CHAP. 11: ELECTROCHEMISTRY [CONTENTS] 374
where the activity of water is considered to be one.
The ionic product of water depends on temperature and pressure. At a temperature of
298.15 K and the standard pressure 101.325 kPa it isKw= 1. 005 × 10 −^14. This very low value
allows for the simplification of the equation to
Kw=cH+cOH−
(cst)^2. (11.49)
Note: Relation (11.49) can be applied only for pure water. If it contains other ions, we
have to consider activity coefficients and use relation (11.48).For the dependence of the ionic product of water on temperature we have, see equation
(8.18), (
∂lnKw
∂T
)p=
∆rH◦
RT^2, (11.50)
where ∆rH◦is the standard reaction enthalpy of water dissociation. (Symbol◦(or equivalently
st) for an “unspecified standard state” should be replaced by the respective standard state
of a compound occurring in the dissociation reaction. It is the state “pure substance in the
liquid state (•)” for water and “infinite dilution extrapolated tocst([c])” for ions H+and OH−,
see8.2.3for details.) But for the sign it is equal to the enthalpy of the neutralization of a
strong acid by a strong base
∆rH◦=−∆neutrH◦. (11.51)
Example
Calculate the ionic product of water at the standard pressure and at temperatures of 0◦C and
100 ◦C. Assume that in the given temperature range the reaction enthalpy does not depend on
temperature and equals∆rH◦= 56500 J mol−^1.