Monday, January 22, 2018

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Continuous Analytical Measurement - pH Measurement

pH is the measurement of the hydrogen ion activity in a liquid solution. It is one of the most common forms of analytical measurement in industry, because pH has a great effect on the outcome of many chemical processes. Food processing, water treatment, pharmaceutical production, steam generation (thermal power plants), and alcohol manufacturing are just some of the industries making extensive use of pH measurement (and control). pH is also a significant factor in the corrosion of metal pipes and vessels carrying aqueous (water-based) solutions, so pH measurement and control are important in the life-extension of these capital investments.

In order to understand pH measurement, you must first understand the chemistry of pH. Please refer to the pH section of Industrial Chemistry for a theoretical introduction to pH.


Colorimetric pH measurement

One of the simplest ways to measure the pH of a solution is by color. Certain specific chemicals dissolved in an aqueous solution will change color if the pH value of that solution falls within a certain range. Litmus paper is a common laboratory application of this principle, where a color-changing chemical substance infused on a paper strip changes color when dipped in the solution. Comparing the final color of the litmus paper to a reference chart yields an approximate pH value for the solution.

A natural example of this phenomenon is well-know to flower gardeners, who recognize that hydrangea blossoms change color with the pH value of the soil. In essence, these plants act as organic litmus indicators1. This hydrangea plant indicates acidic soil by the violet color of its blossoms:


Potentiometric pH measurement

Color-change is a common pH test method used for manual laboratory analyses, but it is not well-suited to continuous process measurement. By far the most common pH measurement method in use is electrochemical : special pH-sensitive electrodes inserted into an aqueous solution will generate a voltage dependent upon the pH value of that solution.

Like all other potentiometric (voltage-based) analytical measurements, electrochemical pH measurement is based on the Nernst equation, which describes the electrical potential by ions migrating through a permeable membrane:


Where,

V = Voltage produced across membrane due to ion exchange, in volts (V)

R = Universal gas constant (8.315 J/molK)

T = Absolute temperature, in Kelvin (K)

n = Number of electrons transferred per ion exchanged (unitless)

F = Faraday constant, in coulombs per mole (96,485 C/mol e)

C1 = Concentration of ion in measured solution, in moles per liter of solution (M)

C2 = Concentration of ion in reference solution (on other side of membrane), in moles per liter of solution (M)

 

We may also write the Nernst equation using of common logarithms instead of natural logarithms, which is usually how we see it written in the context of pH measurement:


Both forms of the Nernst equation predict a greater voltage developed across the thickness of a membrane as the concentrations on either side of the membrane differ to a greater degree. If the ionic concentration on both sides of the membrane are equal, no Nernst potential will develop.

In the case of pH measurement, the Nernst equation describes the amount of electrical voltage developed across a special glass membrane due to hydrogen ion exchange between the process liquid solution and a buffer solution inside the bulb formulated to maintain a constant pH value of 7.0 pH.

Special pH-measurement electrodes are manufactured with a closed end made of this glass, a small quantity of buffer solution contained within the glass bulb:

 

 

Any concentration of hydrogen ions in the process solution differing from the hydrogen ion concentration in the buffer solution ([H+] = 1 × 107 M) will cause a voltage to develop across the thickness of the glass. Thus, a standard pH measurement electrode produces no potential when the process solution’s pH value is exactly 7.0 pH (equal in hydrogen ion activity to the buffer solution trapped within the bulb).

The glass used to manufacture this electrode is no ordinary glass. Rather, it is specially manufactured to be selectively permeable to hydrogen ions2. If it were not for this fact, the electrode might generate voltage as it contacted any number of different ions in the solution. This would make the electrode non-specific, and therefore useless for pH measurement.

Manufacturing processes for pH-sensitive glass are highly guarded trade secrets. There seems to be something of an art to the manufacture of an accurate, reliable, and long-lived pH electrode. A variety of different measurement electrode designs exist for different process applications, including high pressure and high temperature services.

Actually measuring the voltage developed across the thickness of the glass electrode wall, however, presents a bit of a problem: while we have a convenient electrical connection to the solution inside the glass bulb, we do not have any place to connect the other terminal of a sensitive voltmeter to the solution outside the bulb3. In order to establish a complete circuit from the glass membrane to the voltmeter, we must create a zero-potential electrical junction with the process solution. To do this, we use another special electrode called a reference electrode immersed in the same liquid solution as the measurement electrode:

 

Together, the measurement and reference electrodes provide a voltage-generating element sensitive to the pH value of whatever solution they are submerged in:

 

The most common configuration for modern pH probe sets is what is called a combination electrode, which combines both the glass measurement electrode and the porous reference electrode in a single unit. This photograph shows a typical industrial combination pH electrode:

 

The red-colored plastic cap on the right-hand end of this combination electrode covers and protects a gold-plated coaxial electrical connector, to which the voltage-sensitive pH indicator (or transmitter) attaches.

