Ketones react with sodium acetylide (the sodium salt of acetylene, $\left.\mathrm{Na}^{+-}: \mathrm{C} \equiv \mathrm{CH}\right)$ to give alcohols. For example, the reaction of sodium acetylide with 2 -butanone yields 3 -methyl-1-pentyn-3-ol:
(a) Is the product chiral?
(b) Assuming that the reaction takes place with equal likelihood from both $R e$ and $S i$ faces of the carbonyl group, is the product optically active? Explain.