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the question is,
The two square planar isomers of $\ce{Pt[BrCl(PR_{3})2]}$ have a different $\ce{^{31}P}$-nmr spectra. One shows single group of lines, the other shows two distinct resonances, each one being similar to the single resonance region of the first one. Which isomer is cis and which is trans? Thanks.

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Look at the two structures drawn below

enter image description here

In the trans-isomer each phosphorous atom is in the exact same chemical environment. Each one has a chlorine on one side, a bromine on the other side and a phosphorous diagonally across. Therefore only one signal is observed for the phosphorous.

In the cis-isomer, each phosphorous is in a different chemical environment. One phosphorous has a chlorine diagonally across from it, the other has a bromine diagonally across from it. In this case we observe two phosphorous signals, one for each of the two different phosphorous environments.

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Chemical shifts and multiplicity are always controlled by:

Who sees what?

If two centres have the same environment/neighbours or are related by a symmetry operation, they will have identical shifts.

Here, the phosphor atoms in the trans isomer both "see" the same and appear as a single set of lines.

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