Another model of pH probe appears in the next photograph. Here, there is no protective plastic cap covering the probe connector, allowing a view of the gold-plated connector bars:

 

A close-up photograph of the probe tip reveals the glass measurement bulb, a weep hole for process liquid to enter the reference electrode assembly (internal to the white plastic probe body), and a metal solution ground electrode:

 

It is extremely important to always keep the glass electrode wet. Its proper operation depends on complete hydration of the glass, which allows hydrogen ions to penetrate the glass and develop the Nernst potential. The probes shown in these photographs are shown in a dry state only because they have already exhausted their useful lives and cannot be damaged any further by dehydration

The process of hydration – so essential to the working of the glass electrode – is also a mechanism of wear. Layers of glass “slough” off over time if continuously hydrated, which means that glass pH electrodes have a limited life whether they are being used to measure the pH of a process solution (continuously wet) or if they are being stored on a shelf (maintained in a wet state by a small quantity of potassium hydroxide held close to the glass probe by a liquid-tight cap). It is therefore impossible to extend the shelf life of a glass pH electrode indefinitely.

A common installation for industrial pH probe assemblies is to simply dip them into an open vessel containing the solution of interest. This arrangement is very common in water treatment applications, where the water mostly flows in open vessels by gravity at the treatment facility. A photograph showing a pH measurement system for the “outfall” flow of water from an industrial facility appears here:

 

Water flowing from the discharge pipe of the facility enters an open-top stainless steel tank where the pH probe hangs from a bracket. An overflow pipe maintains a maximum water level in the tank as water continuously enters it from the discharge pipe. The probe assembly may be easily removed for maintenance:

 

An alternative design for industrial pH probes is the insertion style, designed to install in a pressurized pipe. Insertion probes are designed to be removed while the process line remains pressurized, to facilitate maintenance without interrupting continuous operation:

 

The probe assembly inserts into the process line through the open bore of a 90o turn ball valve. The left-hand photograph (above) shows the retaining nut loosened, allowing the probe to slide up and out of the pipe. The right-hand photograph shows the ball valve shut to block process liquid pressure from escaping, while the technician unlatches the clamps securing the probe to the pipe fitting.

Once the clamp is unlatched, the probe assembly may be completely detached from the pipe, allowing cleaning, inspection, calibration, repair, and/or replacement:

 

The voltage produced by the measurement electrode (glass membrane) is quite modest. A calculation for voltage produced by a measurement electrode immersed in a 6.0 pH solution shows this. First, we must calculate hydrogen ion concentration (activity) for a 6.0 pH solution, based on the definition of pH being the negative logarithm of hydrogen ion molarity:


pH = log[H+]
 
6.0 = log[H+]
 
6.0 = log[H+]
 
10-6.0 = 10log[H]
 
10-6.0 = H+
 
H+ = 1 × 10-6 M

 This tells us the concentration of hydrogen ions in the 6.0 pH solution (hydrogen ion concentration being practically the same as hydrogen ion activity for dilute solutions). We know that the buffer solution inside the glass measurement bulb has a stable value of 7.0 pH (hydrogen ion concentration of 1 × 10-7 M, or 0.0000001 moles per liter), so all we need to do now is plug these values in to the Nernst equation to see how much voltage the glass electrode should generate. Assuming a solution temperature of 25o C (298.15 K), and knowing that n in the Nernst equation will be equal to 1 (since each hydrogen ion has a single-value electrical charge):


If the measured solution had a value of 7.0 pH instead of 6.0 pH, there would be no voltage generated across the glass membrane since the two solutions’ hydrogen ion activities would be equal. Having a solution with one decade (ten times more: exactly one “order of magnitude”) greater hydrogen ions activity than the internal buffer solution produces 59.17 millivolts at 25 degrees Celsius. If the pH were to drop to 5.0 (two units away from 7.0 instead of one unit), the output voltage would be double: 118.3 millivolts. If the solution’s pH value were more alkaline than the internal buffer (for example, 8.0 pH), the voltage generated at the glass bulb would be the opposite polarity (e.g. 8.0 pH = -59.17 mV ; 9.0 pH = -118.3 mV, etc.).

