Step 1: Understanding the Chemistry of Lanthanoids:
The lanthanoids (Ln) are a series of elements in the f-block. Their most common and most stable oxidation state is +3. This is due to the initial loss of the two 6s electrons, followed by the loss of one 5d or 4f electron, leading to a stable Ln\(^{3+}\) ion.
Step 2: Predicting the Formula of Lanthanoid Sulphide:
Sulphide is the ion of sulfur, which is in Group 16 of the periodic table. To achieve a stable octet, sulfur typically gains two electrons, forming the sulphide ion, S\(^{2-}\).
To form a neutral ionic compound, the total positive charge must balance the total negative charge.
Lanthanoid ion: Ln\(^{3+}\)
Sulphide ion: S\(^{2-}\)
We can use the "criss-cross" method to find the formula. The magnitude of the charge on the cation becomes the subscript for the anion, and vice-versa.
\[ \text{Ln}^{3+} \quad \text{S}^{2-} \quad \rightarrow \quad \text{Ln}_2 \text{S}_3 \]
Let's check the charges: (2 \(\times\) (+3)) + (3 \(\times\) (-2)) = +6 - 6 = 0. The compound is neutral.
Step 3: Final Answer:
Given that the most stable oxidation state of lanthanoids is +3, they react with sulfur (which forms the S\(^{2-}\) ion) to form sulphides of the general formula Ln\(_2\)S\(_3\).