If very small concentrations of NaCl and AgNO3 are mixed, no precipitate forms. However, if large concentrations are mixed, a white precipitate forms.

Can someone tell me a method for testing the hypothesis that "insoluble" salts would dissolve to some extent in water and are slightly soluble. If the Ksp is low,the solid is not soluble and if high, it is soluble and if it the product of the ion concentration does the exceed the Ksp value, no precipate would form.So that's the hypothesis.So, can someone give me a experiment to test this hypothesis.

I don't think this is something you can whip out in a couple of hours. Something along these line might be what you're looking for.

Pick out four or five salts that have varying degrees of solubility. Some examples are AgCl, Ca(OH)2, Fe(OH)3 etc.
You could make saturated solution of each, filter the excess, evaporate the filtrate to dryness and weigh the salt. That way you can show that some salts are more soluble than others.

For the second part, you could make a dilute solution of FeCl3 (quite dilute) and an equally dilute solution of NaOH. Then add one drop NaOH soln to the FeCl3 sol. No ppt if you have the solutions dilute enough. Another drop NaOH. Continue until a ppt starts to form. That way you can show that no ppt forms until the ion-product is exceeded. I picked Fe(OH)3 only because it is easy to see the ppt but the Ksp may be so small (it's in the neighborhood of 10E-36 or so) that it would be difficult to get solutions so dilute that one drop NaOH would not form a ppt. In that case, pick one of the other materials from you list of salts and try again. Remember research isn't something one draws up on paper, writes up, draws conclusions, then performs the experiment. You get an idea, you try it, then redesign to outflank the draw backs, and try again This should get you started.

To test the hypothesis that "insoluble" salts would dissolve to some extent in water and are slightly soluble, you can conduct a simple experiment to determine the solubility of different salts. Here's a step-by-step procedure:

1. Start by collecting a variety of salts that are known to have different solubility characteristics. Some common examples include NaCl, AgNO3, PbCl2, and CaCO3.

2. Prepare a series of test tubes or small containers, each labeled with the name of the salt you are testing.

3. Add a small amount of distilled water to each container. The amount of water should be sufficient to fully cover the salt but not excessive.

4. Begin with the salt you suspect to be highly soluble, such as NaCl. Add a small amount of the salt to the corresponding test tube and stir gently to aid in dissolution. Observe whether the salt dissolves completely or leaves any undissolved particles.

5. Repeat this process for each salt, making note of their solubility characteristics. For salts that are not soluble or slightly soluble, you may observe the formation of a precipitate (a solid that settles at the bottom of the container).

6. Once you have gathered data on the solubility of each salt, compare your observations with the hypothesis you initially proposed. If a salt is highly soluble, the product of the ion concentrations should exceed the Ksp value. If a precipitate forms, the product of the ion concentrations may not exceed the Ksp value, indicating limited solubility.

7. It's important to note that in some cases, the solubility of a salt may be affected by factors like temperature or pH. If desired, you can repeat the experiment under varying conditions to explore these effects.

By conducting this experiment, you can test your hypothesis and gain a better understanding of the solubility characteristics of various salts.