246 OUTLINES OF PHYSICAL CHEMISTRY
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k a—x and by integration,
t= 1 In _J_ + c. k a—x
At the time 0, that is to say at the beginning of the reaction, the value of x is 0, and consequently
= I In i + c. k a
From these two last equations we find : l
. 1 7 a
£= -In
��k a—x
1 n
k = In (equation 1).
t a—x
As the study of the speed of reactions is of great theore- tical interest, and as no very special apparatus is required for the work, it may be desirable to give here some idea of
and is composed of two factors : the speed-coefficient h and the concentration of the acid. In reality, therefore,
K-kc,
1 The constant c is often eliminated in another way. Two polarimetric tests are made, one at the time t, and the other at the time t v and from the equations
t = _ In + c.
k a — x
L = - In + c.
e a—x x
we find
k = In a ~ x (equation 2).
£i — t a — x t
According to theory, the value of k must be constant. By ex P?^"
mentally determining the values x, x v x 2 , which correspond to
the times t, t v t v we can prove that this really is the case.
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