I would try not to calibrate my cell with a too dilute KCl solution; concentrations below 0.01 mM are less stable by adsorption processes and carbon dioxide uptake from the air; 0.1 mM would be OK from this point of view. To go down to lower conductivities the quality of your electronic circuit will be important (e.g. in case of an electronic micro balance one calibrates with a certified one milligram weight and switches to more sensitive range by a resistors network accurate to 0.1 %; by this the whole microgram range is calibrated better than it is possible with certified weight standards because of interfering moisture and dirt adsorption processes.

!. Firtst of all you can tink about using non-aqueosus calibrating solution. This is important and valuable if you later work with other one of this type during real measurements. I will come back to that issue later.

2. If you stick to water take extreme care about the purity. A so called milipore water (believed to be of high purity) has conductivity in the 1-2 microsemens range.

3. Store your water as well as the solutions in quartz or polypropylene flasks (i preffer quartz) to avoid the alkaline traces dissolution from glass.

4. Remove carbon dioxide just before measurement (e.g. by heating the solution - avoid water evaporation).

5. You can use many less conductive salts instead of KCl. Any stable salt is ok if you have data tabelarized.

Finally,

if you work with non-aqueos conductvity measurement you should use as acalibrating solution a solvent similar (in terms of viscosity, polarity, surface tension) to the working one. This issues are of bigger or lesser importance depending on the design and materials of your measurement cell.

This is with reference to answer mentioned by Karl Cammann. It is mentioned to improve the quality of electronic circuit. But how can you do that? Moreover how the micro balance example is related to conductivity measurement? It is better to elaborate the answer how to improve the electronic circuit.

This is with respect to the answer mentioned by Siekiersky. Which are the non aqueous conductivity standards suggested internationally as KCl of suitable concentrations are suggested as aqueous standards for cell constant measurement? From the answer it is clearly understood that a lot of precautions have been mentioned which to be followed by the user while measuring conductivity. But these precautions will not give any answer to the basic question asked for determination of cell constant.

Generally, tis levels of conductivity are out of the range of the typical solution conductivity measurements. Thus, reffering to the "internationally suggestewd standards" is quite troublesome. At first view you can think about LiCl in anhydrous ethanol. Concerning precautions which have to be taken and the electronic circuit improvement. If you use a typical FRA for that you will have quite well compensated cables and input electrometer impedance of about 1TOhm + 30 pF. Which is far above the measured levles of resisitivity. But consider that any additional cable (and the cell itself are both inductrors and capacitors. Shunt resistivity of a typical laboratory bench is in a range 10e7-10e8 Ohm (depeending on the material, cleaning compounds (antistaic means conductive!!!!) and momentous air humidity. And so on. I am now analyzing impedance spectra registered by some my collegaues (to measure conductivity) "as it is" and the "cable effect" is much bigger than the sample response. Look on the provided graph everything below vertical axes zero comes from the cables....

This is with respect to the answer given by Siekierski. It is quit obvious that for minimising error in conductivity measurement one has to take care of of suitable cable. Impendance spectra as suggested is well appreciated. But a simple approach of solution is to be considered. The purpose of raising this question is due to my personal analysis of errors in conductivity measurement which I experienced. In fact for high purity water there is a challenge in measurement of conductivity even if one takes precautions for environmental contamination. Most of the commercial instruments used to display a figure which seems to be acceptable by the user. But it is difficult to verify the reliability in measurement. The cell constant of such cell is 1 or lee than 1. However there is a knob to adjust cell constant by using KCl of 0.001N or 0.01N. In this point I differ. If you measure cell constant by using different KCl standards as recommended in literature the values differ. Hence we developed a new approach of measurement of conductivity. We suggested multi point calibration approach where a series of KCl solutions whose specific conductance values were computed based on the equivalent conductivity data available in literature. When conductivity is less than 1 microS/cm, we suggested cell constant approach and calibrated the oscillator circuit using know resistors of different ranges. Our work appeared in Review of Scientific Instruments, vol.81, issue no. 6, p. 065109(1-7), 2010 may please be referred.

OK then we finally come to the point of your question. Yuo use the conductivity metter with (I guess single frequency resonanse type of measurement. Thus, when you move along the conductivity scale the frequency is changes in some range of the resonanse circuit of the apparatus. This should not lead to any change of the result when a frequency disperssion of the geometrical capacitance of the cell is equla zero (ideal and non-exixsting case. You have to as well consider the resitivity disperssion in the frequency domain. The impact of both of these problems cannot be determined with the single frequency system. JIn addition to that, the resistor based calibration will not only solve the problem but shifts you from the solution from the real system descritpion as the disperssion function for your cell and a resistor are totally different.

It is with respect to the answer given by Siekierski. For further clarification I wish to add the following information. We have developed a new class of sensors called pulsating sensors. Pulsating sensor works purely in digital domain. It is designed in such a way that the output of sensor is a train of rectangular pulses. Frequency is determined from number of pulses received from the sensor (number of pulses per second). The pulse frequency is a function of sensed parameter. In conductance measurement we use a specially designed logic gate oscillator circuit (LGO). In the LGO our conductance cell is the resistance part and a fixed capacitor is used in the LGO. When LGO is powered by 5 V DC, the output frequency will change with change in conductance of solution. Hence conductance is directly related to pulse frequency. The relation between pulse frequency and conductivity is established by multi-point calibration using a series of KCl standards. For conductivity measurement below 1 microS/cm level the LGO is calibrated with standard resistors by replacing conductance cell. Hence relation between f and R even at very low conductivity zone is established. This relation is used for cell constant determination. The details are given in the reference cited by me. Moreover the paper is downloaded in my research gate.

At 10-6 S/cm your cell is mainly a capacitor (non-ideal of course) not the resistor and the capactitance of the cell has an important impact on fresonanse requency of any oscillator analog, gate based or even quartz cristal based. With this I woul like to finifh this topic as I see that we have a totally different point of wiev on the same problem.