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Looking at the 2 hydrogens connected to the Carbon-carbon double bond, which hydrogen is more deshielded or shielded?

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Presumebly the one in β.

Here I report the ChemDraw prediction.

Prediction of ChemDraw

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To confirm that (that maybe is not necessary), you might run an HMBC experiment. You should be able to determine which hydrogen is closer to the carbonyl group. Probably the signal at 5.32 will couple with the carbon signal of the carbonyl group (around 170 ppm?)

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    $\begingroup$ HMBC experiments typically emphasise three-bond correlations - if anything I would expect the beta proton to show a crosspeak to the carbonyl carbon. Two-bond correlations are often absent or weak. Also, there's no peak at 5.32 ppm in the actual spectrum, it's only a crude prediction. $\endgroup$
    – orthocresol
    Nov 25, 2022 at 17:52

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