Sea water is a mixture of 96.5% pure water and 3.5% other material, such as salts, dissolved gases, organic substances, and undissolved particles. Its physical properties are mainly determined by the 96.5% pure water. The physical properties of pure water will therefore be discussed first.

Pure water, when compared with fluids of similar composition, displays most uncommon properties. This is the result of the particular structure of the water molecule H₂O: The hydrogen atoms carry one positive charge, the oxygen atom two negative charges, but the atom arrangement in the water molecule is such that the charges are not neutralized (See figure 3.1; the charges would be neutralized if the angle were 180º rather than 105º).

The major consequences of the molecular structure of pure water are:

1. The water molecule is an electric dipole, forming aggregations of molecules (polymers), of on average 6 molecules at 20ºC. Therefore, water reacts slower to changes than individual molecules; for example the boiling point is shifted from -80ºC to 100º C, the freezing point from -110ºC to 0ºC.
Figure 3.2
2. Water has an unusually strong disassociative power, i.e. it splits dissolved material into electrically charged ions (Figure 3.2). As a consequence, dissolved material greatly increases the electrical conductivity of water. The conductivity of pure water is relatively low, but that of sea water is midway between pure water and copper. At 20ºC, the resistance of sea water of 3.5% salt content over 1.3 km roughly equals that of pure water over 1 mm.
3. The angle 105º is close to the angle of a tetrahedron, i.e. a structure with four arms emanating from a centre at equal angles (109º 28'). As a result, oxygen atoms in water try to have four hydrogen atoms attached to them in a tetrahedral arrangement (Figure 3.1). This is called a "hydrogen bond", in contrast to the (ionic) molecular bond and covalent bonding. Hydrogen bonds need a bonding energy 10 to 100 times smaller than molecular bonds, so water is very flexible in its reaction to changing chemical conditions.
Figure 3.3
4. Tetrahedrons are of a more wide-meshed nature than the molecular closest packing arrangement. They form aggregates of single, two, four and eight molecules. At high temperatures the one and two molecule aggregates dominate; as the temperature falls the larger clusters begin to dominate (Figure 3.3). The larger clusters occupy less space than the same number of molecules in smaller clusters. As a result, the density of water shows a maximum at 4ºC.

Physical properties of most substances show uniform variation with temperature. In contrast, most physical properties of pure water show a minimum at some intermediate temperature. Sound velocity shows a maximum at 74ºC (Table 3.1).

A list of some minimum temperatures
The physical property is given first, followed by the temperature in º C at which the minimum occurs.
oxygen solubility	80
specific volume	4
specific heat	34
hydrogen solubility	37
compressibility	44
speed of light	-1
speed of sound (maximum)	74

When freezing, all water molecules form tetrahedrons. This leads to a sudden expansion in volume, ie a decrease in density. The solid phase of water is therefore lighter than the liquid phase, which is a rare property. Some important consequences are:

1. Ice floats. This is important for life in freswater lakes, since the ice acts as an insulator against further heat loss, preventing the water to freeze from the surface to the bottom.
2. Density shows a rapid decrease as the freezing point is approached. The resulting expansion during freezing is a major cause for the weathering of rocks.
3. The freezing point decreases under pressure. As a consequence, melting occurs at the base of glaciers, which facilitates glacier flow.
4. Hydrogen bonds give way under pressure, i.e. ice under pressure becomes plastic. As a consequence, the inland ice of the Antarctic and the Arctic flows, shedding icebergs at the outer rims. Without this process all water would eventually end up as ice in the polar regions.

The Concept of Salinity

As mentioned before, sea water contains 3.5% salts, dissolved gasse organic substances and undissolved particulate matter. The presence of salts influences most physical properties of sea water (density, compressibility, freezing point, temperature of the density maximum) to some degree but does not determine them. Some properties (viscosity, light absorbtion) are not significantly affected by salinity. (Particle and dissolved matter do affect light absorption in sea water and this influence is used in most optical applications.) Two properties which are determined by the amount of salt in the sea are conductivity and osmotic pressure.

Ideally, salinity should be the sum of all dissolved salts in grams per kilogram of sea water. In practice, this is difficult to measure. The observation that - no matter how much salt is in the sea - the various components contribute in a fixed ratio, helps overcome the difficulty. It allows determination of salt content through the measurement of a substitution quantity and calculation of the total of all material making up the salinity from that measurement.

Determination of salinity could thus be made through its most important component, chloride. Chloride content was defined in 1902 as the total amount in grams of chlorine ions contained in one kilogram of sea water if all the halogens are replaced by chlorides. The definition reflects the chemical titration process for the determination of chloride content and is still of importance when dealing with historical data.

Salinity was defined in 1902 as the total amount in grams of dissolved substances contained in one kilogram of sea water if all carbonates are converted into oxides, all bromides and iodides into chlorides, and all organic substances oxidized. The relationship between salinity and chloride was determined through a series of fundamental laboratory measurements based on sea water samples from all regions of the world ocean and was given as

\[ S(\text{‰}) = 0.03 + 1.805\;Cl\;(\text{‰}) \quad (1902) \]

The symbol $\text{‰}$ stands for "parts per thousand" or "per mil"; a salt content of 3.5% is equivalent to $35\;\text{‰}$, or 35 grams of salt per kilogram of sea water.

