Step 1: Reaction of lanthanoids with carbon.
When lanthanoids (such as Lanthanum, \(Ln\)) react with carbon at elevated temperatures, they form carbide compounds. The general product of this reaction is a lanthanum carbide with the formula LaC\(_2\), where lanthanum is bonded to two carbon atoms.
Step 2: Analyze the options.
- LaC\(_2\): This is the correct compound formed by the reaction of lanthanum with carbon.
- LaC\(_3\): This is incorrect because lanthanum typically forms LaC\(_2\) and not LaC\(_3\).
- LaC\(_2\)Cl: This is incorrect as it involves a chlorine atom, which is not formed in this reaction.
- LaCl\(_3\): This is incorrect because it represents a lanthanum chloride, not a carbide.
Step 3: Final Answer.
Thus, the correct answer is option \((1)\) LaC\(_2\).