Write the following reactions:
$1$. Complete combustion of ethyne in the presence of air.
$2$. Reaction of propyne with alkaline $KMnO_4$.

(N/A) $1$. Complete combustion of ethyne:
$HC \equiv CH + \frac{5}{2} O_2 \rightarrow 2CO_2 + H_2O + 1300 \ kJ$
$2$. Reaction of propyne with alkaline $KMnO_4$:
At $300 \ K$:
$CH_3C \equiv CH \xrightarrow{KMnO_4, Na_2CO_3, H_2O, 300 \ K} CH_3COCOOH$ (Pyruvic acid)
At $380 \ K$:
$CH_3C \equiv CH \xrightarrow{KMnO_4, Na_2CO_3, 380 \ K} CH_3COOH + CO_2$