# Application of binomial distribution to interpret ^{31}P NMR for aqueous solution of alpha-dodecatungstophosphoric acid, H_{3}[PW_{12}O_{40}]

## In-Class Activity

Submitted by Mariusz Kozik, Canisius College31-P NMR spectrum of alpha-dodecatungstophosphoric acid is a combination of thirteen spectra, each spectrum representing the compound with a different number of ^{183}W 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 ^{183}W 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.

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Worksheet for students to guide them in interpreting the spectrum. | 148.8 KB |

In answering these questions, a student will

- apply binomial distribution to calculate probabilities for presence of various numbers of NMR active isotopes of tungsten in the species containing multiple tungsten atoms.
- use the calculated probabilities to interpret experimentally observed
^{31}P NMR spectrum for alpha-dodecatungstophosphoric acid.

None.

The spectrum was never published in the literature. Only ^{183}W NMR of this compound, 1:1 doublet, was published.

I do this in-class exercise in Modern Synthetic Method course after one class on multinuclear NMR. Students are given this problem with seven leading questions. I walk around the class and make sure that the teams (4-5 teams of 4 students per team) are on track. The class ends with teams reporting on the blackboard their predicted intensities and comparing their answers with other teams’ answers. Completing this asctivity requires around 50 minutes.

The power point listed as the web resource has some information on the NMR satellites when there is more than one NMR active nucleus with less than 100% abundance. This information is near the very end of the ppt. It discusses coupling with two Pt atoms.

I found no web resource on using binomial distribution in NMR spectroscopy for interpreting satellites.

## Comments

## n+1? I hope you teach them