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1. Acid-base equilibria
1.c. Determination of conductivity of strong and weak electrolyte
The solvated ions 𝐻𝐻+
and 𝐴𝐴−
are occurred when a substance 𝐻𝐻𝐻𝐻 of analytical
concentration 𝑐𝑐𝐻𝐻𝐻𝐻 is dissolved in water or other polar solvent. The thermodynamic
equilibrium exists in the solution:
𝐻𝐻𝐻𝐻 →←R
𝐻𝐻+
+ 𝐴𝐴−
𝐾𝐾𝐴𝐴 =
[𝐻𝐻+][𝐴𝐴−]
[𝐻𝐻𝐻𝐻]
(1.1.)
The degree of dissociation α determines whether the equilibrium is shifted in favour of
the dissociated ions or original undissociated compound.
[ ]( )
HA
HA
c
HAc −
=α (1.2.)
Rearranging of equation and apply of electroneutrality condition give (if we neglect
solvent dissociation) following:
[ ] ( )α−⋅= 1HAcHA and [𝐻𝐻+] = [𝐴𝐴−] = 𝑐𝑐𝐻𝐻 𝐻𝐻⋅α (1.3.)
The dissociation degree α is determined not only by the properties of the substance HA
but also by the solvating ability of the solvent.
The dissociated solute HA increases the initial electrical conductivity of the solvent.
Dissolved solute is called weak electrolyte in a given solvent (eg aqueous solutions of
carboxylic acids, H2S, H3BO3, NH3) if the dissociation degree is small or close to zero (
0→α ). Dissolved solute HA is called a strong electrolyte if the dissociation degree is
close 1≅α . For example, aqueous solutions of inorganic acids and bases (HCl, NaOH,
...) and ionic salts (KCl, NaNO3, ...).
The concentration of dissociated ions in the solution has a significant effect on its total
electrical conductance 𝐺𝐺 (meassured in Simens 1𝑆𝑆 = 1 𝛺𝛺−1
= 1 𝐶𝐶 𝑉𝑉−1
𝑠𝑠−1
) that is the
reciprocal quantity of electrical resistance 𝑅𝑅 (unit 𝛺𝛺). Similarly to metal conductors, a
specific resistance [𝛺𝛺 𝑐𝑐𝑐𝑐] can be detected for solutions, but it is prefered to monitor the
specific conductivity of solutions [𝑆𝑆 𝑐𝑐𝑐𝑐−1
], which is as well the reciprocal value of
specific resistance.
The specific conductivity κ of the solution is calculated from its conductivity 𝐺𝐺 that is
measured by conductivity probe with known resistance constant 𝐶𝐶 [𝑐𝑐𝑐𝑐−1
] according to
relationship:
κ = C G. (1.4.)
The geometric constant of conductivity probe 𝐶𝐶 can be most easily determined by
measuring the conductivity of solution 𝐺𝐺 with known specific conductivity. Usually, the
aqueous KCl solution is used as standard electrolyte.
Specific conductivity of 0,01 M KCl (i.e. κ0.01𝑀𝑀 𝐾𝐾𝐾𝐾𝐾𝐾 in [S cm-1
] ) depending on temperature
𝑡𝑡 (in ºC) can be found in tables or calculated using polynomial:
κ0.01𝑀𝑀 𝐾𝐾𝐾𝐾𝐾𝐾 = 𝑎𝑎1 + 𝑎𝑎2⋅𝑡𝑡 + 𝑎𝑎3⋅𝑡𝑡2
where: 𝑎𝑎1 = 7.728⋅10−4
, 𝑎𝑎2 = 2.345⋅10−5
, 𝑎𝑎3 = 7.816⋅10−8
. (1.5.)

