Page 138 - Mechanism and Theory in Organic Chemistry

Bronsted Acids and Bases 127

activitie~,~ and then converting to the more usual form given in Equation 3.17 by
incorporating the water activity, which is essentially constant in dilute solution
when water is the solvent, into the equilibrium constant. It is often convenient
to write Ka in terms of concentrations and activity coefficients, as indicated in
Equation 3. 18.7

-
The standard state is defined as the hv~othetical state that would exist if
-- - -
1'1 -,-__l--
--
---
-.--
the I~_C____I-- soffi-e were at _ a concentration of 1 x but with the molecules experiencing
. _ __
the environment of an extremely -- dilute ~_ solution; _ with this standard st~~aaivity-.
T---
coefficients--approach unit~,yithw~-eaing, dTTution. =-electrolytes in dilute
solution in water, the departure of the coefficients from unity can be calculated
from the Debye-Hiickel relationship.* . .
It is possihl~ tn define -rium constant, K, (Equation 3.19),
which do es not incm art anrl

stant except in very dilute solutions, where it approaches the thermodynamic KO-
that we have been considering so far. The constant Kc is often used for con-
venience, but it is not satisfactory for careful work, nor where comparisons
between different solvents must be made.
Base strengths can be defined similarly by the equilibrium constant for
Reaction 3.20:

Bm+ + H,O BH('"+ l)+ + OH- (3.20)

Or, adopting the same convention as before with respect to the water activity,

However, it is more convenient to consider instead of Reaction 3.20 the acid
+ :
dissociation of the acid BH(m +

If Ka for equilibrium 3.23 is known, K,, as defined by Equation 3.22, can easily
be found by use of the constant K,, the ionization constant of pure water. K, is

W. J. Moore, Physical Chemistry, 3rd ed., Prentice-Hall, Englewood Cliffs, N.J., 1962, p. 191.
The activity coefficient y is defined so that a = yc, where a is activity and c is concentration. See
Moore, Physical Chemistry, p. 198.
See Moore, Physical Chemistry, p. 351.