Solution to the chemical uncertainty principle challenge

Abstract

This expression summarizes the relationship between both uncertainties relative and absolute (Fig. 1). One must remember that this expression describes the approximate trend, not the exact relationship. Nevertheless, the trend is obvious standard analytical practice cannot provide both low absolute uncertainty and low relative measurement uncertainty. The lower the absolute measurement uncertainty (error), the larger the relative measurement uncertainty and vice versa. Philosophically speaking, the very fact that the exponent in Eq. (1) is less than unity leads to an increase in the relative standard deviation as the amounts of analyte decreases. Mathematically this implies the existence of an “absolute zero” for analytical chemistry, a concentration at which reliable measurement is no longer practically possible. This level is reached at the relative measurement uncertainty of ∼66%. This is evident from the standard definition of the detection limit, γDL=3 s. Remember that u=2 s, therefore uR=2/3 at the classical detection limit (3 s). Combining the expressions uR=2/3 and uR≅0.020γ leads to: lg g ffi 10:1 or g ffi 1 10 10 0:1 ppb ð Þ