The fact that the equation of 1902 gives a salinity of $0.03\;\text{‰}$ for zero chlorinity is a cause for concern. It indicates a problem in the water samples used for the laboratory measurements. The United Nations Scientific, Education and Cultural Organization (UNESCO) decided to repeat the base determination of the relation between chlorinity and salinity and introduced a new definition, known as absolute salinity,

\[ S(\text{‰}) = 1.80655\;Cl\;(\text{‰}) \quad (1969) \]

The definitions of 1902 and 1969 give identical results at a salinity of $35\text{‰}$ and do not differ significantly for most applications.

The definition of salinity was reviewed again when techniques to determine salinity from measurements of conductivity, temperature and pressure were developed. Since 1978, the "Practical Salinity Scale" defines salinity in terms of a conductivity ratio:

" The practical salinity, symbol S, of a sample of sea water, is defined in terms of the ratio K of the electrical conductivity of a sea water sample of 15º C and the pressure of one standard atmosphere, to that of a potassium chloride (KCl) solution, in which the mass fraction of KCl is 0.0324356, at the same temperature and pressure. The K value exactly equal to one corresponds, by definition, to a practical salinity equal to 35." The corresponding formula is:

\[ S = 0.0080 - 0.1692\;K^{1/2} + 25.3853\;K + 14.0941\;K^{3/2} - 7.0261\;K^2 + 2.7081\;K^{5/2} \]

Note that in this definition, salinity is a ratio and ($\text{‰}$) is therefore no longer used, but an old value of $35\text{‰}$ corresponds to a value of 35 in the practical salinity. Some oceanographers cannot get used to numbers without units for salinity and write "35& psu", where psu is meant to stand for "practical salinity unit". As the practical salinity is a ratio and therefore does not have units, the unit "psu" is rather meaningless and strongly discouraged. Again, minute differences occur between the old definitions and the new Practical Salinity Scale, but they are usually negligible.

Electrical Conductivity

The conductivity of sea water depends on the number of dissolved ions per volume (i.e. salinity) and the mobility of the ions (ie temperature and pressure). Its units are mS/cm (milli-Siemens per centimetre). Conductivity increases by the same amount with a salinity increase of 0.01, a temperature increase of 0.01º C, and a depth (ie pressure) increase of 20 m. In most practical oceanographic applications the change of conductivity is dominated by temperature.

Density

Density is one of the most important parameters in the study of the oceans' dynamics. Small horizontal density differences (caused for example by differences in surface heating) can produce very strong currents. The determination of density has therefore been one of the most important tasks in oceanography. The symbol for density is the Greek letter ρ (rho).

The density of sea water depends on temperature T, salinity S and pressure p. This dependence is known as the Equation of State of Sea Water.

The equation of state for an ideal gas was is given by

\[ p = \rho\;R\;T \]

where R is the gas constant. Seawater is not an ideal gas, but over small temperature ranges it comes very close to one. The exact equation for the entire range of temperatures, salinities and pressures encountered in the ocean

\[ \rho = \rho (T, S, p) \]

(where S is salinity) is the result of many careful laboratory determinations. The first fundamental determinations to establish the equation were made in 1902 by Knudsen and Ekman. Their equation expressed ρ in g cm^-3. New fundamental determinations, based on data over a larger pressure and salinity range, resulted in a new density equation, known as the "International Equation of State (1980)". This equation uses temperature in º C, salinity from the Practical Salinity Scale and pressure in dbar (1 dbar = 10,000 pascal = 10,000 N m^-2) and gives density in kg m^-3. Thus, a density of 1.025 g cm^-3 in the old formula corresponds to a density of 1025 kg m^-3 in the International Equation of State.

Density increases with an increase in salinity and a decrease in temperature, except at temperatures below the density maximum (Figure 3.4). Oceanic density is usually close to 1025 kg m^-3 (In freshwater it is close to 1000 kg m^-3). Oceanographers usually use the symbol $\sigma_t$ (the Greek letter sigma with a subscript t) for density, which they pronounce "sigma-t". This quantity is defined as $\sigma_t = ρ - 1000$ and does not usually carry units (it should carry the same units as ρ). A typical seawater density is thus $\sigma_t = 25$ (Figure 3.5).

A useful rule of thumb is that $\sigma_t$ changes by the same amount if $T$ changes by 1º C, $S$ by 0.1, and $p$ by the equivalent of a 50 m depth change.

Notice that the density maximum is above the freezing point for salinities below 24.7 but below the freezing point for salinities above 24.7. This affects the thermal convection:

• S < 24.7: The water cools until it reaches maximum density; then, when the surface water becomes lighter (ie after the density maximum has been passed) cooling is restricted to the wind-mixed layer, which eventually freezes over. The deep basins are filled with water of maximum density.
• S > 24.7: Convection always reaches the entire water body. Cooling is slowed down because a large amount of heat is stored in the water body. This is because the water reaches freezing point before the maximum density is attained.

If your browser supports JavaScript you can check the range of seawater density and its dependence on temperature and salinity at surface pressure with this density calculator: Enter a value for temperature, a value for salinity and press the calculate button. Verify your result against the appropriate TS-diagram (Figure 3.4 or Figure 3.5).

Calculation based on Fofonoff, P. and R. C. Millard Jr (1983)