Theory and Practice of pH Measurement
PN 44-6033/rev. D
December 2010
THEORY AND PRACTICE OF pH MEASUREMENT TABLE OF CONTENTS
THEORY AND PRACTICE
OF pH MEASUREMENT
TABLE OF CONTENTS
Section Title Page
1.0 OVERVIEW.............................................................................................................. 1
1.1 Introduction .............................................................................................................. 1
1.2 Operational Definition of pH..................................................................................... 2
1.3 pH Measurements in Industry .................................................................................. 3
2.0 CELLS FOR MEASURING pH................................................................................ 4
2.1 General .................................................................................................................... 4
2.2 Measuring Electrode ................................................................................................ 5
2.3 Reference Electrode ................................................................................................ 6
2.4 Liquid Junction Potential .......................................................................................... 6
2.5 Double Junction Reference Electrodes.................................................................... 8
3.0 MAKING THE pH MEASUREMENT ....................................................................... 9
3.1 Converting Voltage to pH ......................................................................................... 9
3.2 Glass Electrode Slope ............................................................................................. 9
3.3 Buffers and Calibration............................................................................................. 10
3.4 Precautions Using Buffers........................................................................................ 12
3.5 Isopotential pH ......................................................................................................... 13
3.6 Solution Temperature Compensation....................................................................... 14
3.7 Shields, Insulation, and Preamplifiers...................................................................... 14
3.8 Sensor Diagnostics .................................................................................................. 14
4.0 FUNDAMENTAL LIMITATIONS .............................................................................. 15
4.1 Junction Potential Mismatch .................................................................................... 15
4.2 Sodium Error............................................................................................................ 16
5.0 ORP MEASUREMENTS.......................................................................................... 17
5.1 Introduction .............................................................................................................. 17
5.2 Measuring Electrode ................................................................................................ 18
5.3 Interpreting ORP Measurements ............................................................................. 18
5.4 Calibration................................................................................................................ 20
6.0 INSTALLING THE SENSOR ................................................................................... 21
6.1 General .................................................................................................................... 21
6.2 Safety.......................................................................................................................21
6.3 Immersion and Insertion Applications ...................................................................... 21
6.4 Electrical Connections ............................................................................................. 22
7.0 MAINTENANCE ...................................................................................................... 23
7.1 General .................................................................................................................... 23
7.2 Cleaning pH Sensors ............................................................................................... 23
7.3 Calibrating pH Sensors ............................................................................................ 25
7.4 Storing pH Sensors.................................................................................................. 25
8.0 TROUBLESHOOTING ............................................................................................ 26
8.1 Introduction .............................................................................................................. 26
8.2 Installation................................................................................................................ 26
8.3 Wiring.......................................................................................................................26
8.4 Problems with Calibrations ...................................................................................... 26
8.5 Noisy Readings........................................................................................................ 28
8.6 Drift........................................................................................................................... 28
8.7 Ground Loops .......................................................................................................... 29
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THEORY AND PRACTICE OF pH MEASUREMENT TABLE OF CONTENTS
THEORY AND PRACTICE
OF pH MEASUREMENT
LIST OF APPENDICES
Section Title Page
A Silver/Silver Chloride Electrode Potentials............................................................... 30
B Isopotential pH ......................................................................................................... 31
C Glossary................................................................................................................... 32
LIST OF FIGURES
Figure # Title Page
1-1 Operational Definition of pH..................................................................................... 2
2-1 pH Measurement Cell .............................................................................................. 4
2-2 Measuring Electrode................................................................................................ 5
2-3 Cross-Section through the pH Glass ....................................................................... 5
2-4 Reference Electrode ................................................................................................ 6
2-5 The Origin of Liquid Junction Potentials .................................................................. 7
2-6 Comparison of Large Pore and Small Pore Liquid Junctions .................................. 7
2-7 Junction Plugging Caused by Silver Chloride.......................................................... 8
2-8 Double Junction Reference Electrode ..................................................................... 8
3-1 Glass Electrode Slope ............................................................................................. 10
3-2 Two-Point Buffer Calibration .................................................................................... 11
3-3 Isopotential pH......................................................................................................... 13
4-1 Liquid Junction Potential Mismatch.......................................................................... 15
4-2 Sodium Error............................................................................................................ 16
5-1 Oxidation-Reduction Potential ................................................................................. 17
5-2 ORP Measurement Cell ........................................................................................... 18
5-3 Measuring Electrode................................................................................................ 18
5-4 ORP Measurement Interpretation ............................................................................ 19
6-1 pH Sensor Installation in Flow-Through Piping........................................................ 22
7-1 Checking the Potential of the Reference Electrode ................................................. 24
A-1 Silver/Silver Chloride Electrode ............................................................................... 30
B-1 Cell Voltage as a Function of pH.............................................................................. 31
LIST OF TABLES
Table No. Title Page
3-1 NIST Standard Buffers ............................................................................................. 11
7-1 Cleaning Procedures ............................................................................................... 23
8-1 RTD Resistance Values ........................................................................................... 27
8-2 Input Signals for Simulated Buffer Calibration ......................................................... 27
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1.0 OVERVIEW
The determination of pH is one of the most common process chemical measurements made today. This booklet
explains the principles behind the measurement and discusses ways of avoiding common pitfalls. The booklet also
discusses industrial ORP (oxidation-reduction potential) measurements. Although the determination of ORP is not
nearly as common as pH, certain industries make valuable use of the measurement.
