Application of the Kinetic Theory to Liquids

Application of the Kinetic Theory to Liquids

It is a familiar fact of observation that gases and vapo(u)r, if cooled sufficiently and subjected to sufficiently high pressures, condense into liquids, and it is evident from its nature that in a liquid the particles or molecules comprising the substance are definitely exerting a force of attraction upon each other, whatever may be true to gases in this regard.

The discussion of the implication of the Gas Laws and in particular of Charles’s Law, has led to a conception of an absolute scale of temperature, the absolute zero being taken to be -273 °C. The Kinetic Theory gives a further meaning to the absolute zero, since, in terms of that theory, it is that temperature at which all molecular motion ceases.

Conversely, molecular motion only ceases entirely, according to the Kinetic Theory, at the absolute zero, and it follows, therefore, that in ordinary liquids, molecular motion must still occur although, owing to the existence of molecular attractions of considerable magnitude, its extent will be much restricted when compared with gases. In liquids there will be practically no free path (as is believed to exist in gases) and the motion of the molecules is thought to be more in the nature of a gliding of particles over and amongst each other.

A molecule in the body of a liquid will experience attraction on all sides equally, whereas one in the surface will experience a resultant force directed towards the interior of the liquid due to the absence of any marked attraction exerted on it from outside the liquid itself.

This is illustrated and shows that there will be in the surface of a liquid a force acting inwards towards the bulk of the liquid. The effects of this force are observed in the phenomenon of surface tension, which thus becomes a logical consequence of the Kinetic Theory.

Although there can be practically no free path in liquids, nevertheless, the speeds with which individual molecules are moving will, at any instant, vary considerably. Thus there will be a few molecules possessing kinetic energy greater than the average of the molecules as a whole, and if such a molecule should approach the surface it may have sufficient energy to travel clean through the surface into the space outside the liquid. This effect is observed in the phenomenon termed evaporation. The removal of such molecules from the liquid will result in a reduction in the mean kinetic energy of the liquid, which thus will become cooler, or, if the temperature is to remain unchanged, heat must be supplied from the surroundings. This is the latent heat of evaporation.

The molecules of the substance, which have escaped from the liquid in this way constitute a vapo(u)r *(* The distinction between “gas” and “vapo(u)r” is somewhat vague. If the “elastic fluid” be very far from its temperature of liquefaction, it is generally called a “gas” ; and “vapo(u)r” if it is near its temperature of liquefaction. E.g., oxygen, nitrogen, etc., at ordinary temperatures are gases ; whereas water or alcohol on evaporation would furnish vapo(u)r. Otherwise expressed, a gas is an elastic fluid at a temperature above its critical temperature, and a vapo(u)r is an elastic fluid below its critical temperature, but not in a liquid state) in the space above liquid. These molecules of vapo(u)r behave like those of an ordinary gas, and so they will be moving with high speeds, Some of these molecules will approach the surface of the liquid where some of them will be attracted by the molecules in the surface of the liquid and so be dragged into the liquid again. These molecules will be accelerated as they enter the liquid, owing to the forces acting upon them, and their capture will result in an increase in the mean kinetic energy of the liquid, whose temperature will rise in consequence. Heat is therefore given out on condensation.

Suppose now that a liquid is evaporating in a closed vacuous space. The fleetest molecules accumulate as a gas or vapo(u)r in the space above the liquid. The concentration of the vapo(u)r in the space above the liquid will go on increasing but certain percentage will plunge back into the liquid. The number of molecules which return to the liquid from the space above per second increases as the concentration of the vapo(u)r increases, although the rate at which the molecules leave the liquid probably decreases as the concentration of the vapo(u)r increases. When the number of molecules which return to the liquid in a given time is equal to the number of molecules which leave the liquid in the same time, the vapo(u)r is said to be saturated, and the system in equilibrium. Thus,

Water_liquid

100 °

⇌

Water_Steam

This equilibrium, it will be observed, is not a static condition, that is, a state of rest ; both processes are active (kinetic). There is a shower of molecules streaming into the liquid, and an efflux of molecules away from liquid. The effect of one is neutralized by the other ; neither can produce any visible result. Anything which disturbs this equality – e.g., a desiccating agent or a condenser in the space above (as in distillation), etc. – will alter the condition.