The following table shows the relationship between hydrogen ion activity, pH value, and probe voltage4:


  Hydrogen ion activity 
  pH value 
  Probe voltage (at 25o C) 
1 × 103 M = 0.001 M 3.0 pH 236.7 mV
1 × 104 M = 0.0001 M 4.0 pH 177.5 mV
1 × 105 M = 0.00001 M 5.0 pH 118.3 mV
1 × 106 M = 0.000001 M 6.0 pH 59.17 mV
1 × 107 M = 0.0000001 M 7.0 pH 0 mV
1 × 108 M = 0.00000001 M 8.0 pH -59.17 mV
1 × 109 M = 0.000000001 M 9.0 pH -118.3 mV
1 × 1010 M = 0.0000000001 M 10.0 pH -177.5 mV
  1 × 1011 M = 0.00000000001
11.0 pH -236.7 mV

This numerical progression is reminiscent of the Richter scale used to measure earthquake magnitudes, where each ten-fold (decade) multiplication of power is represented by one more increment on the scale (e.g. a 6.0 Richter earthquake is ten times more powerful than a 5.0 Richter earthquake). The logarithmic nature of the Nernst equation means that pH probes – and in fact all potentiometric sensors based on the same dynamic of voltage produced by ion exchange across a membrane – have astounding rangeability: they are capable of representing a wide range of conditions with a modest signal voltage span.

Of course, the disadvantage of high rangeability is the potential for large pH measurement errors if the voltage detection within the pH instrument is even just a little bit inaccurate. The problem is made even worse by the fact that the voltage measurement circuit has an extremely high impedance due to the presence of the glass membrane5. The pH instrument measuring the voltage produced by a pH probe assembly must have an input impedance that is orders of magnitude greater yet, or else the probe’s voltage signal will become “loaded down” by the voltmeter and not register accurately.

Fortunately, modern operational amplifier circuits with field-effect transistor input stages are sufficient for this task6:

 
Even if we use a high-input-impedance pH instrument to sense the voltage output by the pH probe assembly, we may still encounter a problem created by the impedance of the glass electrode: an RC time constant created by the parasitic capacitance of the probe cable connecting the electrodes to the sensing instrument. The longer this cable is, the worse the problem becomes due to increased capacitance:
 

This time constant value may be significant if the cable is long and/or the probe resistance is abnormally large. Assuming a combined (measurement and reference) electrode resistance of 700 M and a 30 foot length of RG-58U coaxial cable (at 28.5 pF capacitance per foot), the time constant will be:

τ = RC

τ = (700 × 106 ) ((28.5 × 1012 F/ft)(30 ft))

τ = (700 × 106 )(8.55 × 1010 F)

τ = 0.599 seconds

Considering the simple approximation of 5 time constants being the time necessary for a first-order system such as this to achieve within 1% of its final value after a step-change, this means a sudden change in voltage at the pH probe caused by a sudden change in pH will not be fully registered by the pH instrument until almost 3 seconds after the event has passed!

It may seem impossible for a cable with capacitance measured in picofarads to generate a time constant easily within the range of human perception, but it is indeed reasonable when you consider the exceptionally large resistance value of a glass pH measurement electrode. For this reason, and also for the purpose of limiting the reception of external electrical “noise,” it is best to keep the cable length between pH probe and instrument as short as possible.

When short cable lengths are simply not practical, a preamplifier module may be connected between the pH probe assembly and the pH instrument. Such a device is essentially a unity-gain (gain = 1) amplifier designed to “repeat” the weak voltage output of the pH probe assembly in a much stronger (i.e. lower-impedance) form so the effects of cable capacitance will not be as severe.

A unity-gain operational amplifier “voltage buffer” circuit illustrates the concept of a preamplifier:

 

A preamplifier module appears in this next photograph:

 

The preamplifier does not boost the probes’ voltage output at all. Rather, it serves to decrease the impedance (the Th´evenin equivalent resistance) of the probes by providing a low-resistance (relatively high-current capacity) voltage output to drive the cable and pH instrument. By providing a voltage gain of 1, and a very large current gain, the preamplifier practically eliminates RC time constant problems caused by cable capacitance, and also helps reduce the effect of induced electrical noise. As a consequence, the practical cable length limit is extended by orders of magnitude.

Referring back to the Nernst equation, we see that temperature plays a role in determining the amount of voltage generated by the glass electrode membrane. The calculations we performed earlier predicting the amount of voltage produced by different solution pH values all assumed the same temperature: 25 degrees Celsius (298.15 Kelvin). If the solution is not at room temperature, however, the voltage output by the pH probe will not be 59.17 millivolts per pH unit. For example, if a glass measurement electrode is immersed in a solution having a pH value of 6.0 pH at 70 degrees Celsius (343.15 Kelvin), the voltage generated by that glass membrane will be 68.11 mV rather than 59.17 mV as it would be at 25 degrees Celsius. That is to say, the slope of the pH-to-voltage function will be 68.11 millivolts per pH unit rather than 59.17 millivolts per pH unit as it was at room temperature.

The portion of the Nernst equation to the left of the logarithm function defines this slope value:


Recall that R and F are fundamental constants, and n is fixed at a value of 1 for pH measurement (since there is exactly one electron exchanged for every H+ ion migrating through the membrane). This leaves temperature (T) as the only variable capable of influencing the theoretical slope of the function.

