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How do you synthesize 1,3-pentadiene from butanal? Butanal to 1,3-pentadiene

I have the (possible) last steps of bromination of 1-pentene at the allylic position and then an E1 reaction to give the final product. I don't understand how to get from butanal to 1-pentene though. Also if you know another way to do the synthesis then feel free to share.

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I believe one way would be to start with butanal participating in a Wittig reaction to form 1-pentene.

$\ce{CH3CH2CH2CHO + H2C=PPh3 -> CH3CH2CH2CH=CH2}$

Then allylic bromination, as you said.

$\ce{CH3CH2CH2CH=CH2 ->[{NBS}][{hv}] CH3CH2CHBrCH=CH2}$

Dehydrohalogenation with a hindered base like t-butoxide (to favor the elimination reaction) should give the diene. The only thing I'm not sure about is whether it would be E1 or E2. It isn't very hindered, but it is a secondary halide. With those factors, plus the alkoxide, I think it will be an E2 mechanism.

Let me know if I made a mistake somewhere.

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How about :

Step 1:

Add $CH_3MgX$ to butanal to get pentan-2-ol.

Step 2:

Dehydrate the alcohol to pent-2-ene

Step 3:

Add $Br_2$ to pent-2-ene to get 2,3-dibromopentane

Do a double elimination to get 1,3-pentadiene

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