ALLOTROPY.) (3) Influence of Temperature.—The influence of temperature on the thermal effects of a chemical reaction is sometimes con siderable. If we know the change in total energy associated with any reaction at one temperature, the first law enables us to calculate it for any other temperature. If, for example, the total energy content at temperature T1 is for z mol. of hy drogen, for i mol. of oxygen, and U1120 for 1 mol. of water vapour, the change in total energy due to the combination of hydrogen and oxygen to form 2 mols. of water vapour is, say, If we raise the temperature of 1 mol. of hydrogen (etc.) from to its total energy is increased by where (Q., is the mean capacity for heat of I mol. of hydrogen at constant volume between the temperatures T2 and This is simply a definition of what we mean by molecular specific heats. Hence the total energy change at the higher temperature T2 is: We can express this most simply by saying that the rate of change of U with the temperature (dU/dT) is equal to the sum of the heat capacities of the reacting compounds minus the sum of the heat capacities of the products of the reaction.
(a) Heats of Combustion.—Experiment has shown that the heat of combustion of organic substances of various kinds varies regu larly with the molecular weight. The difference between the heats of combustion of two neighbouring members in a series of homolo gous compounds is practically constant, and the value of the con stant shows very little variation as we pass from one series to another. Thus the heat of combustion of methane, to carbon dioxide and liquid water at constant pressure is 212,000 calories; of ethane, C2116, is 370,500 calories, a difference of 158,50o cal ories; of propane, is 529,200 calories, which is 158,700 above that of ethane ; and the heat of combustion of all paraf fin hydrocarbons (C,,H2,,+2) can be expressed by the formula 212,000+158,500 or 158,500 n+53,500 calories, where n is the number of carbon atoms in the molecule, and the mass to which the heat of combustion refers is the molecular weight in grams of the compound.
Similarly the heat of combustion of alcohols C„H2„,10H, can be expressed by the formula : As a rule the addition of a group to any organic molecule will increase the molecular heat of combustion by about 158,800 calories, but the rule is not exact, and the actual figure varies somewhat from series to series. In particular the heat of combus tion of two isomeric substances, i.e., substances with the same number of carbon, hydrogen, oxygen, etc., atoms in the molecule, but differently arranged, are very nearly but not exactly the same. It follows that there are similar regularities in the heats of forma tion of organic compounds, for the heat of formation is the dif ference between the heat of combustion of a compound and the total heats of combustion of the carbon, hydrogen, etc., it contains.
(b) Heats of Neutralization.—The heats of neutralization of acids and bases in aqueous solution are additively composed of two terms, one being constant for a given base, the other constant for a given acid. In addition to this the further regularity has been observed that, when the powerful monobasic acids are neu tralized by the powerful monacid bases in dilute solution, the heat of neutralization is in all cases the same. The following table gives the heats of neutralization of the commoner strong monobasic acids with soda: Within the error of experiment these numbers are identical.
It was at one time thought that the greater the heat of neutral ization of an acid with a given base, the greater was the strength of the acid. It is now known, however, that when weak acids or bases are used, the heat of neutralization may be either greater or less than the normal value for powerful acids and bases, so that there is no proportionality, or even parallelism, between the strengths of acids and their heats of neutralization (see CHEMICAL ACTION ).