Step 1: Understanding the Concept
The hydrogen atoms of ethyne are weakly acidic because they sit on \(sp\) carbons (50 percent s-character).
Step 2: Reaction
\(\text{LiNH}_2\) is a strong base. The amide ion \(\text{NH}_2^{-}\) removes a proton from ethyne.
\(\text{HC}\equiv\text{CH}+\text{NH}_2^{-}\rightarrow\text{HC}\equiv\text{C}^{-}+\text{NH}_3\)
Step 3: Conclusion
The proton combines with the amide ion to give ammonia, so no \(\text{N}_2\), \(\text{H}_2\) or \(\text{O}_2\) is formed.
Final Answer:
The by-product (A) is ammonia gas.
\[ \boxed{\text{(C) }\text{NH}_3} \]