4
CONDUCTIVITY
4.1 General Principles
In general, conductivity refers to the ability of a substance to conduct heat or electricity – it is the
opposite of resistance. In the context of this subject, it will refer the ability of a solution to conduct
electricity. In a solution, the conduction between electrodes is carried out by movement of ions to the
electrodes: anions to the positive electrode, and cations to the negative. The ability of a solution to
conduct is determined by a number of factors, including:
•
the number of ions – the more ions, the greater the conductivity
•
the nature of the ions – certain ions have greater conductivity per mole than others due to charge
and size
•
the dimensions of the electrodes – the greater the area of the electrodes, the greater the
conductivity
•
the distance between the electrodes – the closer together the electrodes, the greater the
conductivity
•
temperature – the higher the temperature, the greater the conductivity
While conductivity is the property, conductance (G) is the actual measured value. The unit of
conductance is the Siemen (S).
Solution conductance is also affected significantly by temperature variations. Correction can be
made by either measuring all solutions in a thermostatted water bath or by using a correction factor, as
in Equation 4.1, which standardises all conductances to 25°C.
G25 =
Gt
0.02 t + 0.5
Eqn 4.1
where G25 and Gt are the corrected (to 25°C) and measured conductances, and t the temperature in
degrees Celsius.
CLASS EXERCISE 4.1
The conductance of a solution is measured as 1.23 mS at 22°C. Calculate the conductance
corrected to 25°C.
It is not possible to calculate the exact conductance of a solution, even if its composition is known.
However, its conductivity relative to other solutions can be estimated from the molarity of the
individual ions and their relative ionic conductances, as given in Table 4.1. Equation 4.2 shows how
this is done.
Relative conductivity = sum of (molarity x ionic conductance) for all ions
Eqn 4.2
4. Conductivity
TABLE 4.1 Relative ionic conductances
Ion
+
H
Na
Ion
K+
+
Ag
+
Mg2+
Rel cond.
-
350
+
NH4
Rel cond.
OH
200
-
50
F
60
70
Cl-
80
60
Br
-
80
70
-
I
110
NO3-
80
70
Ca
2+
-
Ba
2+
130
HCO3
Hg2+
130
C2O42-
120
CH3COO
Fe
2+
Fe
3+
210
CO3
Pb2+
140
PO43-
110
SO4
-
40
40
150
2-
160
2-
140
240
We can use these values as a guide to the level of conductance in a solution. The example below
shows how the conductance of a given ionic solution is estimated.
EXAMPLE 4.1
Estimate the relative conductivity of a solution of the following composition: 0.05M H+,
0.025M Cl- and 0.025M NO3-.
Relative conductivity
= (0.05 x 350) + (0.025 x 80) + (0.025 x 70)
= 21.25
This number does not mean anything by itself, but could be compared to other solutions,
indicating which would be expected to be more conductive.
CLASS EXERCISE 4.2
Which of the following solutions are more conductive than the solution in Example 4.1:
(a) 0.1 M HCl (b) 0.1 M NaCl (c) 0.1 M H2SO4
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4. Conductivity
4.2 Conductivity Apparatus
Various types of conductivity cells are commercially available, their actual design being dependent on
the use to which they will be put. They all have in common a pair of platinum electrodes.
The simplest and most commonly used cell is a dip
cell, shown in Figure 4.1. The bottom of the cell is open
and there are also holes in the sides to allow ready flow of
the sample liquid into the space between the electrodes.
The cell is very simply to maintain: it can be stored
dry, and only needs rinsing at the end of use. The electrode
surfaces should not be cleaned with anything abrasive,
because this can affect their performance. If necessary,
cleaning of the electrode is done with a potassium
dichromate/sulfuric acid mixture.
The manufacturer will generally supply the cell
constant for the electrode. This is a numerical value which
describes the physical properties (surface area and distance
between electrodes). The cell constant can be determined
by calibration, and should not change by more than ±5%
over the lifetime of the cell, unless it is physically
damaged. The cell affects the measured conductance value,
because
of its physical dimensions. This will be discussed
FIGURE 4.1 Dip-type conductivity cell
more in the next section.
A conductance meter, to which the cell is attached, is designed around the electrical circuit known as a
Wheatstone bridge. This is a combination of resistors where the resistance of one half is defined by
the cell, and the other half by a pair of variable resistors. The bridge is adjusted manually or
electronically so that the resistance of each half is equal. This indirectly determines the resistance of
the cell. The power supply provides alternating (AC) current to avoid the development of currents that
would cause a change in the solution composition.
