The reaction between silver nitrate and aluminum sulfate in aqueous solution is a double displacement reaction. In this type of reaction, the positive ions (cations) of one compound exchange with the positive ions of another compound, and the negative ions (anions) of one compound exchange with the negative ions of the other compound.

The balanced chemical equation for the reaction between silver nitrate and aluminum sulfate is:

$$3AgNO_3(aq) + Al_2(SO_4)_3(aq) → 3Ag_2SO_4(s) + 2Al(NO_3)_3(aq)$$

In this reaction, the silver ions (Ag+) from silver nitrate exchange with the aluminum ions (Al3+) from aluminum sulfate, and the nitrate ions (NO3-) from silver nitrate exchange with the sulfate ions (SO42-) from aluminum sulfate. The products of the reaction are silver sulfate, which is a precipitate (a solid that forms when two solutions are mixed), and aluminum nitrate, which is soluble in water.

The net ionic equation for the reaction is:

$$2Ag^+ + SO_4^{2-} → Ag_2SO_4(s)$$

This equation shows that the actual reaction that occurs is between silver ions (Ag+) and sulfate ions (SO42-).