Centre for Statistical & Survey Methodology Working Paper Series

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It is of interest to understand how phosphorus cycles through organic pools in the environment. Much of the cycling phosphorus is in the form of orthophosphates (species derived from H3PO4) which are thus an important part of the global phosphorus cycle. An understanding of the flows of orthophosphate species is important in understanding the loss of phosphorus from soil and the environmental effects of using phosphorus in fertilisers. A methodology has been proposed for tracking orthophosphate flows using isotopomers of this substance. Using this methodology in practice requires the application of multinomial probabilities. This article describes the main chemistry concepts involved, derives the expected distribution of molecular weights for two models describing how elements mix in the formation of orthophosphate, and compares the models to observed data from two experiments. A simple random mixing model agrees reasonably well with the available data.