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How do I convert $\ce{CH3CH2OH}$ (ethanol) to $\ce{CH3CH2C#CH}$ (but-1-yne) ?

I'm not too good with reaction mechanisms and conversions are beyond me.

My Attempt:

I've searched through a couple of textbooks and notes and I don't see any direct way to do the reaction.

I think I can use thionyl chloride to to convert from alcohol to chloroalkane: $$\ce{CH3CH2OH + SOCl2 -> CH3CH2Cl + HCl + SO_2\uparrow}$$ The $\ce{SO2}$ escapes but I'm not sure how I can get rid of the $\ce{HCl}$.

Assuming that I do get rid of it somehow, I can take the resulting chloroalkane and add an alkynyl group to it hence forming the required higher alkane. $$\ce{CH3CH2Cl + C2HNa + NaCl -> CH3CH2C#CH + \dots}$$

Again, the mechanism of these reactions elude me. I've only figured out the above from randomly stated properties of reagents. A detailed method of the conversion would be helpful.

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The first reaction is the conversion of the alcohol to an alkyl chloride using thionyl chloride. The mechanism of the reaction starts with nucleophilic attack of the alcohol oxygen on sulphur, followed by displacement of $\ce{Cl-}$. Chloride then substitutes the alkyl chlorosulfite group in an $\ce{S_{N}2}$ reaction, and the latter decomposes into $\ce{SO2}$ and $\ce{HCl}$.

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(Image source)

In the second reaction, chloroethane is alkylated with sodium hydrogen acetylide to yield the desired product.

$$\ce{C2H5-Cl + HC#C^{-} ->~ C2H5-C#CH + Cl-}$$

This is a simple $\ce{S_{N}2}$ reaction, in which $\ce{Cl-}$ is substituted by $\ce{HC#C^{-}}$. Acetylide salts of alkali metals can be prepared by deprotonation of ethyne with a strong base, for example, with butyllithium in THF or sodium amide, which can be generated in situ by dissolving sodium metal in liquid ammonia.

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