Kinetic Theory : Solution

When a gas is brought in contact with a liquid, solution occurs until the concentration of gas dissolved in the liquid is in a fixed ratio to that in the gas-space, as required by Henry's law. A state of kinetic equilibrium is set up: Gas <=> Gas (dissd.), with the same number of gas molecules entering and leaving the liquid through the surface of separation in unit time.

The mass of gas impinging on the liquid surface per second is ½Dū = ½Dx½Ω=DG/√(6π) = 0.230DG. In the case of oxygen at S.T.P., D = 0.001429 gm. per c.c., G = 4.61 x 10⁴ cm. per sec., the mass of oxygen striking 1 sq. cm. of the liquid surface per second is 0.230 x 0.001429 x 4.61 x 10⁴ gm. =15.1 gm. This contains

molecules,

or the number in about 10 litres.

A proportion at least of the impinging gas molecules passes through the surface into the liquid, owing to molecular attraction between them and molecules of the liquid. Some of the gas molecules moving in the liquid will be approaching the surface, and if the kinetic energy of one of these is sufficiently above the average value, it will leave again into the gas-space. This occurs the oftener the more gas molecules are dissolved. A state of kinetic equilibrium is reached when equal numbers of molecules leave and enter the liquid per second.

When the pressure of the gas is raised, the number of molecules per c.c. is increased, and the number striking the surface becomes larger in the same ratio. The number of molecules per c.c. in the liquid is also increased. Hence more molecules leave the liquid than previously. When equilibrium is established, the same number leave as enter per second, but if the number entering is increased n times the number per c.c. of liquid also increases n times. This is Henry's law.

At first sight it may seem that the gas could have any concentration in the liquid, since as many molecules enter as leave. But if we imagine people walking into a room through one door and out through another, so that as many enter as leave, then if they enter twice as fast there will be double the number in the room, although they are also leaving it at twice the previous rate.

The solution of a solid in a liquid may be considered from the same point of view. Molecules are torn away from their centres of oscillation on the surface of the solid, and in a saturated solution molecules are caught into positions of oscillation. In this case the kinetic nature of the equilibrium can be observed, because if an irregular or broken crystal is suspended in a saturated solution, it tends to become more perfect in shape, one portion dissolving and being deposited again in another place. Ultramicroscopic investigations (Traube and v. Behren, 1928) show that, in dissolving, a crystal is often resolved into small aggregates of molecules, submicrons, which then disperse as molecules or ions after a very short interval. In the formation of crystals the reverse process occurs, strings of submicrons building up small "blocks," of which the crystal aggregate consists.

Attempts have been made to find the radii of particles in solutions by assuming them to be spheres and applying Stokes's law:

Stokes law

where v is the mobility (= speed under unit force on the particle) and η the viscosity of the liquid. The force acting on the particle may be osmotic pressure as in the case of diffusion, or an electric potential gradient as in the case of a migrating ion, or both combined, as in the diffusion of ions. This method gives certain results only for large (colloidal) particles.

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Kinetic Theory
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