Provide the chemical reactions for the following conversions:
$(1)$ Propyne from ethyne
$(2)$ $2-$butyne and $1-$butyne from ethyne

(N/A) $(1)$ Synthesis of propyne from ethyne:
$HC \equiv CH$ $\xrightarrow{NaNH_2 / NH_3(l)} HC \equiv C^- Na^+$ $\xrightarrow{+CH_3Cl} HC \equiv C-CH_3$ (Propyne)
$(2)$ Synthesis of $1-$butyne and $2-$butyne from ethyne:
$HC \equiv CH$ $\xrightarrow{NaNH_2} HC \equiv C^- Na^+$ $\xrightarrow{+CH_3CH_2Cl} HC \equiv C-CH_2CH_3$ ($1-$butyne)
$HC \equiv CH$ $\xrightarrow{2NaNH_2} Na^+ - C \equiv C^- Na^+$ $\xrightarrow{+2CH_3Cl} CH_3-C \equiv C-CH_3$ ($2-$butyne)