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34 GENERAL AND PHYSICO-CHEMICAL.
example is the inversion of cane-sugar by means of acid. This reac-
tion is monomolecular because only the cane sugar is consumed. If
the concentration of the cane-sugar at the beginning is C moles, and if
x moles are transformed in t time, then at that time there are (C —x)
moles remaining. If dx indicates the quantity which is transformed
dx
in dt time, then the reaction velocity is —. According to the law
dt
of mass action this is at every moment proportional to the concentration
of the decomposing substance, or
~=k.(C-x) ’. . . (1)
dt
For practical use this equation is integrated into the following:
A,- = -nat. log. -— (2)
t C — x
If the theoretical considerations upon which this formula is based
are correct, then the x values determined by the polariscope after various
times must give the same figure for k. This is indeed the case. 1
k is
called the velocity coefficient (also velocity constant or specific reaction
velocity). If in the equation (1) C — x or the concentration of the still
dx
undecomposed cane-sugar =1, then the equation becomes ~r = k, from
which it follows that k indicates the reaction velocity if the concentra-
tion of the substrate could be kept the entire time at =1.
In these experiments k retains the same value. If in different experi-
ments the quantity of catalyst (acid) varies, then the obtained value
for k is proportional to the concentration of the H ions. This is so
prominent that the catalytic action of acids is due to the H ions (Ar-
rhenius 2
) . Still irregularities occur as the anions of acids as well as
of salts present can under certain circumstances influence the action of
H ions (see page 70).
Frankel 3
has recently studied the decomposition of diazoacetic ether under
the influence of different acids. The reaction is as follows:
Na : HC.CO.O.C2 H& +H20=HO.CH2 .CO.O.C2 H5+i\2 .
1
See Poggend. Ann., 81, 413 and 499 (1850).
2
Zeitschr. f. physik. Chem., 4, 226 (1889).
3
Ibid., 60, 202 (1907).
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