Welcome to the dissolved oxygen (D.O.) theory Page. Dissolved oxygen from A to Z.

• Basic principles of Polagrography cell (electrode)

• Polar gram

• EID’s dissolved oxygen electrode picture

• Electrode reactions

• Number of electrons involved

• Calibration

• Calibration in air saturated with water vapor

• Calibration in air saturated water

• Checking the sensor function

• Measurement and analytical quality assurance

• Cleaning of sensors

• Regeneration of sensors

• Polarization periods (startup periods) prior to measurement

• Approach flow

• Correction for salt content

• Influence of interfering gases

• Solubility functions

• Checking the oxygen meter and or logger

• Dissolved oxygen Applications

• Practical experiments

Dissolved Oxygen:

The air we breathe contains about 20% oxygen. Fish and other aquatic organisms require oxygen as well. The term Dissolved Oxygen (DO or D.O.) refers to the amount of free oxygen dissolved in water which is readily available to respiring aquatic organisms. State water quality standards often express minimum concentrations of dissolved oxygen which must be maintained in order to support life as well as be of beneficial use. Levels of dissolved oxygen below 4-5 milligrams per liter affect fish health and levels below 2 milligrams per liter can be lethal to fish.

Additionally, biochemical oxygen demand (BOD) is commonly used with reference to effluent discharges and is a common, environmental procedure for determining the extent to which oxygen within a sample can support microbial life. The test for BOD is especially important in waste water treatment, food manufacturing, and filtration facilities where the concentration is crucial to the overall process and end products. High concentrations of DO predict that oxygen uptake by microorganisms is low along with the required break down of nutrient sources in the medium.

Basic principles of Polagrography cell:

Liquid and Air state of equilibrium is reached when the partial pressure of oxygen, i.e. the part of the total pressure that is due to oxygen, is equal in air and in liquid. The liquid is then saturated with oxygen.

Figure 1.1 Air and liquid oxygen equilibrium

Polargram:

When an electrode of noble metal such as platinum or gold is made 0.6 to 0.8 V negative with respect to a suitable reference electrode such as AgAgCl or an calomel electrode in a neutral KCI solution (see Figure 1.2), the oxygen dissolved in the liquid is reduce at the surface of the noble metal.

Figure 1.2 Polarographhy diagram

This above phenomenon can be observed from a current to voltage diagram called a polarogram of the electrode. As shown in Figure 1.3a, the negative voltage applied to the noble metal electrode (called the cathode) is increased, the current increases initially but soon it becomes saturated. In this plateau region of the polarogram, the reaction of oxygen at the cathode is so fast that the rate of reaction is limited by the diffusion of oxygen to the cathode surface. When the negative bias voltage is further increased, the current output of the electrode increases rapidly due to other reactions, mainly, the reduction of water to hydrogen. If a fixed voltage in the plateau region (for example, - 0.6V) is applied to the cathode, the current output of the electrode can be linearly calibrated to the dissolved oxygen (Figure 1.3b). It has to be noted that the current is proportional not to the actual concentration but to the activity or equivalent partial pressure of dissolved oxygen, which is often referred to as oxygen tension. A fixed voltage between -0.6 and -0.8 V is usually selected as the polarization voltage when using Ag/AgCl as the reference electrode or any other EID's dissolved oxygen electrodes.

Additionally for physical and chemical correctness, partial pressure in a liquid actually refers to the fugacity. In the pressure range relevant to the measurements at hand, it is acceptable to equate the two values and this allows us to restrict the following considerations to the partial pressure. In dry, atmospheric air, the partial pressure of oxygen is 20.95% of the air pressure. This value is reduced over a water surface because water vapor has its own vapor pressure and a corresponding partial pressure.

Figure 1.3 (a) Current to voltage diagram at different oxygen tension; (b) Calibration obtained at a fixed polarization voltage of –600 mV.

When the cathode, the reference electrode, and the electrolyte are separated from the measurement medium by a polymer membrane, which is permeable to the dissolved gas but not to most of the ions and other species, and when most of the mass transfer resistance is confined in the membrane, EID’s electrode system can measure oxygen tension in various liquids. This is the basic operating principle of the membrane covered polarographic Dissolve oxygen probe (Figure 1.4).

