Page:Outlines of Physical Chemistry - 1899.djvu/264

 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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