When we analyze the solubility of the given compounds, we need to rank them from the most soluble to the least soluble. The compounds provided are [tex]$CoCl_2$[/tex], [tex]$KMnO_4$[/tex], [tex]$Co(NO_3)_2$[/tex], and [tex]$AuCl_3$[/tex].
After carefully evaluating their solubility properties, we can categorize them as follows:
1. Most Soluble:
- [tex]$KMnO_4$[/tex], Potassium permanganate, is known for its high solubility in water. It dissociates completely into potassium ions (K⁺) and permanganate ions (MnO₄⁻).
2. Second Most Soluble:
- [tex]$Co(NO_3)_2$[/tex], Cobalt(II) nitrate, also exhibits high solubility in water. The nitrate ion (NO₃⁻) contributes to the solubility of this salt when dissolved in water.
3. Third Most Soluble:
- [tex]$CoCl_2$[/tex], Cobalt(II) chloride, is soluble in water but not as highly as potassium permanganate or cobalt(II) nitrate. It dissociates into cobalt ions (Co²⁺) and chloride ions (Cl⁻).
4. Least Soluble:
- [tex]$AuCl_3$[/tex], Gold(III) chloride, is less soluble in water compared to the other compounds listed. Its solubility properties make it the least soluble among these options.
Hence, when ranking these compounds from most to least soluble based on their solubility in water:
1. [tex]$KMnO_4$[/tex]
2. [tex]$Co(NO_3)_2$[/tex]
3. [tex]$CoCl_2$[/tex]
4. [tex]$AuCl_3$[/tex]
Therefore, the most soluble compound is [tex]\( KMnO_4 \)[/tex] and the least soluble compound is [tex]\( AuCl_3 \)[/tex].
