In a similar vein, the TDS has been used to estimate the ionic strength of natural waters via the Langlier approximation:

Combining these two, one gets:

This is exactly the value reported by Evangelou (1998) for waters dominated by chloride. He also found that sulfate-dominated waters gave higher TDS values at the same conductivity in accordance with the following model:

Others have reported a range of values for the ratio: TDS/K. For example, Hounslow (1995) cites 0.54 to 0.96, with 0.55 to 0.76 being most typical.

Conductivity can also be used as an indicator of the endpoint of a titration. Skoog (1985) shows some example titration curves for acid/base titrations where the endpoint occurs at a well-defined inflection point. He also shows its use with chloride analysis by addition of silver salts and precipitation of AgCl.

Table 18.1

Some Typical Solids and Conductivity Values

Conductivity Meter. Theory tells us that conductivity is a function of the concentration and type of ions present, and the temperature. For a pure solution of an inorganic salt, the conductivity should be a nearly linear function of concentration. The following table shows that the conductivity per equivalent (equivalent conductance) of KCl changes little with order of magnitude changes in concentration.

The conductivity or specific conductance (K) is related to the resistance (R; in ohms) of an aqueous sample and the cell constant (C; in cm-1) of the conductivity meter.

K = C/R (18.2)

The cell constant is equal to the distance between the parallel electrodes (l) in cm divided by the cross-sectional area of the electrodes (A), in cm2 all multiplied by the efficiency.

(18.3)

Note that most conductivity meters employ alternating current so as to avoid problems of polarization. While the electrode characteristics, l and A, may be fixed and easily determined, the electrode efficiency is known to change as the electrode ages. Thus, it should be checked each time conductivity measurements are made. This is done by running a series of standards of known conductivity, usually KCl.

Table 18.2

Conductance of KCl Standards

Equivalent conductance (L ) can be determined for a pure substance by dividing the specific conductance by the normality.

(18.4)

In an ideal solution the equivalent conductance will be constant and independent of concentration. In reality, it is affected by ionic strength. The infinite dilution (or "limiting") equivalent conductance (extrapolated to I=0) can be calculated from the infinite dilution ionic conductances of the constituent ions (Table 18.3).

(18.5)

Table 18.3

Ionic Conductances, mho-cm2/equivalent

(I=0, 25oC)

In the Environmental Engineering teaching laboratory we have a Yellow Springs Model 33 conductivity meter. This is a portable, battery-powered instrument. The probe has a cell constant of 5.0 ± 2% with platinized nickel electrodes and a low-capacitance cable. Be careful not to touch the soft platinum black coating inside the probe.

All conductivity probes will eventually become coated with scale, organic deposits, etc. When this happens the "cell test" function should alert the user (see step 7 below). The electrode may be cleaned by soaking for 5 minutes in a solution made from 10 parts distilled water, 10 parts isopropyl alcohol, and 1 part HCl. If this still does not restore proper performance, the probe will have to be re-platinized (refer to manual). It is best to store the conductivity probe in distilled water when not in use. Probes that have been stored dry should be soaked in distilled water for 24 hours prior to use.

The YSI meter is calibrated from a standard solution of 0.0100 M KCl. The following table shows the accepted conductivity values for this solution.

Figure 18.1 Typical field conductivity meter (YSI Model 33; left) and research-grade meter (YSI Model 32, right).

Table 18.4

Conductivity of KCl vs. Temperature

Figure 18.2

Estimated Error for the YSI Model 33: Temperature

Figure 18.3 Estimated Error for the YSI Model 33: Conductivity

pH is commonly measured with a potentiometric glass electrode. A reference electrode is also required. This may, however, be combined into a single probe, called a "combination pH electrode". pH electrodes always contain a bulb at the end covered with a thin glass membrane (Figure 18.4). This membrane becomes hydrated in the presence of water. Hydrogen ions can enter the silicon-oxygen structure of the glass and alter the charge. This creates a change in electrical potential with respect to the silver/silver chloride reference. The free energy change is related to the change in hydrogen ion activity by equation 18.6.

