Application of binomial distribution to interpret 31P NMR for aqueous solution of alpha-dodecatungstophosphoric acid, H3[PW12O40]
31-P NMR spectrum of alpha-dodecatungstophosphoric acid is a combination of thirteen spectra, each spectrum representing the compound with a different number of 183W isotopes per molecule. In order to fully interpret the spectrum one needs to apply binomial distribution to calculate the mole fractions of the molecules with various numbers of 183W isotopes.
This LO requires an understanding of the satellites concept in NMR spectroscopy, originating from coupling with nuclei whose NMR active isotopes are not 100% abundant.