You have three solutions, A, B, and C, each of which are believed to be one of the following: calcium hydroxide, potassium sulfate, and sodium chloride. Combining B and C results in the formation of a precipitate, but neither solution forms a precipitate with A. Also, adding iron (II) nitrate to each of the solutions only produces a precipitate with C.

You need to know solubilities for this.

B+C = ppt which means B or C must be Ca(OH)2 or K2SO4 (The ppt is CaSO4)

This means A definitely is NaCl.

Adding Fe produces a ppt with C so C mut be Ca(OH)2 (Fe(OH)2 is the ppt) and means B must be K2SO4.

To identify the solutions A, B, and C, we can use some chemical reactions and solubility rules.

1. Test for Precipitation:
- Take solutions B and C separately and mix them together.
- If a precipitate forms, it means that the two solutions contain ions that react to form an insoluble compound.

Observation:
- When B and C are mixed, a precipitate forms.

Conclusion:
- Solution B and C contain ions that react to form an insoluble compound.

2. Test for No Precipitation:
- Take solution A and mix it separately with solutions B and C.
- If no precipitate forms, it means that the solution A does not contain ions that react to form an insoluble compound.

Observation:
- There is no precipitate formed when either solution B or solution C is mixed with solution A.

Conclusion:
- Solution A does not contain ions that react to form an insoluble compound.

3. Test for Precipitation with iron (II) nitrate:
- Take iron (II) nitrate and mix it separately with each of the solutions A, B, and C.
- If a precipitate forms, it means that the iron (II) ions react with certain ions present in the solution to form an insoluble compound.

Observation:
- Only solution C forms a precipitate when mixed with iron (II) nitrate.

Conclusion:
- Solution C contains ions that react with iron (II) nitrate to form an insoluble compound.

Based on the above observations and conclusions:

- Solution A does not form a precipitate with either of the solutions B or C.
- Solution B and C produce a precipitate when mixed together, suggesting that they contain ions that react to form an insoluble compound.
- Solution C forms a precipitate when mixed with iron (II) nitrate, indicating the presence of ions that react with iron (II) nitrate to form an insoluble compound.

By comparing these observations to the solubility rules, we can determine the identity of each solution:

- Solution A: Does not form a precipitate with either B or C, so it is likely calcium hydroxide (Ca(OH)2). Calcium compounds are usually soluble, and hydroxide compounds are typically insoluble except for those of Group 1 metals and a few others.
- Solution B: Forms a precipitate with C, but not with A. This suggests that it contains an ion that reacts with an ion in solution C to form an insoluble compound. Given the options, it is likely potassium sulfate (K2SO4). Sulfates are typically soluble, but potassium sulfate is an exception and forms an insoluble compound (precipitate) when mixed with certain ions.
- Solution C: Forms a precipitate with iron (II) nitrate, indicating the presence of an ion that reacts with iron (II) ions to form an insoluble compound. Given the options, it is likely sodium chloride (NaCl). Chlorides are typically soluble, but silver chloride (AgCl) is an exception and forms an insoluble compound (precipitate) when mixed with silver ions.

So, the identities of the solutions are:
- Solution A: Calcium hydroxide (Ca(OH)2)
- Solution B: Potassium sulfate (K2SO4)
- Solution C: Sodium chloride (NaCl)