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TRANSACYIONS OF SECTION B. 751 
5. On the Velocity of Reaction before Perfect Equilibrium takes place. 
By MEYER WILDERMANN, 
As we know, there are two kinds of equilibrium: perfect and imperfect. 
Gibbs gives us the rule for distinguishing the two kinds: when kinds of mole- 
cules constitute n+ 1 phases or parts of a system, the equilibrium is a perfect one; 
and when z kinds of molecules constitute a system of less than x +1 phases, the 
equilibrium is an imperfect one. To perfect equilibrium belong first the so-called 
‘physical’ reactions, where one and the same substance is in different states of 
aggregation, thus forming different parts or phases of the heterogeneous system— 
e.g., where solid and liquid or gas, liquid and solid or gas, &c., are in equilibrium. 
To perfect equilibrium belongs also the great range of ‘chemical’ reactions, which 
have the common feature with the physical, that to a given temperature only a 
certain pressure corresponds at which the system can be in equilibrium, and the 
one may change in their mass but not in their constitution—e.g., the system 
aCQO, and CaO, CO,, &c. The velocity of reaction before imperfect equilibrium 
takes place (in homogeneous systems) was thoroughly investigated by Wilhelmy, 
Harcourt and Esson, Gouldberg and Waage, van ’t Hoff, and others. But as the 
velocity of reaction before perfect equilibrium takes place has remained to the 
present time a large and scarcely known field, and the few investigations which have 
been carried out have not led to any simple results or quantitative conclusion, the 
author has been induced to make the following investigation. 
1. Velocity of solidification of liquids and solutions (phenol and solutions of 
water in phenol). The author has investigated the velocity of solidification of 
phenol and of solutions of water in phenol in a U-tube, one part of which was 
replaced by a narrow tube of very thin platinum; the U-tube was immersed in 
baths of different temperatures below the melting-point. By good arrangement 
for stirring, the temperature of the bath was kept constant within the limits of 
0°05 C. The time was observed to a } second. A fine, very sensitive thermo- 
meter was placed in the platinum tube to measure the rise of temperature of the 
liquid while the reaction takes place (the rise equals more than 40 per cent. of the 
total value of overcooling to—¢,,). If abscisse represent the amount of overcool- 
ing below the melting-point, and ordinates, the velocities of reaction, or -the time 
required for the passage of the solidified mass from one end of the platinum tube 
to the other, we obtain straight lines, cutting the melting-point (instead of the 
irregular curves of Gernez or Moore, which cut the abscisse considerably below 
the melting-point)—7.c., the equation - =c(t,—t), (1.), where = is the time, ¢ is 
dz 
the temperature of equilibrium, holds good. The surface of the solid in contact 
with the liquid remaining the same, the velocity of reaction is directly proportional 
to the remoteness from the melting-point. 
2. Velocity of reaction before equilibrium between liquid and solid solutions 
takes place (solidification of phenol and meta-cresol). It was found that phenol 
and m-cresol form solid solutions. The m-cresol is partly dissolved in the liquid 
phenol, partly in the separated solid phenol, following the laws of van ’t Hoff. 
The velocities in a U-tube have been investigated, and the author finds that the 
equation (1.) holds good. 
3, Velocity of crystallisation of overcooled liquids and solutions (the solid 
solvent is in equilibrium with the liquid solvent or solution). In the case of 
crystallisation only a part of the liquid becomes solid as far as necessary to bring 
it to the freezing temperature. The method used is based on the principle that 
the heat freed during the reaction is as completely as possible absorbed by the 
liquid. Good arrangements for stirring are required. The cooling of the liquid 
stirred by the surrounding medium must be so small that it may be neglected or 
only a small correction required (1,250 c.c. liquid is used, t,-¢ is kept small). A 
very sensitive 1/100° thermometer is of first importance (with a long thin bulb as 
thin as possible). The time was observed to 4 second. From the results obtained 
the equation, lgn(t, — toy) — lgn(t, — toc) + lgn(to —t,) — I(t — t,) = C(Z,—Z,)(to — tov) 
