Salinity differences

Useful chemical energy may be defined as energy that can be released through exotermic chemical reactions. In general, chemical energy is associated with chemical bindings of electrons, atoms and molecules. The bindings may involve overlapping electron wave-functions of two or more atoms, attraction between ionised atoms or molecules, and long-range electromagnetic fields created by the motion of charged particles (notably electrons). In all cases, the physical interaction involved is the Coulomb force. Examples of chemical energy connected with molecular binding structure have been given in section

3.6 (bioenergy sources, including fossil fuels).

The organisation of atoms or molecules in regular lattice structures represents another manifestation of chemical bindings. Some substances possess different crystalline forms, which may exist under given external conditions. In addition to the possibility of different solid phases, phase changes associated with transitions among solid, liquid and gas phases all represent different levels of latent energy. Examples in which such latent energy differences have been considered as potential energy sources have been mentioned, for example in section 3.4.2.

Solutions represent another form of chemical energy, relative to the pure solvent. The free energy of a substance with components i = 1, 2,..., there being ni mol of the ith component, may be written

i where ¡li is called the "chemical potential" of component i. For a solution, ¡ii can be expressed in the form (see e.g. Maron and Prutton, 1959)

where R is the gas constant (8.3 J K-1 mol-1), T the temperature (K) and xi = n/(Lj nj) the mole fraction. is the chemical potential that would correspond to x{ = 1 at the given pressure P and temperature T, and f is the "activity coefficient", an empirical constant which approaches unity for "ideal solutions", an example of which is the solvent of a very dilute solution (whereas in general f cannot be expected to approach unity for the dissolved component of a dilute solution).

It follows from (3.49) and (3.50) that a solution represents a lower chemical energy than the pure solvent. The most common solution present in large amounts on the Earth is saline ocean water. Relative to this, pure or fresh water such as river run-off represent an elevated energy level. In addition, there are salinity differences within the oceans, as shown in Figs. 2.63-2.65.

Taking the average ocean salinity as about 33 x 10-3 (mass fraction), and regarding this entirely as ionised NaCl, nNa+ = na- become about 0.56 x 103 mol and nwater = 53.7 x 103 mol, considering a volume of one cubic metre. The chemical potential of ocean water, j, relative to that of fresh water, j 0, is then from (3.50)

1 — 1 = iM T log xwater ~ "2 T nNa+ 1 nwater

Consider now a membrane which is permeable for pure water but impermeable for salt (i.e. for Na+ and Cl- ions) as indicated in Fig. 3.81. On one side of the membrane, there is pure (fresh) water, on the other side saline (ocean) water. Fresh water will flow through the membrane, trying to equalise the chemical potentials j 0 and j initially prevailing on each side. If the ocean can be considered as infinite and being rapidly mixed, then nNa+ will remain fixed, also in the vicinity of the membrane. In this case each m3 of freshwater penetrating the membrane and becoming mixed will release an amount of energy, which from (3.49) is

S G = £(nlSjl +¡¡3 n ) « nwater (10-1)" 2 MTnNa+, (3.51)

Figure 3.81. Schematic picture of an osmotic pump. In order to mix the fresh water penetrating the semi-permeable membrane in the direction towards the right, and maintain the salinity in the salt water compartment, new saline water would have to be pumped into the salt water compartment, and water motion near the membrane would have to be ensured.

For a temperature T ~ 285 K (considered fixed), S G ~ 2.65 x 106 J. The power corresponding to a freshwater flow of 1 m3 s-1 is thus 2.65 x 106 W (cf. Norman, 1974). The world-wide run-off of about 4 x 1013 m3 y-1 (Fig. 2.61) would thus correspond to an average power of around 3 x 1012 W.

The arrangement schematically shown in Fig. 3.81 is called an osmotic pump. The flow of pure water into the tube will ideally raise the water level in the tube, until the pressure of the water head balances the force derived from the difference in chemical energy. The magnitude of this "osmotic pressure", Posm, relative to the atmospheric pressure P0 on the fresh water surface, is found from the thermodynamic relation

V dP - S dT = X, n where V is the volume, S the entropy and T the temperature. Assuming that the process will not change the temperature (i.e. considering the ocean a large reservoir of fixed temperature), insertion of (3.51) yields

Inserting the numerical values of the example above, Posm = 2.65 x 106 N m-2, corresponding to a water-head some 250 m above the fresh water surface. If the assumption of fixed mole fraction of salt in the tube is to be realised, it would presumably be necessary to pump saline water into the tube. The energy spent for pumping, however, would be mostly recoverable, since it also adds to the height of the water-head, which may be used to generate electricity as in a hydropower plant.

An alternative way of releasing the free energy difference between solutions and pure solvents is possible when the dissolved substance is ionised (the solution is then called electrolytic). In this case direct conversion to electricity is possible, as further discussed in Chapter 4.

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