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# Conductivity

Conductivity is the ability of a solution to pass current. The current flowing is proportional to the number of ions present in the solution. Despite the fact that the measuring of conductivity is non-specific, the technique is widely used in analytical chemistry, especially in the characterization of water purity. Conductivity measurement is also used to determine the concentration of chemicals because it gives a well-defined, though not always linear, conductance-concentration plot over a wide concentration range. It is a rapid and inexpensive way of determining the ionic strength of a solution.In Fig. 1, two plates of a given material are placed in a solution. The geometry is given by the lenght L of the liquid column between the plates and the cross sectional area A of the liquid column. If an AC voltage E is connected across the two plates (called electrodes), ions will move between the electrodes, and an electric current I will start to flow.

*Fig. 1: Setup to measure conductivity of a solution*

Conductivity is denoted by the symbol κ (kappa) and bears the unit Siemens per centimeter S / cm.

*Fig. 2: Conductivity versus Resistivity*

For ultrapure water applications the reciprocal value of conductivity, called resistivity is common. Resistivity is expressed as Ohm cm (Ω cm). Some corresponding values are shown in Fig. 2.

### The cell constant

Condutivity is measured by a conductivity cell. Assuming that the mechanical properties of the cell will not change over the entire temperature range, the term L/A will remain constant. This term can be replaced by c, the cell constant, expressed in cm^{-1}.

In a cell using 1 cm squares of platinum, 1 cm apart, the cell constant is 1.0 cm

^{-1}and the conductance reading in µS is numerically equal to the conductivity reading in µS / cm. For low conductivity solutions, the electrodes can be placed closer together (reducing L) to give cell constants of 0.1 cm

^{-1 }or 0.01 cm

^{-1}. This raises the conductance between the plates and makes it easier for the electronic circuitry to obtain a result. Similarly, for high conductivity solutions, L can be increased to give a cell constant of 10.0 or more.

Alternative sensors have been developed to overcome the problems associated with traditional cells : 4-electrode conductivity sensors consist of two current and two voltage electrodes. Polarization occurs only at the current electrodes while a voltage drop is measured between the voltage electrodes where polarization has no effect. The advantage of such a sensor are as follows:

- No polarization
- Wide measuring range with a single cell constant
- Suitable sensor dimensions.

The sensor is designed in a way that part of the liquid media forms a closed conductive current path passing trough the toroids.

The primary coil is activated with a sinusoidal alternating voltage creating a magnetic field. In liquids which conduct electricity, this causes a current flow proportional to the conductivity of the sample solution. The liquid loop acts at the same time as the primary winding of the secondary coil where the magnetic field induces a voltage. This current is rectified to the correct phase and amplified. An inductive sensor has the following advantages:

- No polarization
- Insensitive to contamination, fouling or film formation on the sensor surface
- Total galvanic separation of the measuring components from the process media.

### Temperature effects

Ion mobility (and therefore conductivity) in a liquid solution increases as the temperature increases. The change per ºC is expressed by the temperature coefficient α. Once this coefficient is determined for a specific solution, the conductivity value can be calculated at any temperature:Where:

κ

_{†}: Conductivity at T

_{†}

κ

_{0}: Conductivity at T

_{0}

α

_{0}: Temperature coefficient at T

_{0}

T

_{†}: Measured temperature

T

_{0}: Reference temperature

In ultrapure water, the change in conductivity by increasing the temperature is much greater than in high-conductivity solutions. Fig. 3 shows this dependency over a temperature range from 0ºC to 100ºC. The temperature coefficient changes from 7.3%/ºC at 0ºC to 2.3%/ºC at 100ºC. It is obvious that the function is not linear.

*Fig. 3: Resistivity of ultrapure water at various temperatures*

The temperature-dependency, which also depends on the concentration, is different for each component. Usually the temperature coefficient varies between 1% and 6% per ºC.

For natural water and most salt solutions, the temperature coefficient is approx. 2 %/ºC. For strong acids, the temperature coefficient is approx. 1.9%/ºC. For strong bases, the temperature coefficient is approx. 1.6%/ºC.

### Temperature compensation

To compare measurements made at different temperatures, they must be referenced to a standard temperature. Nowadays, the standard reference temperature is 25ºC. Temperature compensation is the process in wich the conductivity from a given temperature back to the reference temperature is calculated. For most diluted salt solutions, conductivity changes linearly with temperature. Therefore, a linear relation between κ and † can be defined:Where:

κ

_{25}: Conductivity at 25 ºC

κ

_{†}: Conductivity at temperature T

α: Temperature coefficient

T: Temperature

Unfortunately, some solutions do not have a linear relation between conductivity and temperature. These relations require polynomial equations in order to arrive at accurate results. Today’s microprocessor-driven analyzers easily manage customers’ requirements.

### USP <645>

This guideline of USP sets a standard for the quality assessment of pure water based on measurement of the electrolytic conductivity. On the one hand, this method means labor-saving for the pharmaceuticals industry, one the other hand, it places concrete demands on the conductivity technique used. The guideline was implemented in the pharmaceuticals industry in November 1996 and basically replaced a series of chemical test methods to determine water quality for WFI and Purified Water (PW). Described is a three-stage test with stage one allowing online, non-temperature compensated conductivity measurements. Stage two and three describe off-line conductivity measurements in case test one fails. The table below (Fig. 4) shows the maximum allowance for online conductivity values according to stage 1.*Fig. 4: Maximum conductivity limits for online conductivity measurements*

Specific demands for the measurement equipment (sensor and transmitter) are described in the guideline and in Fig. 5.

Sensors must show a cell constant accuracy of less than 2%, while several specifications needs to be fulfilled by the transmitter.

*Fig. 5: Specific demands for measurement equipment*