1.1 INTRODUCTION
pH is a measure of the relative amount of hydrogen and hydroxide ions in an aqueous solution. In any collection
of water molecules a very small number will have dissociated to form hydrogen (H+) and hydroxide (OH-) ions:
H
2
O = H++ OH
-
The number of ions formed is small. At 25°C fewer than 2 x 10
-7
% of the water molecules have dissociated. In
terms of molar concentrations, water at 25°C contains 1 x10-7moles per liter of hydrogen ions and the same concentration of hydroxide ions.
In any aqueous solution, the concentration of hydrogen ions multiplied by the concentration of hydroxide ions is
constant. Stated in equation form:
Kw= [H+] [OH-] (1)
where the brackets signify molar concentrations and K
w
is the dissociation constant for water. The value of K
w
depends on temperature. For example, at 25°C Kw= 1.00 x 10
-14
and at 35°C Kw= 1.47 x 10
-14
.
Acids and bases, when dissolved in water, simply alter the relative amounts of H
+
and OH-in solution. Acids
increase the hydrogen ion concentration, and, because the product [H+] [OH-] must remain constant, acids
decrease the hydroxide ion concentration. Bases have the opposite effect. They increase hydroxide ion concentration and decrease hydrogen ion concentration. For example, suppose an acid is added to water at 25°C and the
acid raises the H+concentration to 1.0 x 10-4moles/liter. Because [H+] [OH-] must always equal 1.00 x 10
-14
,
[OH-] will be 1.0 x 10
-10
moles/liter.
pH is another way of expressing the hydrogen ion concentration. pH is defined as follows:
pH = -log [H
+
] (2)
Therefore, if the hydrogen ion concentration is 1.0 x 10
-4
moles/liter, the pH is 4.00.
The term neutral is often used in discussions about acids, bases, and pH. A neutral solution is one in which the
hydrogen ion concentration exactly equals the hydroxide ion concentration. At 25°C, a neutral solution has pH
7.00. At 35°C, a neutral solution has pH 6.92. The common assertion that neutral solutions have pH 7 is not true.
The statement is true only if the temperature is 25°C.
THEORY AND PRACTICE OF pH MEASUREMENT SECTION 1.0
OVERVIEW
SECTION 1.0
OVERVIEW
1.1 INTRODUCTION
1.2 OPERATIONAL DEFINITION OF pH
1.3 pH MEASUREMENTS IN INDUSTRY
1
1.2 OPERATIONAL DEFINITION OF pH
Although equation 2 is often given as the definition of pH, it is not a good one. No one determines pH by first measuring the hydrogen ion concentration and then calculating pH. pH is best defined by describing how it is measured.
Figure 1-1 illustrates the operational definition of pH. The starting point is an electrochemical cell. The cell consists
of an indicating electrode whose potential is directly proportional to pH, a reference electrode whose potential is
independent of pH, and the liquid to be measured. The overall voltage of the cell depends on the pH of the sample. Because different indicating electrodes have slightly different responses to pH, the measuring system must be
calibrated before use. The second step in the operational definition of pH is calibration. The system is calibrated
by placing the electrodes in solutions of known pH and measuring the voltage of the cell. Cell voltage is a linear
function of pH, so only two calibration points are needed. The final step in the operational definition is to place the
electrodes in the sample, measure the voltage, and determine the pH from the calibration data.
