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

• 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

• 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

• 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 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 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 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

• 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

• 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

• 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

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)0.000 0.050.050 1050.100 2100.150 3150.200 4150.500 10201.000 19901.500 29302.000 3860

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

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 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 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• 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

• 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 KK = κ/L = (3860μS/cm)/(3930μS) K = 0.982 /cm

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: solutionThe 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/cmThis can be converted to SI units

κ = 3560 μS/cm x 100 cm/m x 10-6 siemens/μSκ = 0.356 siemens/m (3 sig fig)

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: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!

• And have fun!