In order for a pH instrument to accurately infer a solution’s pH value from the voltage generated by a glass electrode, it must “know” the expected slope of the Nernst equation. Since the only variable in the Nernst equation beside the two ion concentration values (C1 and C2) is temperature (T), a simple temperature measurement will provide the pH instrument the information it needs to function accurately. For this reason, many pH instruments are constructed to accept an RTD input for solution temperature sensing, and many pH probe assemblies have built-in RTD temperature sensors ready to sense solution temperature.

While the theoretical slope for a pH instrument depends on no variable but temperature, the actual slope also depends on the condition of the measurement electrode. For this reason, pH instruments need to be calibrated for the probes they connect to.

A pH instrument is generally calibrated by performing a two-point test using buffer solutions as the pH calibration standard. A buffer solution is a specially formulated solution that maintains a stable pH value even under conditions of slight contamination. For more information on pH buffer solutions, see section Analytical Standards. The pH probe assembly is inserted into a cup containing a buffer solution of known pH value, then the pH instrument is “standardized” to that pH value7. After standardizing at the first calibration point, the pH probe is removed from the buffer, rinsed, and then placed into another cup containing a second buffer with a different pH value. After another stabilization period, the pH instrument is standardized to this second pH value.

It only takes two points to define a line, so these two buffer measurements are all that is required by a pH instrument to define the linear transfer function relating probe voltage to solution pH:


Most modern pH instruments will display the calculated slope value after calibration. This value should (ideally) be 59.17 millivolts per pH unit at 25 degrees Celsius, but it will likely be a bit less than this. The voltage-generating ability of a glass electrode decays with age, so a low slope value may indicate a probe in need of replacement.

Another informative feature of the voltage/pH transfer function graph is the location of the isopotential point: that point on the graph corresponding to zero probe voltage. In theory, this point should correspond to a pH value of 7.0 pH. However, if there exist stray potentials in the pH measurement circuit – for example, voltage differences caused by ion mobility problems in the porous junction of the reference electrode – this point will be shifted. Sufficient contamination of the buffer solution inside the measurement electrode (enough to drive its pH value from 7.0) will also cause an isopotential point shift, since the Nernst equation predicts zero voltage when ion concentrations on both sides of the membrane are equal.

A quick way to check the isopotential point of any calibrated pH instrument is to short the input terminals together (forcing Vinput to be equal to 0 millivolts) and note the pH indication on the instrument’s display8. This test should be performed after standardizing the instrument using accurate pH buffer solutions.

When calibrating a pH instrument, you should choose buffers that most closely “bracket” the expected range of pH measurement in the process. The most common buffer pH values are 4, 7, and 10 (nominal). For example, if you expect to measure pH values in the process ranging between 7.5 and 9, for example, you should calibrate that pH instrument using 7 and 10 buffers.

 

1Truth be told, the color of a hydrangea blossom is only indirectly determined by soil pH. Soil pH affects the plant’s uptake of aluminum, which is the direct cause of color change. Interestingly, the pH-color relationship of a hydrangea plant is exactly opposite that of common laboratory litmus paper: red litmus paper indicates an acidic solution while blue litmus paper indicates an alkaline solution; whereas red hydrangea blossoms indicate alkaline soil while blue (or violet) hydrangea blossoms indicate acidic soil.

2It is a proven fact that sodium ions in relatively high concentration (compared to hydrogen ions) will also cause a Nernst potential across the glass of a pH electrode, as will certain other ion species such as potassium, lithium, and silver. This effect is commonly referred to as sodium error, and it is usually only seen at high pH values where the hydrogen ion concentration is extremely low. Like any other analytical technology, pH measurement is subject to “interference” from species unrelated to the substance of interest.

3Remember that voltage is always measured between two points!

4The mathematical sign of probe voltage is arbitrary. It depends entirely on whether we consider the reference (buffer) solution’s hydrogen ion activity to be C1 or C2 in the equation. Whichever way we choose to calculate this voltage, though, the polarity will be opposite for acidic pH values as compared to alkaline pH values

5Glass is a very good insulator of electricity. With a thin layer of glass being an essential part of the sensor circuit, the typical impedance of that circuit will lie in the range of hundreds of mega-ohms!

6Operational amplifier circuits with field-effect transistor inputs may easily achieve input impedances in the tera-ohm range (1 × 1012 ).

7With all modern pH instruments being digital in design, this standardization process usually entails pressing a pushbutton on the faceplate of the instrument to “tell” it that the probe is stabilized in the buffer solution.

8A more obvious test would be to directly measure the pH probe assembly’s voltage while immersed in 7.0 pH buffer solution. However, most portable voltmeters lack sufficient input impedance to perform this measurement, and so it is easier to standardize the pH instrument in 7.0 pH buffer and then check its zero-voltage pH value to see where the isopotential point is at.

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