It is apparent that the practical determination of pH requires standard solutions of known pH. The standard solutions are called buffers, and the pH values assigned to them define the pH scale. The procedure by which pH values are assigned to buffers is beyond the scope of this discussion. There is one important point, though.
Determining pH values requires making assumptions concerning the chemical and physical properties of electrolyte solutions. Slightly different assumptions lead to slightly different pH values for the same solution. Therefore,
slightly different pH scales can exist.
Finally, it should be noted that equation 2 is somewhat misleading. The equation implies that pH is a measure of
concentration. In fact, pH is really a measure of ion activity. Concentration and activity are not the same, but they
are related. See Section 3.3 and the Glossary for more information.
THEORY AND PRACTICE OF pH MEASUREMENT SECTION 1.0
OVERVIEW
FIGURE 1-1. Operational Definition of pH.
The figure shows the three steps in the determination of pH. The three steps constitute the operational definition of pH.
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1.3 pH MEASUREMENTS IN INDUSTRY
Although pH is a measure of hydrogen ion activity, the fact is of little interest to anyone but a physical chemist. It
is certainly of scant importance in industrial pH measurements. The major use of pH in industry is process control.
Controlling pH helps ensure product quality, reduces corrosion and scaling in plant equipment, and protects the
environment by helping wastewater dischargers meet regulatory limits.
Process pH control limits are often empirical. It is less important to know why a given pH range works than to keep
the pH in the desired range. It is, therefore, important that the person making and using pH measurements understand how the measurement is made, how to calibrate the measuring instrument, and how to recognize and avoid
common problems.
This booklet has five major sections. The first section discusses the construction and features of the electrochemical cell used for measuring pH. The second section discusses how the pH analyzer converts the measured
cell voltage into pH. The third section discusses some fundamental limitations to pH measurements. The fourth
section discusses industrial ORP measurements. Because ORP measurement cells have much in common with
pH cells, much of the information in the pH cell section applies to ORP measurements. The fifth section deals with
installation, maintenance, and troubleshooting of pH systems.
THEORY AND PRACTICE OF pH MEASUREMENT SECTION 1.0
OVERVIEW
3
2.1 GENERAL
In nearly every industrial and scientific application, pH is determined by measuring the voltage of an electrochemical cell. Figure 2-1 shows a simplified diagram of a pH cell. The cell consists of a measuring electrode, a reference electrode, a temperature sensing element, and the liquid being measured. The voltage of the cell is directly
proportional to the pH of the liquid. The pH meter measures the voltage and uses a temperature-dependent factor to convert the voltage to pH. Because the cell has high internal resistance, the pH meter must have a very high
input impedance.
Figure 2-1 shows separate measuring and reference electrodes. In most process sensors, the electrodes and the
temperature element are combined into a single body. Such sensors are often called combination electrodes.
The cell voltage is the algebraic sum of the potentials of the measuring electrode, the reference electrode, and the
liquid junction. The potential of the measuring electrode depends only on the pH of the solution. The potential of the
reference electrode is unaffected by pH, so it provides a stable reference voltage. The liquid junction potential
depends in a complex way on the identity and concentration of the ions in the sample. It is always present, but if the
sensor is properly designed, the liquid junction potential is usually small and relatively constant. All three potentials
depend on temperature.
The construction of the electrodes and the electrical potentials associated with them are discussed in Sections 2.2
and 2.3.
THEORY AND PRACTICE OF pH MEASUREMENT SECTION 2.0
CELLS FOR MEASURING pH
SECTION 2.0
CELLS FOR MEASURING pH
2.1 GENERAL
2.2 MEASURING ELECTRODE
2.3 REFERENCE ELECTRODE
2.4 LIQUID JUNCTION POTENTIAL
2.5 DOUBLE JUNCTION REFERENCE ELECTRODES
FIGURE 2-1. pH Measurement Cell.
