Portable Conductivity Meter Group T2
The Portable Conductivity Meter
December 11, 1998
Group T2
Kathryn Guterl
Lytal Kaufman
Maryam Malik
Andrea Sultenfuss
ABSTRACT
A portable, inexpensive conductivity meter was constructed using a signal generating circuit, a wheatstone bridge, and a voltage comparator. The conductivity meter was powered by two 9-volt batteries and conductivity cells were constructed from a mixture of tin and copper wire (bench wire) as well as from pure copper wire. Testing numerous cells, the average optimal conductivity cell measurements that caused the constructed circuit to work effectively were determined. The cell constants of these optimal cells were determined to be 3.0 + 0.16 cm-1 and 1.7 + 0.21 cm-1 for the bench and copper wire cells, respectively. Using these cells, the resistance readings of NaCl solutions (0.05, 0.1, 0.15, 0.2, 0.25, and 0.3 M) were determined. It was found that the measured resistance from the constructed bench wire and copper wire conductivity cells deviated from the expected resistance readings by 165% and 51%, respectively; the average voltage error across the wheatstone bridge was 143 mV and 98 mV; the percent deviation from the expected cell constant was 84.7% and 87.3%.
Four urine samples with specific gravity measurements ranging from 1.0036 g/mL to 1.0257 g/mL were tested using the constructed optimal conductivity cells in conjunction with the circuit thus forming the conductivity meter. The constructed bench wire cells were found to be more effective in determining the difference in concentration of the urine samples, illuminating the LED as expected in 66.7% of the trials. From a regression equation for each individual cell relating the resistance reading to the concentration of the sample tested, it was found that highly concentrated urine samples deviated significantly from estimated concentration values determined from the specific gravity measurements.
TABLE OF CONTENTS
Background 4
Urine Analysis 4
Conductivity Meter 4
NaCl Solutions 6
Materials and Apparatus 7
Procedure 8
Cell construction 8
Testing of Cells in NaCl Solution 8
Circuit construction 9
Testing of circuits 10
Urine Specimen Collection 10
Results 12
Testing of Cells 12
Tests of Cells and Circuit with NaCl Solutions 14
Tests of Cells and Circuit with Urine 14
Discussion 16
Testing of the Circuit 16
Optimal Cell Constant 16
Bench Wire vs. Copper Wire 18
Urine Analysis 19
Error Analysis 19
Effectiveness as a Conductivity Meter 21
Appendix A 23
Appendix B 26
References 27
BACKGROUND
Urine Analysis
Sodium concentration in the urine is an important indicator of high sodium intake as well as dehydration. People suffering from high blood pressure must monitor sodium intake throughout the day. As more NaCl is consumed, the osmotic pressure of the blood increases, thus causing water to flow from the body tissues into the capillaries. This increase in blood volume increases blood pressure. In order to counteract this effect, the kidneys remove much of this added NaCl, which is shown by an increase of NaCl concentration in the urine. Similarly, when a person is dehydrated, the kidneys reabsorb as much water as possible, increasing the concentration of NaCl in the urine. (4)
The volume and solute composition of urine can vary greatly depending on an individual’s diet and health. Because of these variables, it is difficult to establish the specific concentration for each component of the urine. In examining the composition of urine, sodium and chloride ions make up the greatest concentrations of ions in the solution. Under normal conditions, there is a 0.1 M concentration of NaCl in the urine. (3) However, when the urine is concentrated due to a high level of salt intake or dehydration, as described above, the concentration of NaCl rises to 0.26 M NaCl or greater.
