Conductance, resistance, conductivity, and resistivity:
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Conductance, resistance, conductivity, and resistivity: a summary for people who weren’t paying attention in PChem or who had PChem long ago by Michael Collins. Solution conductivity. Spans a factor of more than 10 million from ultra pure water to concentrated ionic solutions

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Solution conductivity

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Solution conductivity

Conductance, resistance, conductivity, and resistivity: a summary for people who weren’t paying attention in PChemor who had PChem long agoby Michael Collins


Solution conductivity

Solution conductivity

  • Spans a factor of more than 10 million from ultra pure water to concentrated ionic solutions

  • Remarkably easy to measure with the MicroLab system of FS-522 lab interface, software, and sensor

  • Determined by the

    • Concentration of ions

    • Mobility of ions

    • Temperature

    • Solvent

    • Physical arrangement of electrodes in the conductivity cell


Accurate measurements require a bit more than routine measurements

Accurate measurements require a bit more than routine measurements

  • Rugged, reliable conductivity cell needed

  • Temperature control is essential

    • Ion mobility can change by up to 10% between 20o and 25oC

    • Weak electrolytes can change even more depending on the temperature dependence of Keq

  • High quality distilled or deionized water is a plus

    • Dissolved CO2 is a weak acid, adds ions!

    • Dissolved minerals can swamp the conductivity of dilute solutions

    • In any case, the conductivity of water needs to be measured and can be subtracted to get the net conductivity


Terminology and review of concepts

Terminology and review of concepts

  • Ohm’s Law:

    V = IR

    • V is the applied voltage across the resistor

    • The current flows in proportion to the voltage for a fixed resistance

  • Electrical resistance, R, of a conductor:

    • The measure of the amount of current a circuit can carry for a given voltage

    • An ideal conductor is a material whose resistance R is a constant over all applied voltages at a given temperature

    • SI units for electrical circuits:

      • voltage (aka “potential”) unit is the volt

      • Current unit is the ampere

      • resistance unit is the ohm


  • Terminology and review of concepts1

    Terminology and review of concepts

    • Conductance:

      • The reciprocal of resistance

      • Symbol is L = 1/R

      • “Conductance” as a term is not used much in wired circuits but is used extensively in circuits involving solutions

      • Units are Siemens

        • Olden days: units were ohm-1 and mho

        • Present day: unit is the siemen

          • 1 siemen = 1 ohm-1= 1 mho

          • Not to be confused with the Siemens Corp.


    Terminology and review of concepts2

    Terminology and review of concepts

    • Resistivity (formerly called specific resistance)

      • A measure of the resistance of a wire of length l (meters) and cross sectional area A (m2)

        ρ = R*A/l

        R = ρ* l/A

      • ρ is an intensive property of the conductor

        • Thicker wires have lower resistance

        • Longer wires have higher resistance

        • All wires of a given material have the same R*A/ l !

      • Units are ohm-meters

      • In solution measurements

        • A is the area of the electrodes in the cell

        • l is the distance separating the electrodes


    Terminology and review of concepts3

    Terminology and review of concepts

    • Conductivity (formerly called specific conductance)

      • Defined as the inverse of the resistivity

        κ = 1/ρ = l/A * 1/R = l/A * L = K * L

      • Conductivity has the reciprocal SI units of resistivity

        ohm-1m-1 ≡ siemens.m-1

      • K(= l/A) is called the cell constant and is a measure of the area of the electrodes in the measuring cell and the distance between them.

        • SI unit is m-1

        • though it is often given in cm-1

          Precise value of K for a given cell must be determined by measuring the conductances of standard solutions of known conductivity


    Molar conductivity of salt solutions

    Molar conductivity of salt solutions

    • Λm = κ/c

    • c is given in SI units (mol/m3)

      • So units on Λm are

      • (siemens/m).m3/mol = siemens.m2/mol

    • Usual units for concentration are mol/L

      • c (mol/m3) = M (mol/L) x 1L/1dm3 x (10dm/m)3

      • c (mol/m3) = 1000M (mol/L)

    • So Λm = κ/c = κ/(1000M) (siemens.m2/mol)

      • NOTE: Λm is often given in siemens.cm2/mol

      • In which case, convert (10 cm)2 = (1m)2


    General operational procedure for determining a cell constant

    General operational procedure for determining a cell constant

    • Obtain or prepare aqueous solutions of salt solutions of known conductivity κ using good quality DI or distilled water.

      • Note the units used in the κ value reported!

