 0.37; KHCOI, 37.38 f 0.30; KN03, 40.76 f 0.21; MgCI2, 19.62 f 0.21; MgSOd, 2.86 f 0.48; Mg(HCO&, 35.98 f 0.67; Mg(NO&, 42.75 =t 0.52; CaClz, 22.00 0.28; CaSOd, 5.24 f 0.61; Ca(HCO&, 38.35 f 0.76; and Ca(NO&, 45.13 f 0.64. Except for the partial molal volumes of NaHCOs, KHC03, MgCl2, MgSOI, Mg(HCO&, and Ca(HCO&, the values reported in this paper are in agreement, within experimental error, with previously published estimates in which sea water was approximated as a 0.725 rn NaCl solution.
*
0
wen and Brinkley (1941) has been the source of data for partial molal volumes of salts in sea water. There are several reasons for re-examining their values. For example, none of the values represent measurements that were made in natural or artificial sea water; at best, the values are estimates of partial molal volumes of salts in a 0.725 m NaCl solution which is a solution having about the same ionic strength as nonnal sea water. Furthermore, the values are representative at one temperature (25" C.) and concentration. The present paper reports the partial molal volumes, in sea water, of the following 16 salts: NaCl, N a S 0 4 , NaHC03, NaN03, KCl, K&04, KHCOZ, KNOI, MgCL, MgS04, Mg(HC03X, Mg(NO&, CaCL, CaSO,, Ca(HCO&, and Ca(NO&. Definitions and Calculations
The partial molal volume (VI) of a salt in sea water is defined as -
VI = ( d V / d n l ) p , p , n 2... ,
where 7, is the change in volume (0 of an infinitely large valume of sea water due to the addition of one mole (n) of 706 Environmental Science and Technolosy
salt. The partial molal volumes were computed from the work of Duedall and Weyl(1967), who reported the partial equivalent volume of NaCl (V N a C and the following partial equivalent volume differences (FA): V(x+- N~+), 8 ( M g + 2 - K a + ) , P(C.+~ - Na+), V(sor-2 - C I - ) , P(Hco~- ~ 1 - 1 , and V(NO,-- cI-). They defined the partial equivalent volume, 8,, in the same manner as the partial molal volume except the mass of a salt was expressed in terms of equivalents instead of moles, and defined PA as the difference between partial equivalent volumes of salts containing a similar anion or cation. Duedall and Weyl used a dilatometer method and their measurements covered the salinity (S) 30.13 6 S 6 40.07% and the temperature 0" 6 t 6 24.5" C. Artificial sea water, containing boric acid and the 10 most abundant ions in sea water, was used.They fitted their values of ~ H 1 and ~ C to the following power series: V(S%,
f0
C.)
=
a00
+ + awtz + + ao1t
(a10
a1m
(1)
and they reported the values of the coefi.cients aoo, ao:, am, aol,and all. In Equation 1 , S is the salinity of sea water, expressed as parts per thousand, and t is the temperature on the Celsius scale. The author has added ~ N . C I to combinations of 8, (the additive property of partial volumes) to compute the partial molal volumes of the above mentioned salts; 7, is computed from the following equation:
(v,)
-
V,(SL,
t o C.) =
+
z [ V N ~ C ~ V(eation
- Na+)
+
V(snion
- cI-)I (2)
where z = valence of the salt ( z = 1 for NaCl; z = 2 for MgC12; etc.). Equation 2 is simplified by the following steps: Equation 1 is substituted for the terms 8 ~ ~P(eation ~ 1 ,- N*+), and P(,,,,,, - c,-); the values, reported by Duedall and Weyl (1%7), of the coefficients aOo, ~ O Iam, , ala, and a11for the partial equivalent volume terms are added algebraically, and the proper z is inserted. Therefore, Equation 2 reduces to the following:
-
v,(SL, t o C.) =
a00
+ aolt + a d 2 + + a& (a10
(3)
where aoo,am, am, ala, and all are coefficients for a particular salt; Table I shows the values of these coefficients for 16
a00 S
NaCI' NanSOa NaHC03 NaN03 KC1 KpSOa KHCOs KNO 3 MgClz MgS04 Mg(HC03)2d Mg(N0dz CaClZ CaS04 ca(HC03)?
