How do these react? Some may have no reaction.

a. aqueous chromium(III) nitrate plus magnesium metal

b. aqueous lithium sulfate plus aqueous barium chloride

c. solid lead metal plus aqueous potassium chloride

d. aqueous lithium fluoride with aqueous ammonium phosphate

You need two tables to answer these. You should have a good feel for these two tables and know solubility rules and know the placement of metals in the activity series.

http://www.files.chem.vt.edu/RVGS/ACT/notes/solubility_rules.html

http://www.files.chem.vt.edu/RVGS/ACT/notes/activity_series.html

For example.
a)This is a single replacement type reaction. Any metal in the table will displace an ION of a metal below it in the activity series. Mg is above Cr; therefore,
Cr(NO3)3 + Mg ==> Mg(NO3)2 + Cr(s)
You balance it.

Li2SO4 + BaCl2 ==> BaSO4 + 2KCl. This proceeds because BaSO4 is insoluble.

I'll leave the last two for you. If the metal (in reactions like a), if the metal is not ABOVE the ion, you write no reaction. For reaction in which a solid or a gas is formed, you write the reaction. Otherwise you write no reaction.

a. The reaction between aqueous chromium(III) nitrate and magnesium metal can be represented by the following balanced chemical equation:

2 Cr(NO3)3 + 3 Mg -> 3 Mg(NO3)2 + 2 Cr

In this reaction, magnesium metal displaces chromium from its compound and forms magnesium nitrate, while chromium is reduced. The net ionic equation for this reaction is:

3 Mg + 2 Cr(III) -> 3 Mg(II) + 2 Cr(0)

b. The reaction between aqueous lithium sulfate and aqueous barium chloride can be represented by the following balanced chemical equation:

Li2SO4 + BaCl2 -> 2 LiCl + BaSO4

In this reaction, lithium sulfate and barium chloride react to form lithium chloride and barium sulfate. Barium sulfate is insoluble in water and forms a precipitate. The net ionic equation for this reaction is:

Ba^2+ + SO4^2- -> BaSO4 (precipitate)

c. The reaction between solid lead metal and aqueous potassium chloride can be represented by the following balanced chemical equation:

Pb + 2 KCl -> PbCl2 + 2 K

In this reaction, lead metal reacts with potassium chloride to form lead(II) chloride and potassium metal. The net ionic equation for this reaction is:

Pb + 2 Cl^- -> PbCl2 (precipitate)

d. The reaction between aqueous lithium fluoride and aqueous ammonium phosphate can be represented by the following balanced chemical equation:

3 LiF + (NH4)3PO4 -> 3 Li3PO4 + 3 NH4F

In this reaction, lithium fluoride and ammonium phosphate react to form lithium phosphate and ammonium fluoride. The net ionic equation for this reaction is:

3 F^- + (NH4)+ -> NH4F (s)

To determine the reactions for the given chemical combinations, we need to refer to the solubility rules and activity series of metals. The solubility rules help us identify which compounds are soluble in water and which will form precipitates. The activity series of metals helps us determine the reactivity and displacement reactions between metals.

a. Aqueous chromium(III) nitrate plus magnesium metal:
To determine if a reaction occurs, we need to check the activity series of metals. Magnesium is more reactive than chromium. Therefore, magnesium can displace chromium in a single displacement reaction. The balanced equation would be:
Mg (s) + Cr(NO3)3 (aq) → Mg(NO3)2 (aq) + Cr (s)
The magnesium reacts with the chromium(III) nitrate to form magnesium nitrate, and chromium is reduced to its elemental form.

b. Aqueous lithium sulfate plus aqueous barium chloride:
To determine if a reaction occurs, we need to consider the solubility rules. Lithium sulfate (Li2SO4) and barium chloride (BaCl2) are both soluble in water and therefore dissociate into ions. When we mix the solutions, a double displacement reaction occurs:
Li2SO4 (aq) + BaCl2 (aq) → 2 LiCl (aq) + BaSO4 (s)
The reaction forms lithium chloride and barium sulfate. Barium sulfate is insoluble and forms a precipitate.

c. Solid lead metal plus aqueous potassium chloride:
To determine if a reaction occurs, we need to check the activity series of metals. Lead is less reactive than potassium. Therefore, no reaction will occur between solid lead and aqueous potassium chloride. The balanced equation remains:
Pb (s) + 2 KCl (aq) → No reaction.

d. Aqueous lithium fluoride with aqueous ammonium phosphate:
To determine if a reaction occurs, we need to check the solubility rules. Both lithium fluoride (LiF) and ammonium phosphate [(NH4)3PO4] are soluble. When we mix the solutions, no reaction occurs, as all ions remain in solution. The balanced equation remains:
LiF (aq) + (NH4)3PO4 (aq) → No reaction.

In chemistry, it is important to refer to the solubility rules and activity series of metals to predict whether reactions will occur and to determine the products formed.