how could I determine experimentally whether all the potassium chlorate had been decomposed?

There may be easier ways to do it but could you dissolve the remainder in water and ppt the chloride (from the KCl) with AgNO3 and determine grams Cl^-, then compare to the the theoretical amount of KCl produced if all of the KClO3 were decomposed to KCl.

KClO3 decomposes to KCl and O2 which it escapes. A sample of KClO3 that has had some decomposition will contain some KCl.

A sample of this mixture could be dissolved in water and tested with AgNO3.
Pure KClO3 would not produce a precipitate since AgClO3 is soluble in water. If some KCl is present, AgCl will precipitate.

I disagree with this answer.:-) Everything you say is true about the KClO3/KCl; however, the question isn't asked that way. The question is, "How can we tall if all of the KClO3 has decomposed?" That means we have already driven the oxygen away and we are left with mostly KCl. Of course we will get a reaction with AgNO3. The question is how do we determine if there is a molecule or two of KClO3 that did not decompose and we must do so with a bunch of KCl mixed in. The procedure outlined will work to distinguish KClO3 before it is heated but not after it is heated. And before it is heated, we already know the answer.

To determine experimentally whether all the potassium chlorate has been decomposed, you can perform a simple experiment to assess the presence or absence of potassium chlorate. Here's a step-by-step procedure:

1. Collect the necessary materials: potassium chlorate, a heat source (e.g., Bunsen burner, hot plate), a test tube, a test tube holder, a stirring rod, and a deflagrating spoon.

2. Start by measuring a known mass of potassium chlorate. This will be your initial mass.

3. Transfer the measured potassium chlorate into a clean and dry test tube.

4. Suspend the test tube in a test tube holder and position it above the heat source. Make sure the test tube is properly secured.

5. Apply heat to the test tube gradually. Heat the potassium chlorate until it decomposes. During this process, potassium chlorate decomposes into potassium chloride and oxygen gas.

6. Observe any changes that occur during heating. The potassium chlorate will initially melt and then undergo decomposition, resulting in the release of oxygen gas. You may observe color changes or bubbling as well.

7. Continue heating until there are no further signs of bubbling or gas release. This indicates that the decomposition of potassium chlorate is complete.

8. Allow the residue in the test tube to cool down completely.

9. Weigh the test tube with the residue. This will be your final mass.

10. Compare the initial mass and final mass. If the final mass is significantly less than the initial mass, it implies that the potassium chlorate has decomposed completely. If there is no significant change in mass, it suggests that the decomposition is incomplete, and some potassium chlorate remains.

Keep in mind that this is a simple experimental method, and it might not detect trace amounts of potassium chlorate. For a more accurate determination, you may need to employ analytical techniques such as titration or spectroscopy.