Step 1: Understanding the Reaction.
In the extraction of iron from the blast furnace, the formation of slag occurs at high temperatures. Slag is a byproduct formed when calcium oxide (CaO) reacts with silica (SiO\(_2\)) to form calcium silicate (CaSiO\(_3\)), which is a type of slag. This reaction occurs in the zone of slag formation.
Step 2: Analyzing the options.
(A) C + \(\frac{1}{2}\) O\(_2\) \(\rightarrow\) CO: Incorrect. This is the reaction of carbon with oxygen to form carbon monoxide, which happens in the combustion zone, not in the slag formation zone.
(B) CaO + SiO\(_2\) \(\rightarrow\) CaSiO\(_3\): Correct. This is the reaction that forms slag during the extraction of iron in the blast furnace.
(C) Fe\(_2\)O\(_3\) + 3CO \(\rightarrow\) 2Fe + 3CO\(_2\): Incorrect. This reaction occurs in the reduction zone of the blast furnace, where iron oxide is reduced to iron.
(D) Fe\(_2\)O\(_3\) + 3C \(\rightarrow\) 2Fe + 3CO: Incorrect. This reaction is also part of the reduction zone but is not associated with slag formation.
Step 3: Conclusion.
The correct reaction for slag formation is (B) CaO + SiO\(_2\) \(\rightarrow\) CaSiO\(_3\).