A system of physical chemistry - Index of

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A system of physical chemistry - Index of

WHETHAM'S RULE OF COLLOID COAGULATION 7

The ratios in which these three concentrations stand to one another are—

Ci : C2 : C3 :

= B^

III

B^" : B^"«

L

= I : b'^" : B3».

I

Putting B^" = i/^, the ratios can be written—

I : i/jt- : \lx^.

These represent numbers which indicate relative concentrations of equal

coagulating power. Hence the relative coagulating powers Pj, Pg, P3 of

equal concentrations of these three ions are given by the reciprocal of

the above numbers. That is—

,

The value of x, which depends upon a number of unknown factors

characteristic of the colloid considered, cannot be found on a priori

grounds. If we take Linder and Picton's experiments into account and

set jc = 32, we get for the relative coagulating powers of univalent,

divalent, and trivalent ions respectively, the values i : 32 : 1024.

It will be seen that these numbers are of quite the same order of magni-

tude as those observed. Whetham predicted on this basis that the

coagulating power of a tetravalent ion on the above colloid should be

a large number, approximately 33000. Recent measurements have

corroborated this result in so far as an extraordinarily large coagulating

power is actually obtained.

The Law of Error.— It is a familiar fact in physico-chemical

measurements that repetitions of a certain measurement give rise to a

series of numbers which are not identical. The variations we speak of

as experimental errors. The measurements are as likely to be too high

as too low, that is, the errors are as often positive as negative, provided

is assumed that

we make a very large number of determinations. (It

there is no systematic error in the apparatus or in the method of

measurement.) The treatment of such results so as to obtain the most

probable result, i.e. the most accurate determination, is a further illus-

tration of the application of the theory of probability, somewhat more

complex in nature than that hitherto considered.

Thus, it is possible to construct a probability curve, by means of

the probability equation given below, which has been found to agree

closely with the actual results obtained in a series of experimental determinations

of a given quantity. Examples will be found in a textbook

of mathematics, e.g. Mellor's Higher Mathematics. The large

majority of the readings will fall very closely together, i.e. they will

not be far removed from the true result, a smaller number of readings

will be farther away on either side of the true result, and only a very

small number will be much to one side or the other. This distribution

of values may be represented by an expression of the form—

'

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