REVISED 01/11
CHEMISTRY 232
Dissociation Constant of a Weak Acid: Accurate Conductometric Method
For the exact determination of a dissociation constant, activities rather than concentrations and
the consequences of the Debye-Hückel theory rather than the Arrhenius theory must be
considered. The thermodynamic dissociation constant of an acid is given by:
Ka 
a H  .a A 

C H C A
a HA

C HA
 H  . A 
 HA
(1)
where  H and  A are the activity coefficients of the ions in terms of molarities and  HA is the
activity coefficient of the undissociated acid. If the ionic strength of the medium is not too high,
 HA never differs greatly from unity and we may write:


 C   
2
Ka =
2
(2)
1 a
Where  is the mean ionic activity coefficient. The degree of dissociation can be determined
from conductance data for a weak acid (1) using a modified form of the on sager equation. The
degree of dissociation is given by:
 

(3)
F
o
Where λ is the molar conductance of the solution,  o the molar conductance at infinite dilution
and F is given by:
 B 1 o  B 2 

3/2
o


( C )
F=1+ 
(4)
Where B1 = 0.230, B2 = 60.65 and C is the concentration in moles/lit. Combining equations 3
and 2, we have
F   C
2
F   o 
2
2
(5)
Ka  o
The activity coefficient   can be calculated from dilute solution using Debye- Hückel’s limiting
law:
Log γ± = -0.509
Ca   0 . 509
(C  F /  o )
(6)
CHEMISTRY 232 – Dissociation Constant …: Accurate Conductometric Method
Page 2
For aqueous solutions of 1:1 electrolyte at 25°C.
Equation 5 may be rewritten:
F   o 
Z
Kao
where Z  F    C
2
2
2
Hence, using a provisional value of  o to calculate F as defined in equation (4), a plot of  F
against Z can be prepared. This graph should be linear and when extrapolated to zero gives a
more accurate value for  o . The function F may now be recalculated from equation (4), using
this improved value of  o . This process is repeated until consistent results for  o are obtained.
The thermodynamic dissociation constant may then be calculated from the slope of the final
graph which is equal to 
1
(K a  o )
PROCEDURE:
WASTE DISPOSAL
All solutions in sink with lots of water
Accurately prepare 250 mL of a 0.0200 M solution of KCl (conductivity standard). The specific
conductivity of 0.0200 M solution of KCl at 25°C is 0.002758 S/cm.
Prepare 5 solutions of p-hydroxybenzoic acid by exact dilution of the stock solution provided
with deionized water. Use 1 mL, 2 mL, 3 mL, 4 mL and 5 mL volumes in 50 mL volumetric
flasks.
Measure the conductance of the KCl solution at room temperature. Basic instructions for the
conductivity meters set out beside each meter and additional measuring techniques are provided
here. Rinse the probe with deionized water, gently shake off excess water, and place the probe
into a beaker filled with conductivity standard. The probe should not touch the walls or bottom
of the beaker.
Measure the conductance (μS) of the p-hydroxybenzoic acid solutions beginning with the least
concentrated solution. Rinse the beaker with small portions before adding the solution to be
measured.
Calculations
Calculate the cell constant, k. Calculate the conductivity, κ (S cm-1), for each solution measured
based on the conductance. To obtain a provisional value of λ0, the measured conductivities are
converted to molar conductivities (S cm2 mol-1) and a plot of 1/λ vs λC is prepared.
CHEMISTRY 232 – Dissociation Constant …: Accurate Conductometric Method
Page 3
 In this method, simple Ostwald's dilution law is used, e.g. for a weak acid:
 C
2
Ka =
1 
and    /  o
 C
2
or Ka =
 o ( o   )
 C
2
or rearranging  2o   o  
Dividing by  20   we get
a plot of
1

Ka
1


1
o

C
Ka  o
2
vs  C gives a st. line with an intercept =
1
o
Using this provisional  o value, the value of F is calculated as defined in equation (4) at each
concentration. A plot of  F against Z is prepared. This plot is extrapolated to zero to give a
more accurate value of  o. A second plot of  F against Z is prepared and Ka calculated from
the slope.
REFERENCES:
T. Shedlovsky, Physical Methods of Organic Chemistry, edited by A. Weissberger, Volume 1,
Chap XXV. Interscience Publishers, New York.