The cell consists of a measuring and reference electrode. The voltage between the electrodes is directly proportional to the
pH of the test solution. The proportionality constant depends on temperature, so a temperature sensor is also necessary. A
100
Ω
platinum RTD is commonly used, although 1000 Ωplatinum RTDs, 3 kΩBalco RTDs, and thermistors are also used.
4
2.2 MEASURING ELECTRODE
Figure 2-2 shows the internals of the measuring electrode. The heart of the electrode is a thin piece of pH-sensitive glass, which is blown onto the end of a length of glass tubing. The pH-sensitive glass, usually called a glass
membrane, gives the electrode its common name: glass electrode. Sealed inside the electrode is a solution of
potassium chloride buffered at pH 7. A piece of silver wire plated with silver chloride contacts the solution.
The silver wire-silver chloride combination in contact with the filling solution constitutes an internal reference electrode. Its potential depends solely on the chloride concentration in the filling solution. Because the chloride concentration is fixed, the electrode potential is constant. See Appendix A for a more detailed discussion of how the
chloride concentration determines the electrode potential.
As Figure 2-2 shows, the outside surface of the glass membrane contacts the liquid being measured, and the inside
surface contacts the filling solution. Through a complex mechanism, an electrical potential directly proportional to
pH develops at each glass-liquid interface. Because the pH of the filling solution is fixed, the potential at the inside
surface is constant. The potential at the outside surface, however, depends on the pH of the test solution.
The overall potential of the measuring electrode equals the potential of the internal reference electrode plus the
potentials at the glass membrane surfaces. Because the potentials inside the electrode are constant, the overall
electrode potential depends solely on the pH of the test solution. The potential of the measuring electrode also
depends on temperature. If the pH of the sample remains constant but the temperature changes, the electrode
potential will change. Compensating for changes in glass electrode potential with temperature is an important part
of the pH measurement.
Figure 2-3 shows a cross-section through the pH glass. pH sensitive glasses absorb water. Although the water
does not penetrate more than about 50 nanometers (5 x 10
-8
m) into the glass, the hydrated layer must be present for the glass to respond to pH changes. An ion exchange mechanism involving alkali metals and hydrogen ions
in the hydrated layer is responsible for the pH response of the glass. The layer of glass between the two hydrated layers remains dry. The dry layer makes the glass a poor conductor of electricity and causes the high internal
resistance (several hundred megohms) typical of glass electrodes.
THEORY AND PRACTICE OF pH MEASUREMENT SECTION 2.0
CELLS FOR MEASURING pH
FIGURE 2-2. Measuring Electrode.
The essential element of the glass electrode is a
pH-sensitive glass membrane. An electrical potential develops at glass-liquid interfaces. The potential at the outside surface depends on the pH of the
test solution. The potential at the inside surface is
fixed by the constant pH of the filling solution.
Overall, the measuring electrode potential depends
solely on the pH of the test solution.
FIGURE 2-3. Cross-Section through the pH Glass.
For the glass electrode to work, the glass must be
hydrated. The hydrated layer gradually dissolves and is
replaced by a fresh layer. Thus, the surface of the electrode continuously regenerates itself. The rate of dissolution depends on temperature. At 50°C, the loss is
about ten times greater than at 25°C. Electrodes wear
out faster at high temperatures. To maintain the hydrated layer, the glass bulb must be wet at all times.
5
2.3 REFERENCE ELECTRODE
As Figure 2-4 shows, the reference electrode is a
piece of silver wire plated with silver chloride in contact with a concentrated solution of potassium chloride held in a glass or plastic tube. In many reference electrodes the solution is an aqueous gel, not
a liquid. Like the electrode inside the glass electrode, the potential of the external reference is controlled by the concentration of chloride in the filling
solution. Because the chloride level is constant, the
potential of the reference electrode is fixed. The
potential does change if the temperature changes.
Industrial reference electrodes differ from laboratory types in an important way. Laboratory electrodes
are available with either gelled or liquid filling solutions. Industrial reference electrodes almost always
have gelled filling solutions. Gelled filling solutions
allow industrial sensors to be installed in pressurized pipes and tanks. The reference electrode is sealed above the gel. Therefore, very little process liquid can
enter the reference electrode and contaminate it. There is a drawback, however. Potassium chloride in the gel ultimately becomes depleted. The gel cannot be replenished, so after a while the sensor fails. Maximum life for a geltype sensor is about 12 months. The solution in liquid-filled electrodes can be replenished, and these electrodes
have fairly long operating lives.