The basic principle underlying the electrochemical determination of oxygen concentration is the use of membrane covered electrochemical sensors. The main components of the sensors are the oxygen permeable membrane, the working electrode, the electrolyte solution and a possible reference electrode. A voltage is applied between the gold (platinum or silver) cathode and the anode that consists of either lead or silver (AgAgCl), and causes the oxygen to react electrochemically. The higher the oxygen concentration the higher the resulting electric current. The current in the sensor is measured and, after calibration, converted into the concentration of dissolved oxygen.

If the anode is made of silver, the meter applies the required voltage (polarographic sensor). If it is made of lead, the sensor is self-polarizing, i.e. the voltage is generated in the sensor by the electrodes themselves, comparable to the process in a battery (galvanic sensor). The meter merely evaluates the current.

Figure 1.4 Basic Polarographhy electrode

EID’s polaragraphoc dissolved oxygen electrode picture:

EID’s ELECTRODER - ABS body Dissolved Oxygen Sensor (ADO)

EID’s dissolved oxygen, Probe, polaragraphic, ABS body, 12mm * 120mm, with 10K Negative Temperature Compensation

Figure 1.5 Basic Polarographhy-electrode

Electrode reactions:

For our polarographic electrodes, the reaction proceeds as follows:

• Cathodic reaction:    0₂ + 2H₂ 0 + 2e^- à H₂O₂ + 2OH^-

                                     H₂0₂ + 2e^- -> 20H^-

•  Anodic reaction:       Ag + Cl^- à AgCl + e^-

•  Overall reaction:      4Ag + 0₂ + 2 H₂O + 4 Cl^- à 4 AgCl + 4 OH^-

The reaction tends to produce alkalinity in the medium together with a small amount of hydrogen peroxide.

Number of electrons involved:

Two principal pathways were proposed for the reduction of oxygen at the noble metal surface. One is a 4-electron pathway where the oxygen in the bulk diffuses to the surface of the cathode and is converted to H₂O via H₂O₂ (path a in Fig. 1.6). The other is a 2-electron pathway where the intermediate H₂O₂ diffuses directly out of the cathode surface into the bulk liquid (path b in Figure 1.6). The oxygen reduction path may change depending on the surface condition of the noble metal. This is probably the cause for time-dependent current drift of polarographic sensors. Since the hydroxyl ions are constantly being substituted for chloride ions as the reaction starts, KCI or NaCl has to be used as the electrolyte. When the electrolyte is depleted of Cl^-, it has to be replenished.

                                                                             2e^-

                                                        2e^-         à (a)  à  H₂O₂

                                                        O₂ à O₂ à H₂O₂   

                                                                          Diffusion

                                                                     à (b)   à  H₂O₂

Figure 1.6 alternative pathway of oxygen reduction at cathode surface

Calibration:

Calibration must be carried out for dissolved oxygen measurements on a regular base. This is because the measuring process consumes the electrolyte solution in the sensor head, as shown by the electrode reactions presented above. The ions of the electrolyte solution bind the released metal ions, thereby changing the composition of the solution. The recommended calibration period depends on the oxygen sensor used and ranges from one week for pocket instruments to 1-2 months.

Each linear calibration function is defined by at least two points. For dissolved oxygen measurements with EID meter and/or logger, one of the points on the line is the zero point of the sensor. At the zero point, the sensor signal obtained in the absence of oxygen lies below the resolution of the sensor. This point is called the zero-current point of the sensor. The second point of the calibration line can be set as required. Its position is based on the fact that, in a state of equilibrium, the partial pressure of oxygen in liquid and air is equal.

Figure 1.4b Two-point calibration

The rate at which oxygen enters a dissolved oxygen probe is a function of:

• the concentration of oxygen in the sample

• the diffusion coefficient/permeability of the membrane (function of temperature)

As described above calibration routines for dissolved oxygen probes use a two point linear calibration where one point is at zero mg/L oxygen and the second point is at saturation or equilibrium with the atmosphere, C^* . The zero measurement is not zero volts due to the conductivity of the electrolyte between the electrodes as well as any errors in the analog signal conditioning circuit. For the circuit and probe system used in the Environmental lab the zero measurement is approximately 1 mV (where approximately 200 mV corresponds to saturation levels of oxygen) and hence the zero measurement is not significant. Thus a single point calibration is used.