If two glass tubes are taken, each about 80cms. In length and sealed at one end, filled with dry mercury and inverted in dishes of mercury, the level of the mercury in each tube will sink somewhat but remain at such a height as represent the pressure of the atmosphere at the time of the experiment. The space above the mercury in such a tube is, to all intents and purposes, vacuous and is called a Torricellian vaccum (after Torricelli who, in 1643, first observed that mercury would only stand at a height of about 30 inches in such a tube). If a few drops of water are introduced by means of a small pipette into one of the tubes, the level of the mercury will be depressed further, and this process will continue on introduction of more water until a thin layer of water is seen resting on the surface of the mercury. The pressure exerted by the water vapo(u)r is equal to that of a column of mercury whose height is the difference between the heights of the mercury in the two tubes. The value of this pressure when the space is saturated, that is, when the addition of more water merely increases the amount of the liquid water layer visible on the mercury, without causing any increase in pressure, is called the maximum vapo(u)r pressure.

Experiments of this kind have shown that, at a given temperature, the vapo(u)r pressure of a liquid in contact with its own liquid is a constant quantity, and independent of the absolute amount of vapo(u)r and of liquid present in the system. It is easy to see why this is so. If the surface of the liquid be doubled, it is true that twice as many molecules will leave the surface in a given time, but twice as many molecules will return.

If a barometer tube, such as was employed in the above experiments, be surrounded with a jacket through which warm water can be passed, and the maximum pressure of water (or other) vapo(u)r at various temperatures thus measured, we shall find that the higher the temperature, the greater the vapo(u)r pressure, provided all the liquid is not vaporized ; but for any assigned temperature the vapo(u)r pressure of a given liquid always has one fixed and definite value.

It has been shown that evaporation is (according to the Kinetic Theory) the result of the escape of the fastest-moving molecules in a liquid through the surface of the liquid. Consequently, anything which increases the number of swiftly-moving molecules should assist the process of evaporation. Hence a current of air (through ether, for example) will remove these faster particles and lower the temperature in consequence. Supplying heat to the liquid so as to raise its temperature will also remove these fast-moving molecules, for we have seen that the mean speed of the molecules is increased by rise of temperature. When the temperature is high enough, the exposed surface of the liquid is not sufficient to allow the swift-moving molecules to escape fast enough, bubbles of vapo(u)r are accordingly formed within the liquid. Each bubble as it forms rises to the surface – increasing in size as it rises – and finally escapes into the atmosphere.

The process of vaporization by bubble formation is called boiling ; and the temperature at which boiling commences, the boiling point of the liquid. When the vapo(u)r pressure of the liquid is the same as the external pressure to which the liquid is subjected, the temperature does not rise any higher. Increasing the supply of heat only increases the rate at which the bubbles are formed so long as any liquid remains.

Hence it is sometimes convenient to define: The boiling point of a liquid is the temperature at which the vapo(u)r pressure of the liquid is equal to the external pressure exerted at any point on the liquid surface. This external pressure may be exerted by the atmospheric air, by vapo(u)r and air, by other gases, etc. Hence a table of the vapo(u)r pressure of a liquid at different temperatures also shows the boiling points of that liquid under different pressures. Thus water at a pressure of 4-6 mm. of mercury boils at 0°C. Hence liquids which decompose at their boiling point under ordinary atmospheric pressure can frequently be distilled without decomposition at the lower boiling temperature obtained by reducing the pressure. This is the basis of the process of distillation under reduced pressure, or, as it is sometimes less accurately styled, distillation in vacuum.

Source: Mellor’s Modern Inorganic Chemistry, Revised and Edited by G. D. Parkes, M. A., D. Phil., Fellow of Keble College, Oxford. In collaboration with J. W. Mellor, D. Sc. With diagrams and illustrations. Longmans, Green and Co. London – New York – Toronto.

Other pages for distillation:

Yield (extract) essential oil by steam distillation in atmospheric pressure.

Purification of Water for Scientific Purposes.

Properties of Water.

Application of the Kinetic Theory to Liquids, Equilibrium and Vapo(u)r Pressure of Liquid.

Email: postmaster@arasi.freeservers.com

Last Update February 11^th, 2003.

Essential (Volatile) Oils

17 Gomhoria Street, Assiut 71111, Egypt.

Phone/Fax: +2 088 323800.