ú l o h a J . S o p o u š e k
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6.c
Modern conductivity meters measure specific conductivity κ directly when properly
calibrated to 𝐾𝐾𝐾𝐾𝐾𝐾 standard solution.
A very important characteristic of the solutions is the molar conductivity, which is
calculated from the specific conductivity according to the formula:
c
κ
λ = (1.6.)
where 𝑐𝑐 is molar concentration of solute. The molar conductivity of the solute
extrapolated to zero molarity (in the limit of zero concentration) is called the limiting
molar conductivity:
( )∑ ⋅= i
i 00 λνλ (1.7.)
where λ0
𝑖𝑖
is a limiting molar conductivity of particular ion 𝑖𝑖 presented in the solution
(compare TABLE I), iv is the number of ions to which the solute dissociates in the
solution.
Assuming that the dissociated ions do not affect each other, we can calculate the
dissociation degree for both strong and weak electrolytes:
00 λ
λ
λ
κ
α =
⋅
=
c
(1.8.)
The dissociation constant of weak mono-acidic acids can be determined according to
Ostwald's dilution law obtained by inserting eqn (1.8.) in (1.3.) and then into eqn (1.1.)):
( )λλλ
λ
−
=
00
2
.c
KA (1.9.)
The Ostwald dilution law can be arranged to a linearized formula
( ) 0
2
0
1.1
λλ
λ
λ
+=
AK
c
(1.10.)
that is appropriate for graphical determination of the dissociation constant 𝐾𝐾𝑎𝑎 and the
limiting molar conductivity of solute λ0 .
TASK: Determine the dissociation degree of hydrochloric acid and acetic acid
depending on their concentration in water at 25 °𝐶𝐶. Decide whether they are
strong or weak electrolyte. For both solutes, compare the experimentally measured λ0
to the tabulated value. For acetic acid, calculate its dissociation constant 𝐾𝐾𝐴𝐴.
LABORATORY AIDS AND CHEMICALS: conductivity meter, conductivity vessel and
probe, thermostatic bath, 14 volumetric flasks (50 ml), 1 volumetric pipette (25
ml), 5.10
-2
M hydrochloric acid, 5.10
-2
M acetic acid, 0.01M KCl, redistilled water to
prepare aquatic solutions.
INSTRUCTIONS: We first check the conductivity of the redistilled water. Rinse
thoroughly both the thermostatic measuring vessel and the conductivity probe
with redistilled water. Measure the temperature and conductivity of the redistilled water.
Conductivity should not be higher than 10 𝜇𝜇𝜇𝜇 at 25 ˚𝐶𝐶. Measure the conductivity of the
standard solution of 0,01𝑀𝑀 𝐾𝐾𝐶𝐶𝑙𝑙 in the same way (including rinsing) if the geometric
constant of probe 𝐶𝐶 is not known.
?


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During the previous measurement, prepare the hydrochloric and acetic acid solutions
each in 7 different concentrations. Use 50 ml volumetric flasks, redistilled water
(adjective "redistilled" will be omitted in further text), and stock solutions of both
hydrochloric and acetic acid.
Use gradual dilution of stock solution with water in 1: 1 ratio. Put the stock solution in the
first flask. Prepare the second solution by taking the 25 𝑚𝑚𝑚𝑚 from first solution and
inserting in 50 𝑚𝑚𝑚𝑚 volumetric flask. Add water up to marking and mix by gentle shaking.
Prepare the third solution from the second solution by the same procedure as the
second from the first solution. This is how we continue in a whole series. Do not forget
to add water at the last solution up to 50 𝑚𝑚𝑚𝑚 marking.
Rinse carefully the tempered vessel and the conductivity probe by water. Use a small
part of 𝐻𝐻𝐻𝐻𝐻𝐻 solution with the lowest concentration for definitive rinsing. Finally, let a
sufficient amount of the solution in the thermostatic vessel for temperature equilibrating.
Record the conductivity of the solution when the solution has a temperature of 25 °𝐶𝐶
and the conductivity value is stabilised (remains unchanged).
Subsequently, measure all prepared hydrochloric acid solutions. Proceed from the
lowest concentrations to higher. Do the same way with acetic acid.
REPORT: Table 1: for each measured electrolytes: theoretical value λo . Table 2:
for each electrolyte: 𝑐𝑐, temperature 𝑡𝑡, κ , λ, α. Common graph 1: for both
electrolyte: experimental dependence λ on 𝑐𝑐. Common graph 2: for both electrolyte:
dependence α on 𝑐𝑐. Table 3: for weak acid: 𝑐𝑐, 1/λ, λ⋅𝑐𝑐. Graph 3: for weak acid:
dependence 1/λ on product λ⋅𝑐𝑐 (including regression line). Next: for weak acid:
experimental value λo and AK calculated from intercept and slope of regression line.

TABLE I: Limiting molar conductivities of ions λ0
𝑖𝑖
at 25 °𝐶𝐶.
Ion 𝐻𝐻+
𝐾𝐾+
𝑁𝑁𝑁𝑁+
𝑂𝑂𝑂𝑂−
𝐶𝐶𝐻𝐻3 𝐶𝐶𝐶𝐶𝐶𝐶−
𝐶𝐶𝐻𝐻2 𝐶𝐶𝐶𝐶 𝐶𝐶𝐶𝐶𝐶𝐶−
𝐶𝐶𝐶𝐶−λo
[ cm Smol2 1−
] 349.8 73.5 50.1 198.0 40.9 39.8 76.3