Table 1: Major components of urine. (3)
Component / Initial ultrafiltrate (mmol) / Final urine (mmol) / % reabsorbedWater (1.2 L) / 9,500,000.00 / 67,000.00 / 99.3
Sodium / 32,500.00 / 130.00 / 99.6
Chloride / 37,000.00 / 185.00 / 99.5
Potassium / 986.00 / 70.00 / 92.9
Analysis of urine is used in the laboratory to test for various abnormalities including diabetes, dehydration, thyroid disorders, kidney malfunction, and central nervous system damage. Urine is readily available and easily collected. An inexpensive, portable device to test the concentration of the urine would prove to be an asset to urinalysis. (6)
Conductivity Meter
A conductivity meter serves as an effective tool in measuring the concentration of ions in solution. In an electrolyte solution, the motion of the charged particles constitutes an electric current. The conductivity of an electrolyte solution is a function of the concentration of ions in the solution. Because of this, each solution has a resistance that can be measured with conductivity cells. Conducting sensors are constructed of an insulating material imbedded with metallic pieces. The metal pieces, serving as sensing elements, are placed at a fixed distance apart and make contact with the solution. The cell constant, K, for a particular conductivity cell is determined by the geometry of the cell. The value of K can be estimated by the following equation:
where d is the distance between the sensing elements and A is the surface area of one sensing element exposed to the solution.
By varying K or c, the resistance varies according to the equation:
where R is the resistance, K is the cell constant, L is the equivalent conductance, c is the molar concentration of the electrolyte, and q is the ionic charge. We can see from this equation that as the concentration goes down, the resistance will go up rapidly. (2)
Equation 1 gives an approximation for the cell constant of the conductivity cell. However, for effective calculation of the resistance of a solution, the actual cell constant must be determined through a KCl standardization. The conductance of KCl is known over a wide range of concentrations and thus, using these values of equivalent conductance, and the measured resistance of the solution with a particular conductivity cell, the actual cell constants can be determined. These cell constants, along with the measured resistance, can then be used in the calculation of the equivalent conductance of other solutions. (2)
When measuring the resistance of a solution it is impractical to use an ohmmeter, since passing a current through the solution will lead to errors, such as heating and polarization. Using AC potential eliminates the latter problem, but an AC wheatstone bridge minimizes both of the above problems. In Figure 1, Rf1 and Rf2 are fixed resistors of known resistance; Rb is a resistance box in which the resistance can be changed very precisely over a wide range; and Rm is the resistance to be measured, in this case the conductivity cell with the solution of interest.
The bridge works correctly when V2 = V4 and therefore Rm = Rb(Rf1/Rf2). If the two fixed resistors are chosen to be identical, then Rm is equal to the reading of the variable resistance box Rb. (2)
NaCl Solutions
The expected values of equivalent conductance and resistance, assuming a cell constant of 1 cm-1, are shown in Table 2. The values of equivalent conductance were obtained from an extrapolation of the values given in the CRC. (5) The expected resistance was determined using Equation 2 and a cell constant of 1 cm-1.
Table 2: Expected resistance for a range of NaCl solutions with concentration values similar to that of urine. (5)
Concentration (M) / Equivalent Conductance( cm2S/mol) / Exp. Resistance (W)
0.05 / 111.010 / 180.164
0.1 / 106.690 / 93.729
0.125 / 103.557 / 77.252
0.15 / 101.493 / 65.686
0.2 / 97.829 / 51.110
0.25 / 94.601 / 42.283
0.3 / 91.682 / 36.358
MATERIALS AND APPARATUS
PROCEDURE
Cell Construction
Conductivity cells were constructed using wire made from a mixture of copper and tin (wire from the bioengineering laboratory bench) as well as pure copper wire. The wires were attached to a firm support as shown in Figure 2. An approximation of the cell constant was determined from the following equation:
where d is the distance between the wires, r is the radius of the wire, and L is the length of each wire exposed to the solution. Ten bench wire cells and five copper wire cells were constructed with expected cell constants ranging from 0.77 cm-1 to 83.67 cm-1. The dimensions for these conductivity cells are listed in Appendix A, Table 11 and Table 13.
When using the bench wires, the plastic coating was stripped indicating the length of wire to be submerged in the solutions. Electrical tape was used to cover the copper wire and indicate the length of the wire to be submerged in the solutions.
