Will the following reactions mixed together cause a precipitate reaction, released gas reaction, or no reaction.

Ba(NO3)2 mixed with NaCl
Ba(NO3)2 mixed with HCl
Ba(NO3)2 mixed with Na2CO3
Ba(NO3)2 mixed withNa3SO4

also Ba(NO3)2 is soluble and a solid and HCl is a gas.

Is there some sort of "law" that I should know when soluble solids will do with soluble gases/solids?

Thank you!

Ba(NO3)2 mixed with NaCl NO

Ba(NO3)2 mixed with HCl NO
Ba(NO3)2 mixed with Na2CO3 YES
Ba(NO3)2 mixed with Na3SO4YES but you have a typo in Na2SO4

also Ba(NO3)2 is soluble and a solid and HCl is a gas.
I don't know what you're asking here. HCl is a gas but usually you use an aqueous solution of HCl. Yes, Ba(NO3)2 is a solid.

I'm a little confused about what LAWS you might need to know.
Generally you need to know the following:
Aqueous solution will react if one of the following occurs.
1. An insoluble precipitate is formed. The solubility rules (you should know them) will tell you that. For all of the above the solubility rules will answer them.
2. A gas is formed. The usual gases are CO2, H2, N2, O2, F2, Cl2, SO2, SO3, NO2.
3. A slightly soluble material is formed. The USUAL material formed in freshman chemistry is water.
I have written the equations (with phases) for the reactions at the beginning of the post that react. The others are no reaction.
Ba(NO3)2(aq) + Na2CO3(aq) ==> BaCO3(s) + 2NaNO3(aq)

Ba(NO3)2(aq) + Na2SO4(aq) ==> BaSO4(s) + 2NaNO3(aq)

What kind of reaction does it cause though?precipitate reaction, released gas reaction, or no reaction.

you answered yes, no, yes but didn't explain what reaction it is.

If you know the solubility rules (#1) in my explanation, then you know BaSO4 is a solid (I show solid by BaSO4 in the equation I wrote belowB) and you know BaCO3 is a solid (which I show solid in my equation below). So the first two don't react, the next two react to produce a solid in each; i.e., BaCO3 in #3 and BaSO4 in #4. Therefore, #3 and #4 are ppt reactions.

To determine whether a reaction will result in a precipitate or gas formation or no reaction, you need to consider the solubility of the compounds involved. Solubility rules can help you predict the outcome of these reactions.

Solubility rules generally state that compounds containing alkali metal ions (e.g., Na+) and most nitrate (NO3-) and acetate (C2H3O2-) ions are soluble in water, meaning they will dissolve completely.

Let's examine the reactions one by one:

1. Ba(NO3)2 mixed with NaCl:
Both Ba(NO3)2 and NaCl are soluble compounds, which means they will dissociate into their respective ions when mixed with water. The resulting solution will contain Ba2+, Na+, Cl-, and NO3- ions. Since no insoluble compound is formed, no precipitate will be formed. Therefore, the reaction will not result in a precipitate or gas formation.

2. Ba(NO3)2 mixed with HCl:
Ba(NO3)2 is soluble in water and will dissociate into Ba2+ and NO3- ions. HCl is a strong acid that will ionize into H+ and Cl- ions in water. When Ba2+ ions react with Cl- ions, they can form a precipitate (BaCl2). Therefore, the reaction between Ba(NO3)2 and HCl will likely result in a precipitate formation.

3. Ba(NO3)2 mixed with Na2CO3:
Ba(NO3)2 is soluble in water and will dissociate into Ba2+ and NO3- ions. Na2CO3 is also soluble and will dissociate into 2 Na+ ions and one CO3^2- ion. When Ba2+ ions react with CO3^2- ions, they can form a precipitate (BaCO3). Therefore, the reaction between Ba(NO3)2 and Na2CO3 will likely lead to a precipitate reaction.

4. Ba(NO3)2 mixed with Na3SO4:
Ba(NO3)2 is soluble and will dissociate into Ba2+ and NO3- ions. Na3SO4 is soluble, and it will dissociate into 3 Na+ ions and one SO4^2- ion. When Ba2+ ions react with SO4^2- ions, they can form an insoluble compound (BaSO4), which will precipitate out. Therefore, the reaction between Ba(NO3)2 and Na3SO4 will likely result in a precipitate reaction.

In summary:
- Ba(NO3)2 mixed with NaCl: No precipitate or gas formation.
- Ba(NO3)2 mixed with HCl: Likely precipitate formation.
- Ba(NO3)2 mixed with Na2CO3: Likely precipitate formation.
- Ba(NO3)2 mixed with Na3SO4: Likely precipitate formation.

Regarding your question about a "law," it is not a specific law, but rather a set of solubility rules that will guide you in predicting the outcome of such reactions. These solubility rules are based on experimental observations and can help determine whether a compound is soluble or insoluble in water. It is essential to familiarize yourself with these rules to make predictions about precipitation and gas formation.