Ca(NOd2 a
*
MI./Mole 15.54 8.90 21.52 24.98 26.87 31.56 32.85 36.31 18.76 -3.42 30.72 37.64 19.02 -3.16 30.98 37.90
Table I. Partial Molal Volumes (MI./Mole) of Salts in Sea Water. Salinity 30 to 40% and Temperature0" to 25" C. all X 10* a01 X loe am X lo* aloX lo2 MI./ MI./(Mole X C.) MI./(Mole X C.*) Ml./(Mole X S%) (Mole X S% X "C) 16.0 -0.289 1.16 0.086 43.56 -0.567 14.78 -0.046 26.4 -0.488 3.56 0.086 16.45 -0.034 2.35 0.086 10.34 -0.164 -0.69 0.115 32.24 -0.317 11.08 0.012 20.74 -0.363 1.71 0.115 10.79 0.091 0.50 0.115 2.20 -0.164 -6.00 0.392 13.76 -0.153 6.46 0.174 23.0 -0.562 -1.20 0.392 3.096 0.346 -3.62 0.392 34.82 -1.040 -2.10 0.172 46.38 -1.029 10.36 -0.046 55.62 -1.438 2.70 0.172 35.72 -0.530 0.28 0.172 O
+
+
+
+
P
Ml./Mole k0.08 f 0 . 14 k0.27 f 0 . 17 f 0 . 14 f0.37 f0.30 f0.21 f 0 . 21 +0.48 f0.67 f 0 . 52 +0.28 f0.61 k0.76 ZkO.64
Coefficientsfor Equation 3: t o C . ) = aoo aolr a d * ( 10 a1lt)S. Uncertainty (e) computed as the square root of the sum of the squares of the errors in ~ N ~ and C I (Errors reported by Duedall and Weyl, 1967, Table 111.). Values of aoo, am, 802, am, and all for NaCl were published originally by Duedall and Weyl (1967, Table 111). Physical properties of Mg(HC03)z have not appeared in the literature; nevertheless, the partial molal volume of Mg(HCO& can be calculated.
salts. Using these data (Table I) one can now compute the partial molal volumes at temperatures and salinities characteristic of the world ocean. Discussion Table I1 shows values of at infinite dilution (distilled water, 25" C., data from Owen and Brinkley, 1941; Wirth, 1940; Zen, 1957) and values of 7, in sea water (35.10% (Table 11) 25" C., computed from Table I). The values of in sea water are greater than in distilled water. A reasonable interpretation of this fact is that electrostriction, the shrinkage of the water structure due to electrical attraction of ions and water molecules, is less in sea water than in distilled wnter. A striking example of decreased electrostriction is shown for MgS04 and CaS04. In distilled water, vXgso4 = -7.0 ml. per mole and Vc,so4 = -4.2 ml. per mole; while in sea water, v ~= 2.86 ~ ml.~per mole ~ and , V C ~ S=O ,5.24 ml. per mole. Also shown in Table I1 are the estimates of partial molal volumes made by Owen and Brinkley (1941), who approximated sea water as a 0.725 m NaCl solution. The inadequacy of - their -values is - shown- by the disagreement of VSdHcor, VKHCO~,V Y ~ IC~ , VYgS04, VM~(HCOS)Z, and V C ~ ( H Cwith O ~ ) ~the values reported in this paper. According to the principle of LeChatelier, the effect of increasing hydrostatic pressure should be to increase the solubility in sea water of each of the 16 salts (Table I) because the partial molal volume is less than the molar volume for each salt. [A possible exception is Mg(HCO& whose specific volume has not heretofore been reported 'n the literature.] The extent of this effect, however, cannot be computed with too much certainty, because the partial molal compressibilities of salts in sea water are not known.
v,
v,
VA.
Table 11. Partial Molal Volumes (Fs, MI./Mole) of Salts in Different Aqueous Solutiom at 25" C. Water= Infinite 0.725 m Dilution Sea Waterb S NaCP 16.6 18.90 f 0.08 19.0 NaCl 11.2 21.03 f 0.14 21 Na2S04 22.2 27.07 f 0.27 25 NaHC03 28.0 30.46 f 0.17 30 NaN03 KC1 26.6 29.20 f 0.14 29.3 41.63 f 0.37 41 KzS04 31.2 32.2 37.38 f 0.30 36 KHC03 38.0 40.76 f 0.21 41 KN03 18 13.8 19.62 f 0.21 MgCl? 2.86 f 0.48 1 -7.0 MgS04 31 35.98 f 0.67 Mg(HC03)t 26.2 41 Mg(N0ah 37.8 42.75 f 0.52 CaCI? 17.8 22.00 f 0.28 22.6 cas04 -4.2 5.24 f 0.61 5 G(HCOd2 29.0 38.35 f 0.76 35 Ca(NOd2 40.6 45.13 f 0.64 45 Data are averages of data reported by Owen and Brinkley (1941, Table I), Wirth (1940, Table 11),and Zen (1957, Table I). from data in Table I; salinity = 35.10% which corresponds to a n ionic strength of 0.725. Owen and Brinkley (1941, Table VI).
* Computed
Literature Cited Duedall, I. W., Weyl, P. K., Limnol. Oceanog. 12,52-9 (1967). Owen, B. B., Brinkley, S . R., Jr., Chem. Rec.29,461-74(1941). Wirth, H. E., J . Marine Res. 3, 23047 (1940). Zen, E-an, Geochim. Cosmochim. Acta 12, 103-22 (1957). Receiced for reciew March 14, 1968. Accepted JuIy 8, 1968. Bedford Institute Contribution No. 127. Volume 2, Number 9, September 1968 707