4.3 Direct Measurements
The conductance of a solution is a measure of the concentration of dissolved ions, though, it does not
say anything about what ions are present. Nevertheless, the conductance is an important water quality
test for natural and purified waters. Since, such waters rarely stray from pH levels close to neutral, the
high conductances of H+ and OH- do not cause a problem. To account for variations in different
waters (e.g. sea, distilled, river, boiler), the conductance is often multiplied by a “fudge” factor.
As mentioned above, the measured conductance is affected by the cell. This would be
unsatisfactory, unless some way of standardising the result was available. Imagine an infrared
spectrum that was different from every instrument. The cell constant (Cc) is the means by which the
measured (and temperature corrected) conductance can be standardised to a value known as the
specific conductance (κ). The relationship between the measured and specific conductances is shown
in equation 4.3
κ
= GCc
Eqn 4.3
To determine the specific conductance of a solution requires that the cell constant is known accurately.
While a cell is supplied with a specified constant, this may change over time, and should be calibrated
regularly. To calibrate a cell, a solution of exactly known specific conductance must be prepared. The
most common species used is KCl at a concentration similar to that of the waters being tested. Table
4.2 gives the specific conductance of a number of KCl solutions.
42
4. Conductivity
TABLE 4.2 Specific conductance of KCl solutions at 25°C
Molarity
Specific Cond. (mS/cm)
Molarity
Specific Cond. (mS/cm)
1
111.9
0.05
6.668
0.5
58.64
0.01
1.413
0.1
12.90
0.001
0.147
EXAMPLE 4.2
Water with a specific conductance range of 1-5 mS/cm is monitored by a conductivity cell,
which has a manufacturer’s cell constant of 0.71 cm-1. Determine the specific conductance
for a water sample, given the following data.
A 0.0100 M KCl solution at 23°C was found to have a conductance of 1.88 x 10-3 S.
A water sample measured at 18°C had a conductance of 2.89 x 10-3 S.
Calibration
The 0.01 M KCl standard is chosen because it is closest in conductance to the sample.
Standardise temperature for the standard first:
G25
1.88 x 10 −3
=
= 1.96 x 10 −3 S
0.02 x 23 + 0.5
Calculate the cell constant:
1.413 x 10-3 = 1.96 x 10-3 x Cc
Cc = 0.721 cm-1
This value for the cell constant is very close to the manufacturer’s value, and therefore is OK
to use.
Sample
Standardise the temperature for the sample:
G25 =
κ
2.89 x 10 −3
= 3.36 x 10 −3 S
0.02 x 18 + 0.5
= 3.36 x 10-3 x 0.721 = 2.42 x 10-3 S/cm
This value of κ is independent of the cell: anyone measuring the same water sample, with any cell of
whatever shape or size, should get the same answer. Therefore, if conductivity is a water quality
parameter that needs to be reported to an external organisation (eg the EPA or the council), it must be
as specific conductance. Even within the organisation, it is best to record the value as κ, so that all
values over time can be compared, even if the cell changes.
43
4. Conductivity
CLASS EXERCISE 4.3
Calculate (a) the cell constant and (b) the specific conductance of the sample, given the
following data:
Cell constant: 0.57 cm-1
Solution
0.05 M KCl
Sample
Temperature
22°C
31°C
Conductance
0.011 S
7.3 mS
Conductance
4.4 Conductometric Titrations
This is the conductivity equivalent of the potentiometric titrations from Chapter 2. In this case, a
conductivity cell is used to monitor changes in the solution conductance, and allow us to determine the
endpoint volume.
The method relies on the conductance of the reactants and products of the titration reaction
being significantly different, so that the trend in conductance either side of the endpoint is different. A
typical conductometric titration curve is shown in Figure 4.2.
endpoint volume
Titrant volume
FIGURE 4.2 Typical conductometric titration curve (with endpoint detection method shown)
Enough values are obtained on either side of the equivalence point zone to accurately locate the
equivalence point volume. Unlike potentiometric titrations, here there is no need to take values
carefully at the equivalence point (or even close to it) as the linear regions either side of the
equivalence point define the end point through their point of intersection, as shown in Figure 4.2. In
44
4. Conductivity
fact, values very close to the end point don’t help in obtaining the result. For a normal titration, data
points 1 mL apart are totally adequate for accurate endpoint detection. There is no need to change
addition volumes throughout the titration, making it much easier to actually perform than a
potentiometric titration.
