measurements being, the deduction from the general theory of energy, which states, that the total loss of energy during the passage of a chemical system from a definite initial to a definite final state is independent of the intermediate states. The application of this generalisation was illustrated in par. 120. We are now however in a position more fully to discuss the relations existing between gain or loss of heat, and gain or loss of energy by a chemical system. It will be advantageous to confine our consideration at present to gaseous substances. When heat is imparted to a gaseous system of chemical substances, a portion may be employed in increasing the kinetic energy of motion of the molecules, i.e. in raising the temperature, of the system; another portion may be employed in doing work against external forces, e.g. in causing expansion of the system; and another portion may do work against molecular and atomic forces, and so produce a rearrangement of molecules, or atoms, i.e. may cause chemical changes to proceed within the system. The exact manner of the distribution of the energy imparted in the form of heat will vary in each special case. It is evident that the thermal value of the purely chemical part of a change-say of the system 2H, + O2 to the system 2HO—will vary according to variations in the physical conditions under which the change proceeds, and more especially according to variations of temperature.

2

The difference between the energy of the system 2H, +0, and that of the system 2H2O (both in grams) at ordinary temperatures, say at 15°, is measured by 136,800 thermal units; what will be the value of the difference between the same systems at 200°?1.

Let 15 and 200 represent the two differences: let U= the quantity of heat which must be imparted to the first system (2H,+O2) in order to raise its temperature from 15° to 200°; let the quantity of heat which must be imparted to the second system (2H,O) to raise its temperature through the same interval; then

=

2200=215+ U-V.

1 See Naumann, loc. cit. 212, 213.

To find U, we have the following data:

Specific heat of hydrogen (referred to an equal weight of water) = 3*409.

4.185.3409 =2522 thermal units needed for the hydrogen of the

first system;

and 32.185.0'2175=1288 thermal units needed for the oxygen of the first system;

.. U=3810 thermal units.

To find we have the data:

Specific heat of water = 1; heat of vaporisation of water=536.5.

Spec. heat of water gas=0*4805 (up to temperature somewhat near 200°). .. for raising temperature of system 2H2O from 15° to 100°, are required, 36.85.1=3060 thermal units;

for changing 2H2O, liquid, at 100° into 2H,O, gaseous, at 100°, are required, 36.536.5= 19314 thermal units;

for raising temperature of 2H2O, gaseous, from 100° to 200°, are required, 36. 100.0*4805=1730 thermal units;

And

.. V=24,104 thermal units.

2200=136,800+3810-24,104=116,506 thermal units.

The difference between the energies of the systems, 2H,+O, and 2H,O (in grams) at 15° is measured by 136,800 thermal units; whereas the difference between the energies of the same systems at 200° is measured by 116,506 thermal units. Or we may say [2H2, O2] at 15° - [2H2, O3] at 200° = 20,294 units.

=

We have assumed that the total loss of energy during the chemical change is measured by the quantity of heat evolved.

Thomsen has considered the influence of temperaturechanges on the thermal values of the chemical reactions between liquids'.

:

Let the action which is to be investigated occur between two liquids let A be the number of gram-molecules of the first, and B the number of gram-molecules of the second liquid (using 'molecule' as = amount expressed by formula), and let a = specific heat of the first, and B = specific heat of 1 See especially loc. cit. 1. 65-70.

M. C.

19

the second liquid; further let y = specific heat of the liquid obtained by mixing A and B; then the calorimetric equivalents of the three liquids are (1) A.x=qas (2) B.B = 9o, (3) (A + B). y = 9c. For small variations of temperature the values of the specific heats, and therefore of the calorimetric equivalents, may be regarded as independent of temperature. Then putting R, as the thermal value of the change represented by [A,B] at temperature T, and R, as the value of the same change of temperature t we get1

And from this, the variation in the value of R for each degree of temperature may be found, by the equation

This formula is applied by Thomsen to the reactions between acids and bases at varying temperatures2.

To obtain a perfectly general formula it would however be necessary to study the relation between the specific heat and the temperature of each solution employed, and also of the solution produced by the chemical change: it would also be necessary to know the relation between the variation in the value of the calorimetric equivalent of each solution and the composition of that solution, i.e. the relative number of grammolecules of salt and water contained therein. Thomsen's general conclusion-based on the examination of the influence of water of dilution on H,SO,Aq, HCIAq, NaOHAq, Na,SO,Aq, NaClAq, Na,SO,2HClAq, and H2SO12NaClAq -is, that the calorimetric equivalent of a solution mixed with water is always less than the sum of the calorimetric equivalents of the original solution and the added water: i.e.

