Step 1: Understand Negatively Charged Sols
A negatively charged sol is a colloidal dispersion where the dispersed particles carry a negative charge. This typically occurs when the dispersed phase consists of substances that can gain electrons or form negatively charged species.
Step 2: Analyze Each Option
Option (1): $ \text{TiO}_2 $
$ \text{TiO}_2 $ (titanium dioxide) is a neutral oxide and does not inherently form negatively charged sols.
Not a negatively charged sol.
Option (2): $ \text{Al}_2\text{O}_3 \cdot x\text{H}_2\text{O} $
$ \text{Al}_2\text{O}_3 \cdot x\text{H}_2\text{O} $ (aluminum oxide hydrate) is a neutral oxide and does not inherently form negatively charged sols.
Not a negatively charged sol.
Option (3): $ \text{As}_2\text{S}_3 $
$ \text{As}_2\text{S}_3 $ (arsenic sulfide) is a compound that can form negatively charged sols. When dissolved in water, it dissociates into negatively charged particles due to the presence of sulfur ($ \text{S}^{2-} $), making it a negatively charged sol.
This is a negatively charged sol.
Option (4): Methylene blue
Methylene blue is a cationic dye, meaning it carries a positive charge. It forms positively charged sols, not negatively charged ones.
Not a negatively charged sol.
Step 3: Identify the Correct Option
From the analysis, Option (3) ($ \text{As}_2\text{S}_3 $) is the only example of a negatively charged sol.