Experimental errors

In relation to stability constant determination there are some considerations over and above the usual chemical ones. Chief amongst these is the control of experimental error. The accuracy and precision of calculated stability constants depend on the magnitude of systematic and random errors respectively.

Good accuracy requires that systematic errors be reduced as far as possible. The use of analytical grade reagents will reduce errors due to purity of reagents such as acid or alkali and the salt used for ionic background. Errors in temperature control are systematic errors. Electrode calibration error is also a source of systematic error, of particular importance when comparing duplicate titration curves.

Good precision requires that random errors be reduced as far as possible. All instrumental measurements are subject to random error. The magnitude of this error is instrument specific and, in the case of spectrophotometric measurements is also dependent on the magnitude of the measured quantity.

The objective of the stability constant refinement is to calculate values that correspond to experimental observations within experimental error. This means that estimates are needed of the random errors present in the experimental measurements.


Two error estimates are required by Hyperquad for potentiometric titration data.


A potential source of systematic error is small differences of baseline between different spectra. In order to minimize baseline errors it is preferable that neither sample nor reference cell should be moved between measurements of spectra. In practice this means either using a flow-cell or a fibre-optic probe or building a titration cell for a particular spectrophotometer. If measurements are to be made in alkaline solutions then the necessity of excluding atmospheric CO2 indicates that a closed titration system must be used.

Baseline error is also affected by whether the spectrophotometer is a single- or double-beam device. Instruments based on diode-array detectors are usually single-beam devices, so the background has to be measured on the same cell as the sample spectra.

The type of random error depends principally on the nature of the detector. Older instruments used a photomultiplier detector. The error of this type of detector increases with the intensity of the light falling on it. In Hyperquad there is a module for determining an absorbance error function which is based on the use of repeated scans of a standard spectrum.

In the instance shown below the data were obtained with an instrument that has a photomultiplier detector, using a holmium glass filter as sample. There is a general increase in error as absorbance increases but the trend is irregular because of correlation of errors between absorbance values. They appear to belong to different sets according to whether absorbance is increasing or decreasing.

Modern instruments use semiconductor detectors such as a diode array or charge-coupled detector (CCD). The error associated with these detectors tends to be constant and independent of wavelength. Here is an example from a diode-array spectrometer, also using the holmium filter. The error is virtually constant.


HypNmr works with chemical shift values that change with the position of equilibrium. An error must be supplied for each measured shift, though for a given type of nucleus the values will be the same. Fast exchange is assumed so line width should not be an important factor in determining error.

Contents > Experimental: Errors | Potentiometry | Spectrophotometry | NMR