### Colligative and Other Properties of Sea Water

Colligative Properties. The colligative properties—namely, vapor-pressure lowering, freezing-point depression, boiling-point elevation, and osmotic pressure—are unique properties of solutions. If the magnitude of any one of them is known for a solution under a given set of conditions, the others may readily be computed. Solutions of the complexity and concentration of sea water do not obey the generalized theories of the colligative properties, but in all cases the departures from the theoretical values are proportional.

Salinity (V%) | Temperature, ϑ_{m} (°C) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | |

30.0…… | 3.5 | 5.3 | 7.0 | 8.7 | 10.3 | 11.8 | 13.2 | 14.7 | 16.1 | 17.6 | 18.9 | 20.3 |

32.0…… | 3.9 | 5.7 | 7.3 | 9.0 | 10.6 | 12.1 | 13.5 | 15.0 | 16.4 | 17.8 | 19.1 | 20.5 |

34.0…… | 4.3 | 6.0 | 7.7 | 9.4 | 10.9 | 12.4 | 13.8 | 15.3 | 16.6 | 18.0 | 19.3 | 20.7 |

36.0…… | 4.7 | 6.4 | 8.1 | 9.7 | 11.2 | 12.7 | 14.1 | 15.5 | 16.9 | 18.3 | 19.6 | 20.9 |

38.0…… | 5.1 | 6.8' | 8.4 | 10.0 | 11.6 | 13.0 | 14.4 | 15.8 | 17.2 | 18.5 | 19.8 | 21.1 |

Depth (m) | Temperature, ϑ_{m} (°C) | ||
---|---|---|---|

12 | 13 | 14 | |

1000…………………… | 14.4 | 15.1 | 15.8 |

2000…………………… | 30.0 | 31.4 | 32.7 |

3000…………………… | 46.6 | 48.6 | 50.6 |

4000…………………… | 64.2 | 66.7 | 69.2 |

Only the depression of the freezing point for sea water of different chlorinities has been determined experimentally (Knudsen, 1903; Miyake,

1939a), and empirical equations for computing the vapor-pressure lowering and osmotic pressure have been based on these observations. Thompson (1932) has shown that the depressions of the freezing point, Δϑ

_{f}, may be calculated from the chlorinity by means of the equation

[Equation]

_{f}for various chlorinities are shown in fig. 13. The freezing point of sea water is the “initial” freezing point; namely, the temperature at which an infinitely small amount of ice is in equilibrium with the solution. As soon as any ice has formed, the concentration of the dissolved solids increases, and hence the formation of additional ice can take place only at a lower temperature (p. 216).

#### Osmotic pressure, vapor pressure relative to that of pure water, freezing point, and temperature of maximum density as functions of chlorinity and salinity.

[Full Size]

The vapor pressure of sea water of any chlorinity referred to distilled water at the same temperature can be computed from the following equation (Witting, 1908):

[Equation]

*e*is the vapor pressure of the sample and

*e*

_{0}that of distilled water at the same temperature (fig. 13). Sea water within the normal range of concentration has a vapor pressure about 98 per cent of that of pure water at the same temperature, and in most cases it is not necessary to consider the effect of salinity, since variations in the temperature of the surface waters have a much greater effect upon the vapor pressure (table 29, p. 116).

The osmotic pressure can be calculated from the freezing-point depression by means of the equation derived by Stenius (Thompson, 1932):

[Equation]

The osmotic pressure at any temperature may then be computed:

[Equation]

It will be noted that the freezing-point depression and, therefore, the other colligative properties are not linear functions of the chlorinity, because chlorinity is reported as grams per kilogram of sea water and not as grams per kilogram of solvent water, in which case a linear relationship should be expected. In agreement with this expectation, Lyman and Fleming (1940) found that the freezing-point depression could be written in the form

[Equation]

*Z*is the total salt content per kilogram of solvent water.

The magnitude of the colligative properties depends upon the concentration of ions in the solution and upon their activity. According to present concepts the major constituents of sea water exist as ions whose concentrations may be computed from data in table 35 (p. 173). Within the normal range of sea water the gram-ionic concentration per kilogram of solvent water may be obtained from the following expression:

[Equation]

Maximum Density. Pure water has its maximum density at a temperature of very nearly 4°, but for sea water the temperature of maximum density decreases with increasing salinity, and at salinities greater than 24.70‰ is below the freezing point. At a salinity of 24.70 ‰, the temperature of maximum density coincides with the freezing point: ϑ_{f} = −1.332°. Consequently, the density of sea water of salinity greater than 24.70 ‰ increases continuously when such water is cooled to its freezing point. The temperature of maximum density is shown in fig. 13 as a function of salinity and chlorinity.

p (bars) | Temperature (°C) | ||||||
---|---|---|---|---|---|---|---|

0 | 5 | 10 | 15 | 20 | 25 | 30 | |

0 | 4659 | 4531 | 4427 | 4345 | 4281 | 4233 | 4197 |

100 | 4582 | 4458 | 4357 | 4278 | |||

200 | 4508 | 4388 | 4291 | ||||

400 | 4368 | 4256 | |||||

1000 | 4009 | 3916 |

Compressibility. Ekman (1908) has derived an empirical equation for the *mean* compressibility of sea water between pressures 0 and *p* bars (p. 57), as defined by α_{s,ϑ,p} = α_{s,ϑ,0} (1 − *kp*). Numerical values are given in table 15, where the *bar* has been used as pressure unit.

