It is necessary to distinguish between heats evolved when reac tions take place at constant pressure and at constant volume. Only the latter accurately correspond in all instances to the change in total energy due to the reaction. If the reaction is allowed to take place at constant (atmospheric) pressure and there is a change in volume due to the reaction, then work is done, and the measured heat of reaction will not be the same as the change in total energy. In the case of reactions taking place between solids or liquids the difference is usually negligible ; in cases of gases the necessary correction can be easily applied. For instance, in the combustion of methane to carbon dioxide and liquid water, three volumes of mixture react to form one volume of carbon dioxide and a negligible volume of liquid water. This diminution of volume means that at constant pressure work is performed by the atmosphere. This work reappears as additional heat in the calorimeter. If we take the volume of one mol. of gas (22.4 litres) as the unit volume, the work done, 2PX V, according to the gas laws = 2 RT, where R, the gas constant, is approximately 2 when the work is expressed in heat units, and T is the absolute temperature. Thus the heat of combustion of methane, measured at 18° C (or 291° absolute), should be approx imately 1,200 calories higher when the combustion takes place at constant pressure, e.g., when the gas is burnt in a jet, than when the mixture is burnt in a completely closed vessel. If, however, the combustion takes place above ioo° C so that no water vapour con denses, there is no change of volume, and no difference between the heats evolved at constant volume and constant pressure.
Indirect Determination.—Many heats of reaction are difficult if not impossible to measure directly. This is true of most reactions in organic chemistry which either do not take place rapidly enough to allow of accurate measurement, or yield other products besides those under investigation. But if the heats of combustion of organic compounds are known, the heat of any conceivable reac tion between such compounds can be estimated by means of the first law. Take, for example, the technically important formation of methyl alcohol from carbon monoxide and hydrogen which pro ceeds according to the equation, C0+2H2=CH3OH. The heat of combustion of z mol. of carbon monoxide to carbon dioxide at constant pressure is 68,300 calories. The heat of combustion of 2 mols. of hydrogen to liquid water at constant pressure is 2 >08,400 calories =136,800 calories. The heat of combustion of mol. of methyl alcohol in the form of vapour to carbon dioxide and liquid water is 182,000 calories. Now the total change in en ergy must be the same whether the carbon monoxide and hydrogen are burnt directly to carbon dioxide and water, or whether they are first transformed into methyl alcohol and then burnt. Hence the heat evolved when carbon monoxide and hydrogen unite at con stant pressure to give methyl alcohol in the form of vapour is : 68,300+536,800-182,000= 23,100 calories.
This example will serve to show the importance of accuracy in calorimeter measurements. For suppose Thomsen, whose figures have been taken, underestimated the heats of combustion of carbon monoxide and hydrogen by I %, and overestimated that of methyl alcohol by 1 %, the corrected figure for the heat of reaction to methyl alcohol would then be 69,000+138,200-18o,200= 27,000 calories, which is nearly 20% higher than the estimate made on the basis of Thomsen's recorded results.
(1) Dilution of Solutions.—Generally speaking, there is a con siderable thermal effect when a substance is dissolved in water, and this effect varies in magnitude according to the amount of water employed. It is only, however, when we deal with compara tively concentrated solutions that the heat-effect of diluting the solutions is at all great, the heat-change on diluting an already dilute solution being for most practical purposes negligible. In dealing, therefore, with dilute solutions, it is only necessary to state that the solutions are dilute, the exact degree of dilution being unimportant. It occasionally happens that a change in dilution affects the chemical action that occurs. Thus, if con centrated instead of dilute sulphuric acid acts upon zinc, the action takes place to a great extent not according to the equa tion but according to the equation sulphur dioxide and water be ing produced instead of hydrogen. Here we have a different final system with a different amount of intrinsic energy, so that the thermal effect of the action is altogether different.
(2) Physical State.—The physical state of the reacting sub stances must be considered, since comparatively large amounts of heat are absorbed on fusion and vaporization. Thus the heat of fusion of ice (for 18 grams of is 1,440 cal., and the heat of vaporization of water at oo° for the same quantity is 9,67o'cal. When a substance, e.g., carbon, phosphorus, sulphur, exists in allo tropic forms, the particular variety employed should always be stated, as the conversion of one modification into another is fre quently attended by a considerable thermal effect. Thus the con version of white into red phosphorus evolves about one-sixth of the heat of combustion of the latter in oxygen, and so the knowl edge of which variety of phosphorus has been employed is of es sential importance in the thermochemistry of that element. (See