Figure 18.4

A Standard Glass Combination pH Electrode

G = -RT ln({H+}₁ /{H+}₂ ) (18.6)

And from this the Nerstian slope of 59.16 mV per pH unit can be derived.

-nFE = -RT ln({H+}1/{H+}2) (18.7)

(18.8)

(18.9)

E = L-0.05916(pH) (18.10)

Glass pH electrodes respond to hydrogen ion activity rather than concentration. Recall that activity may be expressed as the product of concentration and an activity coefficient, g .

{H+} = g H[H+] (18.11)

where the activity coefficient is a function of ionic strength and it has a value close to 1 in dilute solution. Therefore, for most applications this is not a serious disadvantage. Glass electrodes will, however, also respond to sodium ions to a slight extent. This will cause errors under conditions of low hydrogen ion activity (i.e., high pH) and high sodium concentrations.

In the UMass Environmental Engineering Teaching Laboratory we use Fisher Model 140A pH Meters. These are analog meters that read either in pH or directly in millivolts of electrode potential. Each has a mirror-backed meter scale to minimize reading parallax. The repeatability is -0.05 pH (-5 mV), and the relative accuracy is -0.1 pH when measured within 2 pH units of a standardization point. The Model 140A meters are used as follows.

Start-up:

Standardization (two point method):

General Operation:

Storage:

pH buffers are available commercially in a powdered form (to be added to distilled water) or as a prepared liquid. All of these solutions contain acids and bases whose equilibria are dependent on temperature. As a result the precise pH is also a function of temperature. For example the buffers available from VWR Scientific vary with temperature as shown in Table 18.5.

It is important to avoid streaming potential effects in dilute solutions. Therefore, such samples should be allowed to stand quiescently for several minutes before measuring (McQuaker et al., 1983; ES&T, 17:431-435).

Table 18.5

Standard Buffers

Most commercially available strong acids and bases are supplied at a standard concentration as shown in Table 18.6. Unfortunately none of these concentrations are very accurate. The exact concentration as supplied by the chemical company may vary by 5% or more. Also the concentrations may change upon storage from volatilization and absorption of atmospheric moisture. Accurate determinations of acidity and alkalinity require an acid or base of known and precise concentration. In order to circumvent this problem the acid (usually hydrochloric acid) or base (usually sodium hydroxide) must first be standardized in the laboratory. This is done by conducting an acid/base titration between the titrant and a weak acid or base whichever is appropriate. There are several weak acids and bases that are available in a stable powdered form of very high purity (e.g., 99.8%). A solution of very accurate concentration can be prepared from these compounds, and it can be compared with the titrant of interest. For the standardization of hydrochloric acid we use anhydrous sodium carbonate. For the standardization of sodium hydroxide, potassium acid phthalate is generally employed.

Table 18.6

Concentrated Laboratory Acids and Bases

Potentiometric Method. This method uses an electrode with an oxygen permeable membrane (usually polyethylene or teflon). Because the membrane severely inhibits the diffusion of ionic species to the electrodes, this method is much less susceptible to interferences than the Winkler test and its modifications. The electrode systems may be either galvanic (spontaneous reaction) or polarographic (reaction due to an applied voltage). For both systems the cathodes are of some inert metal such as silver, gold or platinum. The galvanic systems use basic anode metals such as lead, zinc or cadmium, whereas polarographic systems commonly use silver/silver chloride anodes. For a galvanic system, the cathodic reaction is:

O2 + 2 H2O + 4e- -------------> 4OH (18.12)

And the corresponding anodic reaction might be:

2Pb + 4OH- ----------------> 2PbO + 2H2O + 4e- (18.13)

Whereas, for a polarographic system, the cathodic reaction is:

O2 + 2H⁺ + 2e- -------------> H2O2 (18.14)

And the anodic reaction is:

2Ag + 2Cl- ----------------> 2AgCl + 2e- (18.15)

Normally the overall rate of reaction of oxygen at the electrodes (diffusion current) depends on the rate of diffusion of O2 across the membrane. Temperature is a very important variable as it strongly effects membrane permeability to oxygen. These effects can be mathematically compensated by knowing the relationship between temperature, T (degrees Kelvin), and the sensitivity, l (meter reading divided by actual D.O.):

ln(l ) = -m(1/T) + b (18.16)

where m and b are the slope and intercept of the log-reciprocal plot. Also of concern for highly saline waters is the effect of ionic strength on electrode response. It has been found that ln(l ) increases linearly with increasing ionic strength. The slope is such that a 10% increase in sensitivity occurs for every increase of 0.35 M ionic strength or 35,000 ohm-1cm-1 conductivity.

The YSI Model 54A is a polarographic system using a gold cathode, a silver anode, and a FEP teflon membrane (0.001 in). The electrolyte is KCl at half saturation, and the nominal polarizing voltage is 0.8 volts. The corresponding D.O. electrode (YSI Model #5739) contains a pressure-compensating diaphragm. This permits accurate readings at depth. It also contains a temperature sensor that feeds back and automatically corrects the D.O. reading for changing membrane permeability with changing temperature.

Figure 18.5 YSI Model #57 D.O. Meter and Probe

Proper calibration of the YSI Model 54A dissolved oxygen meter is as follows:

1. With the instrument off, adjust mechanical zero

5. Turn selector to "Temp"

Sample concentrations may simply be read by immersing the end of the probe and stirring. Adequate time must be allowed for the probe to stabilize to the new dissolved oxygen and temperature. It is recommended that the probe be left on between measurements so as to avoid the need to repolarize.

Meter accuracy is ± 0.1 mg/l. The response for 90% of the ultimate reading is 10 seconds at 30° C reducing to 30 seconds at lower temperatures.

Yellow Springs Instrument Company lists the following typical errors for the polarographic determination of dissolved oxygen:

1. The geometric mean of four general errors = 3.1%, these include:

2. If both ranges are used, error due to inter-range tolerances = 1%

3. Error due to probe background current = abs{ Meter Reading -1}%

5. Errors in assuming 100% humidity when air calibrating the probe

One must also consider:

To determine the total expected error, the geometric mean of the six must be calculated and applied to the final reading.

Skoog, D.A. (1985) Principles of Instrumental Analysis, 3^rd edition, Saunders, Philadelphia.

1. The following table contains data from Hem's 1959 USGS Water Supply paper. Using this, estimate the "true" dissolved solids concentrations for this water. How does this calculated value compare with the actual residue determination? Calculate an Anion-Cation balance. How close do the two come to balancing and what is the percent error or fractional difference? Also, estimate the conductivity based on the equivalent ionic conductances. How does this value compare with the measured value? Calculate the ratio of dissolved solids to conductivity. Finally, calculate the ionic strength of this sample. How does this value compare with what you would expect from the Langlier and Russell approximations? (A series of tables may be helpful in this presentation.)

Analysis of Waters in Which Calcium or Magnesium are Major Constituents:

Groundwater from Syndey, OH, April, 1952

Hem, J.D., USGS Water Supply Paper #1473: 1sted. 1959; 2nded. 1970.

2. Explain the underlying reason for the two correlations between TDS and K as attributed to Evangelou. Why are the two correlations different? Develop a theoretical basis for the particular equations (i.e., equations 18.1c and 18.1d).

 

3. One liter of a 0.1M solution of HCl is titrated with a 10M solution of NaOH. Calculate and plot the specific conductance of this solution as a function of the mLs of NaOH solution added from 0 mL to 20 mL. Also show the contributions of the four specific ions (H⁺, Cl^-, Na⁺, and OH^-) to the overall specific conductance. Ignore dilution of the original solution and assume 100% dissociation of the HCl and NaOH.