      • Usually SI units of Siemens/m are not used – more typically millisiemens/cm or microsiemens/cm (μS/cm)

      • Make all measurements with the appropriate units in mind

    • Fill sample cell/beaker/vial with the same batch of DI or distilled water used to prepare sample and measure the conductance of the water

    • Rinse and fill cell/beaker/vial with sample of known conductivity and measure its conductance

      • Subtract conductance of the water from the known conductance to get the net conductance L of the solution

      • Determine the cell constant K = κ/L

    • Rinse and fill cell/beaker/vial with unknown sample and measure its conductance

      • Subtract conductance of the water from the unknown conductance to get the net conductance L of the unknown

      • Determine the conductivity κ = KL


    Check out the microlab video

    Check out the MicroLab video

    • Short video showing via screen capture the process of calibrating the conductivity sensor to determine the cell constant and measuring the conductivity of an unknown

    • INSERT LINK HERE


    Solution conductivity

    The calibration step relates the solution conductivity to the measured conductance to obtain the cell constant.

    Conc. NaCl (g/1000.0 mL) Conductivity (µS/cm)0.0000.050.0501050.1002100.1503150.2004150.50010201.00019901.50029302.0003860

    Thus all measurements made with the MicroLab system after calibration are conductivities in µS/cm


    Microlab method

    MicroLab method:

    • Plug conductivity cell into its jack on the FS-522 lab interface

    • Make sure the latest version of the MicroLab software is installed on the Windows PC

    • Connect the FS-522 interface to the PC and turn it on

    • Open the MicroLab software

    • Run the default experiment. Then

      • Add sensor (conductivity)

        • Choose the range you want to use. 0-20,000 μS/cm for routine use; 0 – 2,000 μS/cm for dilute solutions or weak electrolytes

      • Choose a new calibration file

        • This will relate sensor response (L) to known conductivity (κ)

      • Measure conductance of (each) sample, entering its known conductivity κ (note the units that you use to enter the data – most standards are in μS/cm

      • Add a regression line and save.

        • The slope of the line is the the cell constant. Units will be in cm-1.

        • This will exit you to the main program.

      • Drag the conductivity sensor to the digital display

      • Measure the conductivity of your unknown(s) in the same way you did with setting up the calibration file.

      • Units will be in μS/cm or whatever factor of siemens you used in the calibration.


    Microlab method1

    MicroLab method:

    • Of course you can set up any experiment that you want by adding other sensors.

      • In a kinetics run, you could add time and measure κ vs. time

      • In a titration, you could measure κ vs. volume or drops form keyboard or drop counter

      • In a P Chem experiment you may wish to measure molar conductivity vs. concentration of a weak acid to determine its Ka


    Microlab method2

    MicroLab method:

    • NOTE: conductivity “cell constants” are not actually constant over factors of tens of thousands of μS

      • Limit is about 2 orders of magnitude

    • Best technique is to calibrate with standard solutions that span the range of samples you expect

    • If an exceptionally wide range of conductance is needed, you may wish to use a second order fit to the data for better results, especially in the low ranges


    Sample calculation 1 determination of a cell constant

    Sample calculation 1: determination of a cell constant

    • You prepare standard NaCl solution to be exactly 2.000 g/L using your local DI water and dried reagent grade NaCl. This solution is reported in the literature to have a known conductivity of 3860 μS/cm at 25oC.

    • In your conductivity cell at 25oC, DI water has a conductance of 230 μS.

    • In your conductivity cell 25oC, your solution has a conductance of 4160 μS

    • What is the cell constant for your cell at 25oC?

      (see solution on next slide)


    Sample problem 1 solution

    Sample problem 1: solution

    • Compute net conductance L by subtracting water’s value from the measured value for the standard:

      L = (4160 – 230) μS = 3930 μS

    • Calculate the cell constant K

      K = κ/L = (3860μS/cm)/(3930μS)

      K = 0.982 /cm


    Sample problem 2 computing conductivity from a conductance measurement

    Sample problem 2: computing conductivity from a conductance measurement

    • A solution has a conductance of 3620 μS at 25oC in your conductivity cell.

      What is its conductivity?


    Sample problem 2 solution

    Sample problem 2: solution

    The cell constant K = 0.982/cm (from problem 1)

    The conductance L = 3620 μS

    The conductivity is

    κ= K x L =

    κ = 0.982 /cm x 3620 μS

    κ = 3560 μS/cm

    This can be converted to SI units

    κ = 3560 μS/cm x 100 cm/m x 10-6siemens/μS

    κ = 0.356 siemens/m (3 sig fig)


    Sample problem 3

    Sample problem 3:

    A 0.0100M KCl solution is found to have a conductivity of 1.410 mS/cm at 25oC.

    What is the molar conductivity of the KCl in the solution in the usual units of siemens.cm2/mol?


    Sample problem 3 solution

    Sample problem 3 solution:

    Λm = κ/c = κ/(1000M) (siemens.m2/mol)

    κ = [(1.410 mS/cm) x (10-3siemen/mS) x 102cm/m

    κ = 0.141 siemens/m

    Λm = κ/(1000M) = 0.141/(1000 x 0.01)

    = 0.0141 siemens.m2/mol

    Now convert Λm from SI into siemens.cm2/mol:

    Λm = 0.0141 siemens.m2/mol x (100 cm/m)2 =

    Λm = 141 siemens.cm2/mol


    Good luck

    Good luck!

    • And have fun!


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