Concise Explanations of The Kinetic Theory of Saturation - GulpMatrix

# Concise Explanations of The Kinetic Theory of Saturation

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The kinetic theory of saturation can best be explained when we consider a vapor in contact with its liquid, in an otherwise empty vessel which is closed by a piston. The molecules of the vapor, we suppose, are rushing randomly about, like the molecules of a gas, with kinetic energies whose average value is determined by the temperature of the vapor. They bombard the walls of the vessel. Giving rise to the pressure of the vapor, and they also bombard the surface of the liquid.

The molecules of the liquid, we further suppose, are also rushing about with kinetic energies determined by the temperature of the liquid. The fastest of them escape from the surface of the liquid. At the surface, therefore, there are molecules leaving the liquid, and molecules arriving from the vapor. To complete our picture of the conditions at the surface, we suppose that the vapor molecules bombarding it are not reflected – as they are at the walls of the vessel – but are absorbed into the liquid. We may expect them to be, because we consider that molecules near the surface of a liquid are attracted towards the body of the liquid.

We shall assume that the liquid and vapor have the same temperature. Then the properties of liquid and vapor will not change, if the temperature and the total volume are kept constant. Therefore, at the surface of the liquid, molecules must be arriving and departing at the same rate, and hence evaporation from the liquid is balanced by condensation from the vapor. This state of affairs is called a dynamic equilibrium. In terms of it, we can explain the behavior of a saturate vapor.

The rate at which molecules leave a unit area of the liquid depends simply on their average kinetic energy, and therefore on the temperature. The rate at which molecules strike a unit area of the liquid, from the vapor, likewise depends on the temperature, but it also depends on the concentration of the molecules in the vapor, that is to say, on the density of the vapor. The density and temperature of the vapor also determine its pressure; the rate of bombardment therefore depends on the pressure of the vapor.

Now let us suppose that we decrease the volume of the vessel a vessel by pushing in the piston. Then we momentarily increase the density of the vapor, and hence the number of its molecules striking the liquid surface per second. The rate of condensation thus becomes greater than the rate of evaporation, and the liquid grows at the expense of the vapor. As the vapor condenses its density falls, and so does the rate of condensation. The dynamic equilibrium is restored when the rates of condensation, and the density of the vapor, have returned to their original values. The pressure of the vapor will then also have returned to its original value. Thus the presence of a saturated vapor is independent of its volume. The property of liquid to vapor however increases as the volume decreases.

Let us now suppose that we warm the vessel, but keep the piston fixed. Then we increase the rate of evaporation from the liquid, and increase the proportion of vapor in the mixture. Since the volume is constant, the pressure of vapor rises, and increase the rate at which molecules bombard the liquid. Thus the dynamic equilibrium is restored, at a higher pressure of vapor. The increase of pressure with temperature is rapid, because the rate of evaporation of the liquid increases rapidly – almost exponentially – with the temperature. A small rise in temperature causes a large increase in the proportion of molecules in the liquid moving fast enough to escape from it.