



Goals:
pH
measurements are presented for a series of HCl solutions of increasing
concentration. The data are analyzed to
determine the activities and activity coefficients of the hydrogenion.
The results are
compared to theoretical predictions from the extended
DebyeHuckel equation. Prerequisites: A knowledge of activities, activity coefficients and the DebyeHuckel equation for mean activity coefficients. Resources you will need: The calculations and graphing associated with this exercise can be carried out within any quantitative analysis software. Background: Students of chemistry are well acquainted with the relationship between solution pH and hydrogenion concentration;
(1)
However, this expression is only accurate in the dilute limit. The exact relationship depends on the activity of the hydrogen ion;
(2)
Consequently, activities for hydrogenion in a given solution can be determined through simple pH measurements, and the activity coefficient (γ) can be evaluated using the relationship
(3)
where C is concentration. Activities can be defined in terms of molar concentrations (M) or molal concentrations (m). Activities calculated through the use of equation (2) will be 'molarbased', which in turn yields a molarbased activity coefficient. This distinction is made clear here by rewriting equation (3) as
(4)
The corresponding expression for a 'molalitybased' activity is given by
(5)
where the two types of activity coefficients are related by the expression .
(6)
and D is the solution density. For moderately dilute aqueous solutions at ambient conditions, the density of the solution is equal to that of pure water (D = 1 g/mL), meaning the molar and molal concentration are essentially equal (within experimental error). Consequently, the molar and molal activity coefficients are equal to one another. In electrolytic solutions, a convention has been adopted whereby one assumes that the nonideality of the solution is shared by the cation and anion. This is accomplished by defining a meanactivity coefficient according to the expression
(7)
where and are the number of cations and anions, respectively, in one formula unit of the electrolyte. A number of theoretical approaches are available for estimating mean activity coefficients. One expression that is valid up to moderate concentrations is an empirical modification of the DebyeHuckel limiting law (the ‘extended’ Debye Huckel equation) given by
(8)
where A is a constant the depends on properties of the solvent (0.5085 for water at 25°C), z_{+} and z_{} are the ionic charges, I is the ionic strength, and B is an empirical constant. Activity coefficients calculated using equation (8) are molalbased. The exercise outlined below will involve using pH data to experimentally determine activity coefficients for hydrogenion and subsequently using this data to test the validity of 'extended' Debye Huckel law. Experimental Data: The following table gives experimentally determined pH values for a series of HCl solutions of increasing concentration at 25 °C.
Data
based upon information contained in Christopher G. McCarty and
Ed Vitz*, Journal of
Chemical Education,
83(5), 752 (2006) and G.N. Lewis, M. Randall, K. P:itzer, D.F. Brewer, Thermodynamics
(McGrawHill: New York, 1961; pp. 23334).
Exercise:


Suggestions
for improving this web site are welcome. You are
also encouraged to submit your own datadriven exercise to
this
web archive. All inquiries should be directed to the curator:
Tandy
Grubbs, Department of Chemistry, Unit 8271, Stetson University, DeLand,
FL 32720.
