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Synthesis of 1-pentanone

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Using organic molecules with only 3 carbons or less, and any other reagents, show how to synthesize the product shown in good yield. SHow all steps, the reagents used in each step, and intermediate products. Mechanisms do not need to be shown.

Please see the attached document for the diagram.

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The synthesis of 1-pentanone from 3 carbons or less is shown.

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