C* is a function of the atmospheric pressure and temperature. The functional relationship with temperature is implemented using a lookup table (based on equilibrium at atmospheric pressure) with interpolation. The effect of atmospheric pressure is implemented as shown (Equation 1 below).

P

C^* =------- f (T)

P_atm

The permeability of the membrane increases about 5% per C degree. I chose to use 25 C as the reference temperature and thus K_membrane(T_ref) has a value of 1. The following (equation 2) creates a coefficient that describes this variation.

K_membrane(T)₌K_membrane(T_ref)e^0.05(T-Tref)

The slope of the linear fit (k) can be calculated after the voltage corresponding to saturation oxygen is measured (Equation 3 below).

    C^*_cal  K_membrane

C =------------------

 V^*_cal

The slope coefficient is placed in the polynomial array.

The equation for the dissolved oxygen concentration illustrates that the predicted concentration is a function of sample temperature because K_membrane varies with temperature.  The coefficient, k, should be independent of temperature but will vary as a membrane fouls (Equation 4 below)

      KV

C=-----------

     K_membrane

Pressure

The constituents of air have been well defined, and it is known that air contains 20.946% oxygen. Since the total pressure in the air is the sum of all of the partial pressures (Dalton’s Law), an atmospheric pressure of 760 millimeters Mercury (mmHg) in dry air will contain a partial pressure of oxygen (pO₂) of approximately 159 mmHg (760 mmHg * 0.20946).  Changes in atmospheric pressure will cause a directly proportional change in the partial pressure of oxygen in the air.  Atmospheric pressures will vary depending upon altitude and local weather conditions.  Some average pressures for varying altitudes are listed in Table 1 bellow. 

The relationship between oxygen partial pressure and total atmospheric pressure should be understood and incorporated into the air calibration in order to minimize calibration error, which could be as high as 5-10% dependent upon altitude and local weather conditions.  Most dissolved oxygen meters that have any sort of advanced air calibration (such as temperature compensation, which will be discussed in a later section) will be based upon an atmospheric pressure of 760 mmHg.  Most tables of oxygen solubility are referenced to this value.  Because of the change in oxygen partial pressure with changes in atmospheric pressure, a correction must be made when the pressure varies from this value.  A simple means of incorporating pressure changes is listed in the “correction factor” shown in Table 1 bellow.  The value listed is a rough multiplier, which can be used once the initial oxygen concentration is determined based upon temperature and relative humidity.  A more accurate calculation for incorporating pressure will be discussed after relative humidity and temperature effects are investigated. 

Some EID’s dissolved oxygen meters contain a pressure sensing device which provides compensation for pressure effects when an air calibration is performed.  If you use our electrode on not-EID-meter, since most meters do not have this, it is usually necessary to note the average pressure in the local vicinity of the probe, which will be mostly altitude-based, and adjust the calibration using the simple correction factor or the more complex calculation performed later.  A mercury barometer located in the immediate vicinity of the meter will give a relatively accurate measurement of the local atmospheric pressure if an older meter with no pressure sensor is used.

Table 1: Oxygen Value Corrected for Pressure (25 °C)

Relative Humidity and temperature effect and Temperature compensation

If desired the Eid's probes can be coupled with a temperature thermistor (10K Ohms) to achieve temperature compensation since K_membrane varies with temperature.

