Combination Ion-Selective Electrodes consist of an ion-specific (sensing) half-cell and a reference half-cell. The ion-specific half-cell produces a potential that is measured against the reference half-cell depending on the activity of the target ion in the measured sample. The ion activity and the potential reading change as the target ion concentration of the sample changes. The relationship between the potential measured with the ISE and the ion activity, and thereby the ion concentration in the sample, is described by the Nernst equation:
- E = measured potential (mV) between the ion-selective and the reference electrode
- Eo = standard potential (mV) between the ion-selective and reference electrodes
- R = universal gas constant (R = 8.314 J mol-1 K-1)
- T = temperature in K (Kelvin), with T (K) = 273.15 + t °C where t is the temperature of the measured solution in °C.
- F = Faraday constant (96485 C mol-1)
- n = valence of the ion
- C = concentration of ion to be measured
- Co = detection limit
Since R and F are constant, they will not change. The electrical charge of the ion (valence) to be measured is also known. Therefore, this equation can be simplified as:
E = Eo –S• log(C + Co)
where is the ideal slope of the ISE.
The following table describes ideal behavior:
|Potassium (K+), Ammonium (NH4+)
|Nitrate (NO3-), Chloride (Cl-)
Assuming C0 is near zero, the equation can be rewritten as:
C = 10˄[(E – Eo) / S]
allowing for the calculation of the ion concentration.
It is very important to note that this table reflects ideal behavior. Ion-selective electrodes have slopes that are typically lower than ideal. It is generally accepted that an ISE slope from 88–101% of ideal is allowable. The slope (S) is an indicator of ISE performance. If the slope changes significantly over time, it may indicate that it is necessary to replace the ISE sensor tip.
Potential vs. Concentration
To measure the mV readings from an aqueous sample, calibration is not required. To convert mV readings to concentration (mg/L or ppm), the software uses a modified version of the Nernst Equation:
C = 10˄[(E – Eo) / Sm]
C = concentration of ion to be measured (mg/L or ppm)
E = measured potential of sample (mV)
Eo = measured potential (mV) at a C = 1 mg/L K+ concentration
Sm = measured electrode slope in mV/decade
The value of Sm, the measured electrode slope, is determined by measuring the potential of two standard solutions, and solving the equation below:
Sm = – [(Low Standard – High Standard) / # of decades*]
*A decade is defined as the factor of the difference between the two standard solutions. For example, the difference between a 1mg/L standard and a 100 mg/L standard is 2 decades (a factor of 100 difference, or 1 × 102).
Example Calculation, converting mV to mg/L
For this example, the measured quantities are shown in the chart below:
|1 mg/L K+ standard
|10 mg/L K+ standard
|1000 mg/L K+ standard
C = 10^[(138 mV – (–8 mV))/ 56 mV/decade] = 405 mg/L K+