2.4 LIQUID JUNCTION POTENTIAL
The salt bridge (see Figure 2-4) is an integral part of the reference electrode. It provides the electrical connection
between the reference electrode and the liquid being measured. Salt bridges take a variety of forms, anything from a
glass frit to a wooden plug. Salt bridges are highly porous, and the pores are filled with ions. The ions come from the
filling solution and the sample. Some bridges—for example, those using gelled filling solutions—permit only diffusion
of ions through the junction. In other designs, a slow outflow of filling solution occurs in addition to diffusion. Diffusion
of ions generates a voltage, called the liquid junction potential. The liquid junction potential is in series with the measuring and reference electrode potentials and is part of the overall cell voltage.
Figure 2-5 helps illustrate how liquid junction potentials originate. The figure shows a section through a pore in the
salt bridge. For simplicity, assume the bridge connects a solution of potassium chloride and hydrochloric acid of equal
molar concentration. Ions from the filling solution and ions from the sample diffuse through the pores. Diffusion is driven by concentration differences. Each ion migrates from where its concentration is high to where its concentration is
low. Because ions move at different rates, a charge separation develops. As the charge separation increases, electrostatic forces cause the faster moving ions to slow down and the slower moving ions to speed up. Eventually, the
migration rates become equal, and the system reaches equilibrium. The amount of charge separation at equilibrium
determines the liquid junction potential.
Liquid junction potentials exist whenever dissimilar electrolyte solutions come into contact. The magnitude of the
potential depends on the difference between the mobility of the ions. Although liquid junction potentials cannot be
eliminated, they can be made small and relatively constant. The liquid junction potential is small when the ions
present in greatest concentration have equal (or almost equal) mobilities. The customary way of reducing junction
potentials is to fill the reference electrode with concentrated potassium chloride solution. The high concentration
ensures that potassium chloride is the major contributor to the junction potential, and the nearly equal mobilities of
potassium and chloride ions make the potential small.
THEORY AND PRACTICE OF pH MEASUREMENT SECTION 2.0
CELLS FOR MEASURING pH
FIGURE 2-4. Reference Electrode.
The fixed concentration of chloride inside the electrode
keeps the potential constant. A porous plug salt bridge at
the bottom of the electrode permits electrical contact
between the reference electrode and the test solution.
6
One of the major problems associated with the determination of pH is plugging of the liquid junction. For
the junction to work properly, ions must be free to
migrate through the junction pores. If the pores
become blocked, ions cannot diffuse. The electrical
resistance of the junction increases. The pH readings
drift and become noisy. Severe fouling can even completely block the junction, breaking the electrical connection between the electrode and the sample, and
making the electrode unusable. Plugging can come
from two sources: suspended solids in the sample or
solids resulting from a chemical reaction involving the
electrolyte fill solution. Plugged junctions are difficult
to clean.
If the sample contains suspended solids, the reference junction is always in danger of plugging. The
greater the amount of suspended solids, the greater
the tendency toward fouling. Generally, the smaller the
surface area of the junction, the more rapidly fouling
occurs. Therefore, one way to combat fouling is to use
a junction with a large surface area. Another approach
is to make a junction having pores much smaller than
the smallest particles likely to be present. As Figure
2-6 shows, if the junction pores are small, the particles cannot get into the pores and instead accumulate on the
surface. The pores remain open. Ions can diffuse easily and the junction resistance stays low.
Reactions between the process liquid and the filling solution can also produce solids that plug the reference junction. Potassium, chloride, and silver ions from the filling solution are always present in the junction. The origin of
potassium and chloride is obvious; the source of the silver is discussed later. If the sample contains ions that form
insoluble compounds with the filling solution, a precipitate will form in the junction pores. The precipitate ultimately plugs the junction. Examples of ions that foul the junction are lead, silver, and mercury (II), which form insoluble
chloride salts, and sulfide, which forms an insoluble silver salt.
THEORY AND PRACTICE OF pH MEASUREMENT SECTION 2.0
CELLS FOR MEASURING pH
FIGURE 2-5. The Origin of Liquid Junction Potentials.
