Errors Associated with Beers Law Relationships

All spectrometric measurements are subject to indeterminate (random) error, which will affect the accuracy and precision of the concentrations determined using spectrometric methods. A very common source of random error in spectrometric analysis is instrumental noise. Noise can be due to instability in the light source of the instrument, instability in the detector, and variation in placement of the sample in the light path and is often a combination of all these sources of noise and more. Because these errors are random, they cannot be eliminated. Errors in measurement of radiation intensity lead directly to errors in measurement of concentration when using calibration curves and Beer s law. 

We can evaluate the impact of indeterminate error due to instrumental noise on the information obtained from transmittance measurements. The following discussion applies to UVWIS spectrometers operated in regions where the light source intensity is low or the detector sensitivity is low and to IR spectrometers where noise in the thermal detector is significant. 

The value of AT can be estimated from a large number (n 20) of replicate measurements of the same solution. If we assume that we have a constant error of 1% in the measurement of T, or AT = 0.01, the relative error in concentration can be calculated using Equation 2.15. Table 2.9 presents the 

Because the quantity (A77A log c) is the slope of the curve, the relative analysis error per 1% transmittance error at any point on the curve is equal to 230 divided by the slope at that point. The slope can be determined by constructing a tangent to the curve at the desired concentration. The difference in y for a 10-fold difference in x is calculated. This value, divided into 230, is the percent relative analysis error per 1% transmittance error. For example, the slope between the two points 

Transmittance T, where T = l/l Ratio of light intensity after passing through sample, /, to light intensity before passing through sample, 

---