THEORY AND GENERAL PRINCIPLES

13

tion that the product of their concentrations is a constant, 10~^14
gram-ions per liter. This product is a very small quantity and
it is obvious that an acid solution (essentially a hydrion solu-
tion) must contain extremely minute quantities of hydroxylion,
while basic solutions contain considerable concentrations of
hydroxylion and correspondingly little of hydrion. At the
"neutral point" the ion concentrations are equal, so that each
of these two ions is present to the extent of 10~^7 (=\/10-^14)
gram-ions per liter. This is the relation for pure water also and
it is expressed as follows:
[H+1 = [OE-]=10-^7,	(I)
[H+] X [OH-] = K_w = 10-^1*.	(2)
Since Eq. (2) expresses a condition existing in all aqueous
solutions of electrolytes, it will be seen that the concentrations
of the essential ions of acids and bases cannot be independent but
that they must vary inversely, so that "both "acid" and "basic"
conditions might be represented in terms of either one of these
ions. Polio wing the suggestion of Sorensen the expression
—log [H^+] is used for this purpose and the symbol ph* is used
to indicate this quantity. This symbol has been variously
modified to pH or ph. So long as ion concentrations are ex-
pressed as powers of 10, as a»bove, P_s will be the same as the
negative exponents of 10. Eeference to Eq. (1) shows that the
neutral condition will "be expressed by the statement

P_H = 7 (strictly, 7.03 at 20°).

(3)

For acid solutions P# is always less than 7 and for basic solutions
it is always greater than, 7.
Et has already been remarked that indicators are themselves
acids or bases, as in solution they yield hydrion or hydroxylion,
or both (amphoteric indicators) and the concentrations of these
ions are definitely related to the equilibrium concentrations of
the tautomeric forms of the indicator, finally responsible for the
color changes. Therefore the color changes of the indicator will
follow the change in the value of P_H as neutralization of the
solution is approached.
The use of indicators for the determination of actual hydrogen
ion concentration has been highly developed and this use finds a
wide application in many fields of applied chemistry. This