The Mechanics Behind Measuring Electrical Conductivity of Solutions

Electrical conductivity of a solution refers to its ability to conduct electric current. The metric is used in several real-world applications including the monitoring of water supplies for purity, and when measuring the concentration of plant nutrients in a feed solution. It is also a component of some scientific tools like Fast Protein Liquid Chromatography (FPLC) where it is used to monitor the ionic strength of the mobile phase or buffer.  

Electrical conductivity occurs because of the presence of charged ions within a solution. Applying an electric potential across the solution causes the charged ions to migrate towards their respective oppositely-charged electrodes. As a result, the flow of ions mediates the passage of the electric current. Significantly, the conductivity level of the solution depends on a number of factors, the main ones being the concentration of ions in the solution as well as its temperature.

In this post, we investigate the units normally used to quantify this electrical phenomenon, how to actually measure the conductivity of solutions, and finally, its relationship to the TDS metric.

The Units of Electrical Conductivity

The standard unit of conductivity is the Siemens per metre (S/m). However, you will more likely encounter its fractional units, milliSiemens per centimetre (mS/cm) or microSiemens per centimetre (μS/cm). Importantly, it is not uncommon for these conductivity units to be simply referred to as 'milliSiemens' or 'microSiemens'. Although this is technically incorrect, it is generally tolerated in the name of efficiency. Therefore, when talking about the electrical conductivity of a solution, 'milliSiemens' and 'microSiemens' should be assumed to mean 'mS/cm' and 'μS/cm', respectively.

NB: Historically, the unit of electrical conductivity was the 'μmho/cm' instead of the 'μS/cm'. The 'mho' part of this historical unit was used since it represented the inverse of electrical resistance - cryptically, the unit of electrical resistance, the 'ohm', was spelled backwards to give rise to 'mho' . However, although one still finds it in some electronics texts, 'mho' has mostly been replaced by the newer Siemens unit.

Temperature

Since temperature has a profound effect on electrical conductivity, it too has to be taken into account when specifying the units of conductivity. In general, unless the temperature is specified, it should be assumed that all values for electrical conductivity are determined at 25ºC. 

Some Typical Conductivity Values of Common Solutions

When dealing with electrical conductivity, it is often helpful to have an idea of the electrical conductivity of some common solutions:

How is Electrical Conductivity of a Solution Measured?

Wheatstone Bridge Method

Traditionally, electrical conductivity has been measured by connecting the solution of interest to an electrical circuit called a Wheatstone Bridge. The configuration of the Wheatstone Bridge is shown below:

The Wheatstone Bridge

The unknown resistance R_x represents the the resistance of the solution. Resistance values R₁, R₂ and R₃ are known, and R₂ is adjustable. Using R₂ to adjust the circuit, the voltage V_G (traditionally measured with a galvanometer) is set to 0. At this point, we can then say that both legs of the Wheatstone Bridge have equal voltage ratios. Therefore,

 R₂/R₁ = R_x/R₃

and we can rearrange this to calculate what the resistance of the solution, R_x, is: 

R_x= R₃(R₂/R₁)

Due to the effect the surface area (A) of the electrodes and the distance (L) between them has on conductivity, we have to take them into account as well. As a result, we can calculate the resistivity (ρ; Rho) of the solution from its resistance R_x using the following equation:

ρ = R_x * A / L

Once we know ρ, we can then calculate the conductivity (σ; sigma) of the solution with:

σ = 1/ρ

...

How to Measure Conductivity using a Wheatstone Bridge

So how does one actually go about measuring electrical conductivity of a solution using a Wheatstone bridge?  The answer to that is outlined in the protocol below:  

NB: You may wonder whether it's absolutely necessary to initially balance the Wheatstone bridge (step 2) before introducing the solution into the circuit. For the sake of accuracy, the answer is yes. The main reason for this is that by balancing the bridge before measuring the solution, you nullify the effect of any potential error or resistance in the circuit unrelated to the solution itself. This includes any inherent resistance in the connecting wires, contacts, or other components. In addition, balancing the bridge beforehand, maximises its sensitivity to changes in the solution's resistance so even small changes will be detectable.

2-Electrode Method

Today, electrical measuring devices are sensitive enough to use a simple circular circuit to measure electrical conductivity. To this end, a voltage (V) is applied to the solution and the current (I) running through the solution is measured. By measuring the current at a known voltage, one is able to deduce the resistance (R_x) of an electrolyte solution using Ohm's law:

R_x = V/I

Knowing the resistance (R_x), the surface area of the electrodes (A) and the distance between the electrodes (L), one can work out the resistivity (ρ) of the solution using:

ρ = R_x * A / L

Note that it can be quite hard to get highly accurate dimensions for the electrode surface area (A) and the distance between them (L). Therefore, in practice, a constant (K) is generated by calibrating the apparatus with standard solutions of known conductivity where 

K = L / A

This is then used to calculate the resistivity (ρ) of the unknown solution: 

ρ = R / K

Once again, from the resistivity, the conductivity (σ) of the solution can be derived as before:

σ = 1/ρ

Note that alternating current (AC) is used in order to minimise the accumulation of ions at the electrodes which can lead to their corrosion and which can affect the final result. In addition, the electrodes are usually made of platinum or some other corrosion-resistant material to minimise this effect. To address this potential source of error even further, the 4-electrode method described next, uses separate electrodes to measure the voltage in the solution.

4-Electrode Method

The electrical conductivity-measuring equipment that one finds in laboratories today more often than not uses a 4-electrode method. As has been noted, this is an extension of the simple 2-electrode method described above. However, using four electrodes is superior to using two since the current is not generated in the voltage-measuring probes. Therefore, there is little-to-no ion accumulation and corrosion that could affect the conductivity readings. Once again, the electrodes are usually made of platinum or some other corrosion-resistant material, and are arranged such that a pair of outer electrodes enclose an inner set. Alternating current (AC) is applied to the outer pair of electrodes, while the induced potential or voltage between the inner pair is measured. With a known voltage and current, the resistance, resistivity, and finally, the conductivity of the solution can be calculated exactly as described above in the 2-electrode method.

Total Dissolved Solids (TDS)

Finally, a quick word about Total Dissolved Solids (TDS) and its relationship to conductivity. Conductivity is often used to provide an estimate of the total amount of substances that are dissolved in a solution, also known as TDS. That is because the TDS metric uses the more intuitive milligrams per litre (mg / L) or parts per million (ppm) units (NB: 1 mg/L = 1 ppm), so in some situations, it can be helpful to make the conversion. Indeed, TDS readouts are often used to determine the level of impurities in water samples, or the amount of nutrients in a plant feed.

Electrical Conductivity-to-TDS Conversion

So, all TDS meters work by first measuring the electrical conductivity (EC) of a solution and then internally converting it to a TDS value. However, as you might have guessed, different ions in a solution will influence conductivity differently. Consequently, different conversion factors have to be used for different types of solution. In addition, the EC to TDS conversion is not completely linear, so slightly different conversion factors have to be used depending on the solution's overall level of conductivity. Obviously, conversion factors cannot be established for every known type of solution. So conversion factors for only a few standard solutions have been determined over a range of conductivities. Therefore, to convert conductivity to TDS for your solution of interest, you just use the conversion factors for a standard solution that most resembles your experimental one. 

Some of the more common standard solutions are: 

Conversion factors and TDS values for some standard solutions

Data from ASTi