The *true* compressibility of sea water is described by means of a coefficient that represents the proportional change in specific volume if the hydrostatic pressure is increased by one unit of pressure: *K* = (− l/α)(*d*α/*dp*). The true compressibility can be calculated from the mean compressibility, which was tabulated by Ekman, using the equation

[Equation]

*k*is the mean compressibility referred to

*bar*as pressure unit, and

*p*is the pressure in bars.

Viscosity. When the velocity of moving water varies in space, frictional stresses are present. The frictional stress which is exerted on a

^{2}is proportional to the change of velocity per centimeter along a line normal to that surface (τ

_{s}, = μ

*dv*/

*dn*). The coefficient of proportionality (μ) is called the

*dynamic viscosity*. This coefficient decreases rapidly with increasing temperature and increases slowly with increasing salinity (table 16, after Dorsey, 1940). With increasing pressure the coefficient for pure water decreases at low temperature but increases at high temperature (Dorsey, 1940). If the same holds true for sea water, and if the effect is of similar magnitude, the viscosity of water of salinity 35 ‰ and temperature 0° is 18.3 × 10

^{−3}c.g.s. units at a pressure of 10,000 decibars, as against 18.9 × 10

^{−3}at atmospheric pressure. The difference is insignificant, and the effect of pressure on the viscosity can be disregarded in the oceans.

Salinity (%) | Temperature (°C) | ||||||
---|---|---|---|---|---|---|---|

0 | 5 | 10 | 15 | 20 | 25 | 30 | |

0………… | 17.9 | 15.2 | 13.1 | 11.4 | 10.1 | 8.9 | 8.0 |

10………… | 18.2 | 15.5 | 13.4 | 11.7 | 10.3 | 9.1 | 8.2 |

20………… | 18.5 | 15.8 | 13.6 | 11.9 | 10.5 | 9.3 | 8.4 |

30………… | 18.8 | 16.0 | 13.8 | 12.1 | 10.7 | 9.5 | 8.6 |

35………… | 18.9 | 16.1 | 13.9 | 12.2 | 10.9 | 9.6 | 8.7 |

The viscosity that has been discussed so far is valid only if the motion is laminar, but, as stated above, turbulent motion prevails in the sea, and an “eddy” coefficient must be introduced which is many times larger (p. 91).

Diffusion. In a solution in which the concentration of a dissolved substance varies in space, the amount of that substance which per second diffuses through a surface of area 1 cm^{2} is proportional to the change in concentration per centimeter along a line normal to that surface (*dM*/*dt* = −δ *dc*/*dn*). The coefficient of proportionality (δ) is called the *coefficient of diffusion*; for water it is equal to about 2 × 10^{−5}, depending upon the character of the solute, and is nearly independent of temperature. Within the range of concentrations encountered in the sea the coefficient is also nearly independent of the salinity.

What was stated about the coefficient of thermal conductivity in the sea applies also to the coefficient of diffusion. Where turbulent motion prevails, it is necessary to introduce an “eddy” coefficient that is many times larger and that is mainly dependent on the state of motion.

Surface Tension. The surface tension of sea water is slightly greater than that of pure water at the same temperature. Krümmel (1907) carried out experimental observations from which he derived an empirical equation relating the surface tension to the temperature and salt content. This equation was revised by Fleming and Revelle (1939) to take into account the more recent values for pure water. The revised expression has the form

[Equation]

Refractive Index. The refractive index increases with increasing salinity and decreasing temperature. The problem of determining the relationship between these variables, and the types of equipment to be used, has been discussed by a number of authors (for example, Utterback, Thompson, and Thomas, 1934; Bein, Hirsekorn, and Möller, 1935; Miyake, 1939). Since the index varies with the wave length of light, a standard must be selected, usually the *D* line of sodium.

Utterback, Thompson, and Thomas determined at a number of temperatures the refractive index of ocean-water samples that had been diluted with distilled water. They found that the refractive index could be represented by expressions of the following type:

[Equation]

*n*

_{ϑ}is the refractive index of the sea-water sample at the temperature ϑ°,

*n*

_{0,ϑ}is that of distilled water at the same temperature, and

*k*

_{ϑ}is a constant appropriate for that temperature. This equation gives a straight-line relationship between the refractive index and the chlorinity, but it should be remembered that it is valid for ocean water diluted with distilled water and that at low chlorinities the diluted water does not correspond to sea water of the same low chlorinity, according to Knudsen's Hydrographical Tables. In fig. 14 the relationships between

*n,*ϑ, and Cl determined by Utterback, Thompson, and Thomas are shown. Miyake (1939b) determined the refractive index for the sodium

*D*line at 25° (

*n*

_{D,25°}) for oceanic water samples that were diluted in the laboratory. He represented his results by the same type of equation, but obtained numerical constants that differ slightly from those of the authors mentioned above.

[Equation]

[Equation]

*n*

_{0}is the refractive index of distilled water tind

*v*is the refractive index of solutions of single salts having concentrations comparable to those in which these salts occur in the sea water. It is known that individual ions have characteristic ionic refractions. In sea water the salts are completely ionized, and, as the molar refractions are known for each ion, Miyake was able to compute the refractive index with a fair degree of accuracy.

Electrical Conductivity. Thomas, Thompson, and Utterback (1934), and Bein, Hirsekorn, and Möller (1935) have studied conductivity as a function of chlorinity and temperature and have given tables for the specific conductance in reciprocal ohms per cubic centimeter for a wide range in conditions.

The results of the investigations of Thomas, Thompson, and Utterback are expressed at temperatures of 0, 5, 10, 15, 20, and 25°. Their results are shown graphically in fig. 15. The values for the low chlorinities were obtained by diluting ocean water with distilled water, and hence the density and other properties will not correspond exactly to those of water of the same chlorinity, as represented in Knudsen's Hydrographical Tables.