Each measured conductance value needs to be corrected for dilution as a result of addition of the
titrant, as shown in Equation 4.4. If this is not done, the sharp changes in conductance will be
somewhat masked by the dilution, and the graph will be distorted.
Gcorr =
Gobs( V + v )
V
Eqn 4.4
where Gobs and Gcorr are the measured and corrected conductances, V is the initial solution volume
(before addition and including water) and v is the volume of added titrant.
CLASS EXERCISE 4.4
Determine the endpoint volume for the titration, given the data below.
Sample aliquot
Volume of added water
10 mL
60 mL
Vol. Titrant (mL)
Gobs (mS)
0
2.75
1
2.65
2
2.56
3
2.46
4
2.37
5
2.28
6
2.20
7
2.18
8
2.21
9
2.40
10
2.58
11
2.75
12
2.92
13
3.07
14
3.22
15
3.36
Gcorr
Because in a conductometric titration, you are not interested in the actual conductance values
individually, only the way they change, you do not have to calibrate the cell or standardise the
temperature!
45
4. Conductivity
Advantages and disadvantages
Conductivity and voltage measurements are direct competitors as endpoint detection methods.
Compared to indicator-based methods, they have similar merits and problems (see Chapter 2). But
compared to each other, which is better? Well of course, the answer is that each has its own
advantages and disadvantages.
The advantages of conductometric titrations, compared to potentiometric titrations, are:
•
they are easy to perform (no special care needs to be taken around the end point,
•
the same electrode is suitable for a range of analyses (acid/base and precipitation)
•
the electrode is simple to maintain (compared to indicator and reference electrodes which can
dry out, and be easily damaged),
•
the response is faster (especially around endpoint),
•
endpoint detection is easier (especially for weak acids or bases),
•
they work better in very dilute solutions, and
•
they work better in turbid solutions.
The disadvantages of conductometric titrations, compared to potentiometric titrations, include:
•
they don’t work well in more concentrated solutions or in solutions with high background
conductivity of non-reactive species,
•
they aren’t useful for complexometric and redox titrations,
•
corrections are necessary for volume dilution effects, and
•
graphing of all data is necessary for endpoint detection (can’t use titration to a certain value, or
first derivative methods).
In summary, the use of conductometric titrations could be greater, due to their comparative advantages
over potentiometric titrations, particularly for analysis of weak acids and bases. Why they aren’t more
widely used possible stems from the need for graphing and the great availability of pH electrodes.
Acid-Base Titrations
The high ionic conductances of H+ and OH- make conductometric monitoring of an acid-base titration
an ideal method of detecting the endpoint. Loss or gain of either these species will cause a significant
change in solution conductance, and therefore a clear endpoint from the curve. Figure 4.3 shows
representations of the titration curves for acid/base titrations.
(a)
G
(b)
G
Titrant volume
Titrant volume
FIGURE 4.3 Acid-base conductometric titration curves. (a) strong acid/strong base (b) weak acid/strong base or
weak base/strong acid.
Let us see why the titrations give these shapes. We will use HCl, NaOH and CH3COOH as examples
of the three types of species.
46
4. Conductivity
EXAMPLE 4.3
HCl in the beaker + NaOH in the burette.
Relative ionic conductances: H+ 350, Na+ 50, Cl- 80, OH- 200
Before endpoint
[H+ +Cl- ] + [Na+ + OH-] →
H2O + Na+ + Cl-
Each HCl contributes 350 + 80 = 430 to the conductance in the beaker.
Each time the reaction proceeds, the H+ is lost, and replaced by an Na+. The NaCl
contributes 50 + 80 = 130 to the conductance. Therefore, the conductance drops by 300
units every time the reaction occurs.
After endpoint, excess NaOH is being added. This will cause the conductance to rise by 50
+ 200 = 250 units for each NaOH molecule.
Therefore, the graph will have a V-shape, where the downslope before endpoint (-300) will
be slightly steeper than the upslope after endpoint (+250).
EXAMPLE 4.4
CH3COOH in the beaker + NaOH in the burette.