1 See for details shewing how these formulæ are obtained, Thomsen, loc. cit.

66-67.

2 loc. cit. 1. 68—70.

3 Tabulated data bearing on both of these points will be found in Naumann,

loc. cit. pp. 289-310.

4 loc. cit. 1. 80-88.

E. Wiedemann has recently investigated the connection between the calorimetric equivalents of certain solutions and the relative quantities of salt and water contained therein1.

The calorimetric equivalent of a solution of a salt with molecular-weight, or rather formula-weight, M, dissolved in n molecules of solvent having molecular weight m, is evidently' c (M + nm), when c = specific heat of the solution. Wiedemann finds that in the cases of aqueous solutions of sodium chloride, sulphate, and nitrate, and ammonium sulphate, the calorimetric equivalent (or it may be called the molecular heat, using the term 'molecular' as already defined) of very concentrated solutions is greater than that of the water contained therein; as the solutions are diluted, a point is reached at which the calorimetric equivalents of the solution and of the water therein become equal; and lastly the calorimetric equivalent of still more dilute solutions is less than that of the water alone. In other words, if the calorimetric equivalent of the water in the solution is 18 n, then

for concentrated solutions

c(M+nm)>18n) for aqueous solutions for solutions of mean concentration c (M+nm) = 18n of NaCl, Na2SO4 for dilute solutions c(M+nm)<18n) NaNO, & (NH4)2SO4•

Wiedemann's results seem to give a general confirmation to those of Thomsen3.

The relations between the calorimetric equivalents, and therefore the relations between the thermal changes and the temperature, of solutions of hydrated and dehydrated salts are more complicated than those already considered. Thus, solutions made by dissolving (1) one gram-molecule of MgSO, in 100 gram-molecules of H2O, and (2) one gram-molecule of MgSO 7H2O in 93 gram-molecules of HO, contain the same

1 Wied. Ann. 18. 608.

2 The 'molecular' heat of the solid in solution may be determined by the help of this formula, provided the specific heat of the solvent is known: see Wiedemann, loc. cit.

3 A general treatment of the influence of temperature on the thermal values of changes occurring between liquids will be found in Jahn, loc. cit. Appendix 3, 210-216.

quantities of MgSO, and H.O. Now from observations of the specific heat of solution (1) it is found that

c (MgSO4+100 H2O)=1761.

But, knowing the specific heat of magnesium sulphate, viz. c(MgSO,) = 27, we should calculate that

c (MgSO4+100 H2O)=27+(100 × 18) = 1827.

On the other hand, if the specific heat of the hydrate MgSO, 7H2O is determined, and from this, that of the solution MgSO, 7H2O+93H,O is calculated, we get this result, c (MgSO47H2O) = 100, .. c (MgSO17H2O+93H2O) = 100+(93 × 18)=1774. The observed calorimetric equivalent is, in each case, less than that calculated on the assumption that the equivalent of a solution is equal to the sum of the equivalents of the salt and of the water; but the difference between the observed and the calculated values is smaller when the solution is made from the hydrated, than when it is made from the dehydrated salt'. Thomsen considers various cases of this kind, and draws the general conclusion, that the change in the thermal value of the solution of a hydrated salt in water, as temperature increases, is smaller, the greater the amount of water of hydration in the salt.

When compounds other than hydrated salts, being either solids, liquids, or gases, dissolve in water, the value of the thermal change also varies according to changes of temperature, but this variation is sometimes positive and sometimes negative with reference to the temperature-change.

130. Any chemical reaction occurs only within certain limits of temperature; by passing beyond these limits it is sometimes possible to reverse the process both chemically and thermally, without altering the nature or masses of the reacting substances; thus,

at ordinary temperatures 2H2O+2Cl2=4HCl +O2 .......... but at about 200°

4HC1+0=2H,O+2Cl2........

.(1)

.(2) ;

1 Hence it follows that the specific heat of the water in a solid hydrated salt is less than the specific heat of the same water when the salt is in solution. (Thomsen, loc. cit. 1. 71.)

2 loc. cit. I. 70-74.