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Solution conductivity

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

- 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

- 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

- 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

- 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

- 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.

- 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

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

- 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

- Defined as the inverse of the resistivity

- 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

- 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

- 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

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

- 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.

- Add sensor (conductivity)

- 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

- 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

- 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)

- 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

- A solution has a conductance of 3620 μS at 25oC in your conductivity cell.
What is its conductivity?

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)

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?

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

- And have fun!