Uncertainty in analyte mass for samples containing small numbers of particles

A sampling equation was derived that relates the standard deviation in analyte mass to the number of particles in the sample, the fractions of the different types of particles in the mixture and the masses and analyte concentrations of the individual particles. The equation, which is applicable to samples containing any number of particles, was verified by sampling and analysis of two cereal grain mixtures for manganese, potassium, chlorine and magnesium, and by Monte Carlo computer simulation. Comparison of the sampling precision of analyte mass with the analytical measurement precision was also studied, and it was shown that use of the equation allows the calculation of the minimum number of particles required to hold the sampling relative standard deviation to that of the analytical measurement.