To determine the empirical formula of a compound given the ratio of its elements, follow these steps:
1. Identify the ratio: The ratio given is [tex]\( 1 \, \text{C} : 2 \, \text{S} \)[/tex].
2. Write the empirical formula: The empirical formula represents the simplest whole-number ratio of atoms in a compound.
Since carbon (C) and sulfur (S) are in the ratio 1:2, it means there is one atom of carbon for every two atoms of sulfur. Therefore, the empirical formula of the compound will directly reflect this ratio.
By looking at the given options:
1. [tex]\( C_2S \)[/tex]: This implies 2 atoms of carbon for every 1 atom of sulfur, which is not correct as per the given ratio.
2. [tex]\( CS_2 \)[/tex]: This shows 1 atom of carbon for every 2 atoms of sulfur, which matches the given ratio perfectly.
3. [tex]\( C_2S_2 \)[/tex]: This implies 2 atoms of carbon for every 2 atoms of sulfur, which simplifies to a 1:1 ratio and does not match the given ratio.
4. [tex]\( CS \)[/tex]: This implies 1 atom of carbon for every 1 atom of sulfur, which also does not match the given ratio.
Hence, the correct empirical formula is [tex]\(\textbf{CS}_2\)[/tex], corresponding to option [tex]\(2\)[/tex].