The discussion of pressure effects were based upon atmospheric pressure with dry air (no moisture content).  Whenever air contains a certain amount of moisture, the atmospheric pressure contains another source of partial pressure -- water vapor.  If a comparison of the oxygen partial pressure in air with 100% relative humidity and air with 0% relative humidity is done while both are at the same atmospheric pressure, the air with 100% relative humidity will have a lower oxygen partial pressure due to the presence of the water vapor pressure (pH₂O).  Water vapor pressure in air varies with temperature, and is well defined.  The effect of temperature on oxygen partial pressure in moist air is such that higher temperatures yield lower oxygen partial pressure, while lower temperatures yield higher pressures.  Note that the effects of relative humidity and temperature can cause errors when air calibration is performed in dry air, since most of the current tables and meter temperature compensations are based on air containing 100% relative humidity.  Table 2 bellow shows both the oxygen concentration, which is linear with the partial pressure of oxygen,  that would be present at 100% relative humidity and 0% relative humidity.  The values only differ by a few percent in ambient air conditions, and thus is generally ignored. Most dissolved oxygen meters have temperature compensation for air at 100% relative humidity, and no manual correction is necessary.  However, many older meters do not have temperature compensation included, and therefore this calculation must be done manually.  If temperature is not compensated for in the calibration, the error can be as much as 20 to 30 % for every 10 degrees difference from 25 °C, and therefore temperature compensation is standard on most dissolved oxygen meters today.   Since the effects of relative humidity is minimal at all but the highest temperatures, no current dissolved oxygen meters incorporate any kind of relative humidity sensing device.

In order to ensure an accurate temperature and current reading, the probe must be exposed to the air for enough time to allow thermal equilibrium to occur.  There are often significant temperature differences between the process water and the ambient air.  Larger temperature gradients between the two necessitate additional time for thermal equilibrium to take place.  For instance, a 20 °C difference between ambient air and process water can cause a calibration delay of about 30 minutes in many probes for the probe to fully equilibrate to ambient temperature.  Since most temperature gradients will not be this large, allowing approximately 15 minutes is usually a safe assumption.  It is common for users to calibrate the unit before the dissolved oxygen meter is reading the stabilized temperature and current value, which can cause significant error since a difference of even 5 °C from actual can cause the reading be off by 5 to 10%.  It is often useful to have a calibrated temperature sensor, accurate to 1 °C or better, at the calibration location to know when the probe temperature is reading the correct ambient air temperature. 

It is useful to have an equation which can be used to determine oxygen concentrations in air based upon temperature, relative humidity, and pressure. Since the full equation is quite lengthy and complex, two easier versions are presented to the user, along with Table 2 bellow, to determine the correct oxygen concentration in air.  Equation 5 bellow should be used with air with 100% relative humidity, and Equation 6 should be used for air with 0% relative humidity. 

Equation 5 (100% Relative Humidity): OS = (OS’) * (P - p) / (760 - p)

where:

OS  = Oxygen solubility at barometric pressure of interest

OS’ = Oxygen in saturation at one atmosphere (760 mmHg) at a given temperature

P  = Barometric pressure of interest

p  = Vapor pressure of water at the temperature of interest

Example 1:

The user wishes to calibrate a dissolved oxygen probe in air at an altitude of 3500 feet.  The temperature is 30 °C, and the relative humidity is 100%. 

At an altitude of 3500 feet, the atmosphere pressure will usually be about 668 mmHg (Table 1 above).  The sample temperature is 30 °C, and the relative humidity is 100%.  From water vapor pressure tables, the water vapor pressure at 30 °C is 31.8 mmHg. The oxygen saturation level at 760 mmHg and 30 °C is 7.54 ppm (Table 2 bellow).  Substituting these values in the above (equation 5) gives the following:

OS  =  (7.54)  * (668 - 31.8) / (760 - 31.8) =  6.59 ppm

Example 2:

Assume the same conditions as in example 1, but with a relative humidity of 0%.  In this case, the value used for the oxygen saturation level would be 7.87 (Table 2 bellow), not 7.54.  The calculation will change since there will be no water vapor pressure.

Equation 6 (0% Relative Humidity): OS = (OS’) * (P) / (760 mmHg)  

Substituting the above values into the equation yields the following:

OS = 7.87 * (668) / (760) = 6.92 ppm

Note: that the multiplier of (668) / (760) is actually the simplified correction factor listed in Table 1 above for an altitude of 3500 feet (0.88). Table 3 bellow lists calibration values for varying temperatures pressures at relative humidity levels of 100%.