A system of physical chemistry - Index of

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A system of physical chemistry - Index of

HABERS HEAT RELATION 155

In the case of reactions in which catalytic effects are absent we may

generalise the above expression, and write—

Heat evolved = -

SN/^Vresultants 2N/^i/reactants.

This expression, deduced however by a totally different method, was

first given by Haber (j5^r. Deutsch. phys. Ges., 13, 11 17, 191 It

1).

may therefore be called the Haber expression for the heat effect. The

above mode of deduction is that given by the writer {Trans. Chem. Soc.^

Ill, 457, 1917)-

In the above formulation the heat of reaction at constant volume

has been expressed as the difference of the critical ference of the critical

quanta or the dif-

increments of the resultants and the reactants.

The heat effect at constant volume is also thermodynamically defined as

the difference of the mean internal energies of the reactants and resultants.

To see that these two definitions are concordant we may

proceed in the following manner.

Let us consider the simplest type of reaction, viz. A Ij B. The

various energy terms involved in the process are represented in the accompanying

diagram (Fig. 13). The ordinates denote internal energy,

the length ab corresponding to the mean values Ui of the internal

energy possessed by one gram-molecule of the substance A, and similarly

the length de represents the mean energy Ug of the substance B. Be-

fore one gram-molecule of A, possessing the average internal energy

Uj, can become reactive its internal energy must rise to the point c by

the addition of the critical increment Ej. At this stage the grammolecule

possesses the energy (Ui 4- EJ. It may now change into

one gram-molecule of B, with an evolution of energy denoted by the

dotted line ce. The gram-molecule now possesses the mean energy de, or

U2 characteristic of the substance B. In passing from c X.o e the energy

emitted is - -1- (Uj E^) Ug. In passing from the mean state b to

the mean state e the total energy

evolved is (Uj -f E^ - U2) - 1

Ej,

or -

Uj Ug. The total energy

1

evolved in passing from e Xo b \%

1

(U. -1- Eg - Uj) - E.,, or Uo - Ui.

This expresses the fact that if the

reaction is exothermic in one direc-

tion it necessarily endothermic in

the reverse direction.^

When a molecule is in the

critical state it is impossible to say

whether it belongs to the system A

or to the system B. That is, the

critical state is common to both A

and B. If E^ denotes the total

critical energy— not the critical increment

— Ec will have the same

value for the A and B molecules

^ Note that on the above mechanism the system never passes along the hne he.

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