Acid protonates one methoxy group of 2,2-Dimethoxypropane. methanol departure gives the oxocarbenium species , which is captured by one diol oxygen. After proton transfer, protonation and loss of the remaining methoxy group generate a second oxocarbenium center. Intramolecular attack by the other diol oxygen closes the five-membered ring; deprotonation regenerates acid. The net transacetalization exchanges two methoxy groups for the two diol oxygens, releasing two methanol molecules.
The two starred carbon centers retain their original configurations, and the two carbon side chains on the acetonide are trans. No C–O bond at either original stereocenter is broken; reaction takes place at the reagent-derived CMe acetal carbon. The apparent change in wedge/dash presentation comes from redrawing the backbone into the five-membered ring, not inversion at a starred center. In the planar pentagon used in the diagram, draw the alkynyl-bearing side chain behind and the side chain in front. The unstarred methyl-bearing center also retains its configuration. The acetal carbon itself is not stereogenic because its two methyl substituents are identical.

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