The figure shows a thin section through a pore in the junction plug. The junction separates a solution of potassium
chloride on the left from a solution of hydrochloric acid on the right. The solutions have equal molar concentration.
Driven by concentration differences, hydrogen ions and potassium ions diffuse in the directions shown. The length
of each arrow indicates relative rates. Because hydrogen ions move faster than potassium ions, positive charge
builds up on the left side of the section and negative charge builds up on the right side. The ever-increasing positive charge repels hydrogen and potassium ions. The ever-increasing negative charge attracts the ions. Therefore,
the migration rate of hydrogen decreases, and the migration rate of potassium increases. Eventually the rates
become equal. Because the chloride concentrations are the same, chloride does not influence the charge separation or the liquid junction potential.
Figure 2-6. Comparison of Large Pore and Small
Pore Liquid Junctions.
In A the suspended particles are smaller than the pores in the
junction plug. The particles get into the pores and eventually
plug them. Because ion diffusion, which provides the electrical connection between the electrode and sample, is hindered, the resistance of the junction increases. In B the pores
are smaller than the suspended particles. The particles accumulate on the surface, and the pores remain open. Even
though the particles may pack on the surface, there is usually
sufficient space between them to allow ion diffusion.
7
Precipitation of solids from the filling solution can also occur. Silver/silver chloride reference electrodes contain a
fairly concentrated potassium chloride solution. Although silver chloride is relatively insoluble in water, the solubility increases if a high concentration of chloride is present. The increase in solubility is caused by the formation of
a soluble silver chloride complex ion (AgCl
2
-
). If the chloride concentration drops, the complex ion decomposes
and solid silver chloride forms. The change in solubility with chloride concentration causes junction plugging.
Figure 2-7 shows how insoluble silver chloride forms in the liquid junction. Suppose a silver chloride complex ion
finds its way into a junction pore and begins migrating toward the sample. Because the sample is unlikely to contain as much chloride as the filling solution, the chloride concentration decreases along the length of the pore. At
some point the chloride concentration is too small to sustain the complex, and silver chloride precipitates.
Eventually, enough silver chloride deposits and the pore becomes blocked.
2.5 DOUBLE JUNCTION REFERENCE ELECTRODES
One way to minimize plugging from silver chloride is to use a double junction reference. Figure 2-8 shows a typical arrangement. The concentration of the silver chloride complex in the top chamber—the one containing the reference element—is relatively high. Typically the solution is saturated with the complex ion. However, the concentration in the bottom chamber is substantially lower because the only way the complex ion can get into the lower
compartment is to diffuse through the inner bridge. Because the level of silver chloride complex in the second compartment is small, the rate of pluggage in the sample junction is slow.
A double junction can also be used to reduce plugging caused by reaction of the reference electrolyte with the
sample. If the lower chamber of Figure 2-8 contains an electrolyte that does not react with the sample, no precipitation will occur in the sample bridge. Typical fill solutions for this application are ammonium nitrate, and sodium
and potassium nitrate and sulfate.
A third use of the double junction is to reduce poisoning. Poisoning occurs when an agent in the sample migrates
through the bridge and reacts with the reference electrode. Common poisoning agents are sulfide and cyanide.
Both react with the silver/silver chloride electrode, converting it into a silver/silver sulfide or silver/silver cyanide
complex electrode. Poisoning changes the reference voltage by several hundred millivolts. Poisoning is discussed
in more detail in Section 7.2.2.
THEORY AND PRACTICE OF pH MEASUREMENT SECTION 2.0
CELLS FOR MEASURING pH
FIGURE 2-7. Junction Plugging Caused by Silver Chloride.
The figure shows a junction pore. The circles represent chloride ions
(Cl-). The silver chloride complex is shown as AgCl
2
. Note that the
concentration of chloride decreases moving toward the sample side
of the pore. At some point the chloride concentration becomes too
small to hold the silver chloride complex in solution and solid silver
chloride (AgCl) precipitates.
FIGURE 2-8. Double Junction
Reference Electrode.
Both chambers contain potassium chloride solution. The top chamber contains the silver/silver
chloride reference element. The potassium chloride in this chamber is saturated with the soluble
silver chloride complex. The silver chloride complex diffuses through the inner bridge into the second chamber. The concentration of the complex
ion in the second chamber remains low, so the
rate of pluggage in the sample bridge is slow.
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