Allotropy 3

Lord Kelvin put forward the view in 1851 that the electro motive force of a cell could always be calculated from the heat of the chemical reaction, that is to say from the decrease in total energy. This "law" involves the assumption that no chemical reaction can be made to yield electrical energy unless it is ac companied by a decrease in total energy. It holds approximately for the Daniell cell, and for others such as the standard Weston cell. The Helmholtz equation shows that it can only be true when the electromotive force does not change with the temperature. We are familiar now with cells which yield an electric current even if the chemical reaction is associated with an absorption of heat ; we know of cells the voltage of which increases with tem perature, and others in which it decreases. None of these cells obeys Kelvin's law, but the behaviour of all of them can be shown to be in exact accordance with the Helmholtz equation. The study of electric cells provides the most interesting and exact confirmation of the fundamental laws of thermodynamics.

The Van't Hoff Equation.

Apart from the combustion of coal and oil, most chemical reactions interest us more from the point of view of the nature of their products than from that of the work obtainable from them. As all chemical reactions are in principle reversible, and as many of the more important from a practical point of view can be made to proceed in one or the other direction according to conditions of temperature and pres sure, it is not only of theoretical interest but of great technical importance to get an accurate picture of the relations between chemical equilibrium and thermal changes. Van't Hoff succeeded in doing this by calculating the maximum work that could be obtained from a chemical reaction taking place between gases, by the use of an imaginary "ideal" process. By the application of the second law two important results emerged: (I) The law of mass action, first deduced from consideration of molecular theory, was shown to be a necessary consequence of the thermodynamical laws, that is to say, if a state of equilib rium exists between gases according to the chemical equation (2) The equilibrium constant K was shown to be connected with the temperature and the decrease in total energy through the equation In practical applications it is usually more convenient to express the quantities of gases present in an equilibrium mixture in terms of their partial pressures instead of their concentrations. If there are N molecules of gas present altogether in a mixture which contains ni molecules of one kind, of another, and so on, the partial pressures are etc. where Pis the total pressure. It is simple to show that pressure tends, therefore, to assist combination or to prevent dissociation. This is the case whenever the reaction is accom panied by a decrease in the number of molecules. The synthesis of ammonia is an important technical example. Here one molecule of nitrogen combines with three molecules of hydrogen to form two of ammonia, N2+3H2= The mass action equation is where x is the fraction of nitrogen left over. If the value of v

is diminished, x must also be diminished, and the amount of ammonia formed increases. As is well known, the commercial success of the process depends on very high pressure being used. If no change in the number of molecules is caused by a reaction, 7) cancels out, and therefore an alteration in the pressure has no effect on the equilibrium. If the number of molecules is in creased, v appears in the numerator instead of the denominator, and an increase of pressure will then have the opposite effect.

The effects of pressure and temperatures on equilibrium can be generalized in the statement that the equilibrium will always adjust itself in such a way as to oppose a change in physical conditions. If the pressure is increased, the equilibrium will shift in the direction of smaller volume. When heat is added that reaction will take place which results in an absorption of heat, thus tending to stop a rise of temperature. The same applies to physical processes. Water expands when it freezes; if we corn press ice at the freezing point it will do its best to diminish its volume by melting. Liquids always absorb heat when they evaporate ; if heat is added to water which is boiling at atmos pheric pressure, its temperature is not increased. All that hap pens is that it boils faster.

If a reaction between gases is studied experimentally at any one temperature and pressure, so that the equilibrium conditions are known, then the effect of a variation in pressure at that tem perature can be accurately calculated provided the mixture obeys the "perfect gas" laws. If the heat of reaction is also known at that temperature, then the equilibrium for any other temperature not too far removed can be calculated from van't Hoff's equation. For integration of the equation gives if U does not change much with the temperature. Hence if and K2 are the equilibrium constants at temperatures T1 and T2 Gases and Solids.—Chemical reactions in which gases and solids take part present features of special interest. To take a simple example, carbon dioxide combines with lime to form cal cium carbonate with evolution of heat : Now the pressure of saturated vapour above any solid or liquid is independent of the amount of solid or liquid present, unless the amount is very minute. If a closed space contains carbon dioxide gas, in the presence of solid calcium oxide and carbonate, there will be an equilibrium in the gaseous phase governed by the relation As the concentrations of the vapours of the two solids are constant (though extremely small) at any given temperature, it follows that the concentration of carbon dioxide must also be constant. In other words its pressure is constant. Above a mix ture of calcium oxide and carbonate we have, therefore, our apparent "vapour" pressure of carbon dioxide, which varies with the temperature.