To determine which compound is not soluble in water, we need to examine the solubility rules for each of the given compounds: NaCl, [tex]\( CaCl_2 \)[/tex], [tex]\( FeCl_3 \)[/tex], [tex]\( NH_4Cl \)[/tex], and [tex]\( PbCl_2 \)[/tex].
1. Sodium Chloride (NaCl): Sodium chloride is a common salt that is highly soluble in water. According to solubility rules, all salts containing alkali metal cations (such as sodium) and the ammonium ion ([tex]\( NH_4^+ \)[/tex]) are soluble in water.
2. Calcium Chloride ([tex]\( CaCl_2 \)[/tex]): Calcium chloride is also highly soluble in water. The solubility rules indicate that most chlorides (Cl⁻) are soluble, with very few exceptions.
3. Ferric Chloride ([tex]\( FeCl_3 \)[/tex]): Iron(III) chloride is soluble in water. Again, according to solubility rules, most chlorides are soluble, and [tex]\( FeCl_3 \)[/tex] is not an exception.
4. Ammonium Chloride ([tex]\( NH_4Cl \)[/tex]): This compound is also soluble in water. The ammonium ion ([tex]\( NH_4^+ \)[/tex]) contributes to the solubility, as all ammonium salts are soluble.
5. Lead(II) Chloride ([tex]\( PbCl_2 \)[/tex]): This is an exception to the general rule that most chlorides are soluble in water. [tex]\( PbCl_2 \)[/tex] is only slightly soluble in cold water and more soluble in hot water. This limited solubility places it in the category of compounds that are generally considered insoluble in water under standard conditions.
Based on the solubility rules and comparison, the compound that is not soluble in water is:
[tex]\[ \text{Lead(II) chloride (PbCl}_2) \][/tex]
So, the answer is: [tex]\( PbCl_2 \)[/tex].