Testing of Cells (in NaCl solutions)
After the cells were constructed, the actual cell constants were determined in a 0.01M KCl solution using the variable resistance box as well as the pre-constructed wheatstone bridge. An AC potential was used to measure the resistance of NaCl solutions. The accuracy of the cells was analyzed by comparing the resistance readings from the variable resistance box to the expected readings for solutions of 0.05, 0.1, 0.15, 0.2, 0.25, and 0.3 M NaCl. The expected resistance readings for the NaCl solutions were determined using Equation 2, the measured cell constants, and the values of equivalent conductance. (5)
Circuit Construction
In order to maintain the portability of the conductivity meter, an oscillator circuit that generates a 1 kHz square wave signal from a DC signal was constructed as shown in Figure 3 (1). An AC wheatstone bridge was used to minimize the effects of heating and polarization caused by a current. This bridge was constructed as shown in Figure 1. In order to compare the voltages across the bridge circuit, a voltage comparator circuit was constructed as shown in Figure 4. Appendix B shows the conductivity meter circuit with all three circuits connected.
Testing of Circuits
Each circuit was tested individually with LabView to ensure that it was working as expected. The three circuits were tested in conjunction forming the circuit of the conductivity meter. For reasons explained in the discussion, it was determined to use only a green diode with a rectifier to indicate deviation from normal urine concentration.
The circuit was tested using a resistor in place of the solution resistance (Rm) to ensure the correct orientation of the diode and rectifier. The bridge was then balanced at a resistance of 2 kW using the potentiometer of 5 kW in the Rb position. Then various resistors were placed in the position of Rm to ensure that the diode would illuminate when a solution was tested with a lower resistance than the resistance at which the wheatstone bridge was balanced. Resistors of 470 W, 1 kW, and 3.3 kW were tested in the position of Rm.
Next, the circuit was tested with the 0.05 - 0.3 M NaCl solutions using the constructed cells. However, it was discovered that the resistance readings from these solutions were too low to bring about a large enough voltage difference across the wheatstone bridge to cause the diode to illuminate as expected. Therefore, a 1 kW resistor was placed in series with Rm in order to increase the resistance to a detectable level enabling the wheatstone bridge to cause the voltage comparator to illuminate the diode. In addition, a change from a 5 kW potentiometer to a 1 kW potentiometer was used in the wheatstone bridge. Solutions were then tested with the constructed cells in the position of Rm to determine the optimal cell measurements required to create a cell constant large enough to cause the change in resistance measured by the wheatstone bridge to be detectable. Three copper wire cells and three bench wire cells with optimal measurements were used to detect the resistance of the NaCl solutions (0.05 M to 0.3 M). From this data, the reproducibility of the results when using the constructed cells in conjunction with the conductivity meter circuit was determined.
Urine specimen collection
During the third week of experimentation, urine samples were obtained from four random subjects. A resistance reading with six constructed cells (three bench wire cells and three copper wire cells) having the determined optimal measurements were then taken for each sample. This was done using the variable resistance box and the pre-constructed wheatstone bridge. The specific gravity of each urine sample was then found using the specific gravity bottle. The circuit was balanced at the concentration of the urine sample having a specific gravity of 1.02 g/mL and each urine sample was tested with the constructed conductivity cell in the position of Rm to determine if the diode was illuminated. Finally, estimates of each urine sample’s concentration were determined from the specific gravity measurements as well as from a regression of resistance and concentration for each individual cell. The regression was determined from previous resistance readings of the 0.05M-0.3M NaCl solutions.
RESULTS
Testing of Cells
In order to obtain the optimal cell dimensions for the cell to detect changes in concentration, cells with various measurements were constructed and tested. The actual cell constants of these cells were determined using a 0.01M KCl solution. As a first approximation, the expected cell constants were determined using Equation 3. However, it was found that the actual cell constants varied from the expected cell constants. The actual cell constants were 84.7% and 87.3% lower than the expected cell constant for the bench wire and copper wire cells, respectively.