Alexander M.Nemirovsky (


Method of calibration curve is the simplest from ionometric methods of the analysis. Procedure of analysis contains 2 stages: calibration of the electrodes and measuring of samples.

Calibration consist in measuring of electric potential of ion-selective electrode (E) relative reference electrode in standart solutions. Measured data must be use for construction of graph. Graph's shape is straight line in the coordinates E of pX:

E = B - S pX,

where E is electric potential between ion-selective electrode and reference electrode;

S is slope of line;

B is constant.


pX is accepted unit for the concentration in ionometric measuring and equal to pX = -lg a, where "a" is activity concentration of ion. For example, 0,0001 mol/L of fluoride in water solution equal the 4 in pF unit.
This function is Nernst equation, but only in other style. The slope of curve can be equal to 59,16 mV (at 25 0C) for monovalent ions and 29,58 mV for divalent ions. This values of slope is theoretical. The practical values have some deviation of theoretical. Big deviations testify about fault in the measuring.

The analysis consist in measuring of sample and calculation of sought concentration. Since the calibration graph is a straight line, find the concentration of easily. But linearity of graph have a range. Use of the calibration outside of a linearity range is not recommended. For using non-linear area, you must have knowledge about causes of this non-linearity for control all the side effects.
The method of calibration curve require the same conditions for calibration and analysis. Constancy of the temperature and the ionic strength is main of the conditions. Various conditions make the bigger error.

Nature of the error depends on units of the measurement. For pX unit the error is absolute. It is calculated as follows

ΔpX = ΔE/S ,

where ΔE is absolute error of measurement of electric potential.


The error is relative for measurement in g/L, mol/L and other such units:

δ = 2.3 ΔE/S 100%


If sensibility of instrumentation is 0,5mV, the error is equal 0,09 pX for monovalent ions. The error is 1,9% for measurement of the concentrations in traditional units. The error for divalent ions will be 2 times more.

There are rules which optimise procedure of the analysis and decrease an error!

The stability of electric potential makes the big impact on an error. The majority of electrodes do not have absolutely stable electrical potential . In this connection there is a question: during what moment of time the potential can be considered true? Potential can be considered true just after achieving the desired drift. The magnitude of the drift potential may be different, but the measurements for drift more than 0,5 - 1 mV/min is not recommended.

Is not recommended to measure the concentration of ions outside the calibration curve because can be used non-linear area of calibration curve. This causes greater error of the measurement. In this connection necessary to do calibration again. The exception of a rule makes glass ph electrode. Area of linearity for its calibration is very high.