Relative ionic conductances: CH3COOH 0, Na+ 50, CH3COO- 40, OH- 200
Before endpoint
[CH3COOH] + [Na+ + OH-]
→
H2O + Na+ + CH3COO-
The molecular species, ethanoic acid, contributes nothing to the conductance in the beaker
but there will be a few dissociated ions, giving the solution a low conductance. It is the
dissociated H+ ions that react first and cause the small dip at the start of the titration.
Each time the reaction occurs, the non-ionic acid is converted to the ethanoate ion (40), and
a sodium ion (50) is added to solution. Therefore, the conductance will increase by 90 units.
After endpoint, it is the same as above: a 250 unit rise.
The overall graph will show a slow rise (+90) before endpoint, and a faster one (+250) after
endpoint.
CLASS EXERCISE 4.5
KOH in the beaker + HNO3 in the burette.
47
4. Conductivity
Precipitation titrations
These are equally suited to conductometric titration, since the reaction relies of the removal of an ion
from solution. In this case the spectator ion – the one that simply adds to the solution without being
part of the reaction – should have a low conductivity where possible, so that its presence does not
mask the changes.
EXAMPLE 4.5
Which is the better titrant for silver solutions: HCl or NaCl?
Before endpoint
Ag+ + [H+ + Cl-]
60
→ AgCl (s) + H+
0
350
After endpoint
Excess HCl
Before endpoint
Ag+ + [Na+ + Cl-]
60
Change = +290
Change = +350
→ AgCl (s) + Na+
0
50
After endpoint
Excess NaCl
Change = -10
Change = +110
The difference between before and after is more pronounced with NaCl, because Na+ has a
lower conductivity than H+.
Complexometric and redox titrations
Conductometric measurements are not generally suited to these titrations, because of the common
need for high H+ or OH- concentrations to allow complete reaction. For example, the titration of iron
(II) with permanganate requires at least 0.5 M H2SO4 for completion. The presence of such high
levels of H+ would certainly mask other changes. Furthermore, in the case of complexometric
titrations, the conductances of the reactant and product ions is not greatly different, and the reaction is
such that there are no changes to the number of ions in solution.
What You Need To Be Able To Do
1.
list the factors affecting solution conductivity
2.
define terms associated with conductance
3.
describe the apparatus used for conductance measurements
4.
describe routine maintenance operations for a conductivity cell
5.
calibrate a conductivity cell
6.
describe the major application of direct conductance measurements
7.
outline how the data for a conductometric titration is obtained and plotted
8.
determine the endpoint from conductometric data
9.
explain and derive the shape of conductometric titration curves
10. discuss the advantages and disadvantages of conductometric titrations
48
4. Conductivity
Practice Questions
1.
Determine the cell constant for a 0.01 M KCl solution with a measured conductance of 1.78 mS
at 22°C.
2.
For accurate measurement of very dilute solutions, would a conductivity cell with a larger or
smaller cell constant be better? Explain.
3.
Determine the specific conductance for a water sample, given the following data. A 0.00100 M
KCl solution at 23°C was found to have a conductance of 153.6 µS. A water sample measured
at 19°C had a conductance of 198.9 µS.
4.
Determine the endpoint for the following titration, given a 25 mL sample aliquot and 50 mL of
extra water.
Vol. (mL)
0
1
2
3
4
5
6
7
8
9
5.
6.
7.
8.
9.
10.
Gobs
1.29
1.25
1.32
1.40
1.48
1.55
1.63
1.71
1.78
1.88
Vol. (mL)
10
11
12
13
14
15
16
17
18
19
Gobs
1.92
2.25
2.58
2.83
3.14
3.48
3.77
4.09
4.42
4.75
Show that the titration curve for strong acid/strong base looks essentially the same regardless of
which is the titrant.
Draw a representation of the conductometric titration curve for the titration of:
(a) ammonium chloride with NaOH
(b) ammonia with HCl
(c) HCl with ammonia
(d) sodium chloride with silver nitrate
Explain the changes in solution conductance during the course of the titration.
Mercury (II) ions can be titrated by precipitation with sulfate, since the product is extremely
insoluble. Which titrant would be the better choice - sulfuric acid or sodium sulfate? Explain
your answer.
Explain why conductance measurements are not employed to detect the endpoints in redox and
complexometric titrations.
It is suspected that a water purifier is not removing all the salt from seawater, and that levels of
chloride around 50 mg/L remain. Explain why a conductometric titration would be ideal for this
analysis.
Why would the analysis of ethanoic acid in a brine (high NaCl levels) be difficult by
conductometric titration?
49