Is there a difference between a homogenouos mixture of hydrogen gas and oxygen gas, and a sample of vapor? explain?

Yes. In a homogeneous mixture the hydrogen and oxygen are not chemically combined; in water vapor, they are. You can separate a homogeneous mixture of hydrogen and oxygen by physical means, such as by cooling the mixture until the oxygen liquefies. If you cool water vapor you're just going to get liquid water and then ice - not two separate substances. That's because compounds can only be separated into their elements by chemical means.

Answerthis solution will not form a precipitateexplanationsolubility equilbrium:         pbf₂(s)  ⇄ pb²⁺(aq) + 2 f⁻(aq)the solubility product expression is    (we exclude solids from the equilibrium expression).now suppose we have the trial ion product q, which we can define as    then, we can interpret  q as the product of the concentration of the ions that we have and ksp as the product of the ion concentrations that are needed to form a saturated solution.if q > ksp, then that implies that there will be a surplus of ions that exceed the amount that is required to form a saturated solution. a precipitate will then form (the precipitate continually  forms until the surplus ions are removed and q is decreased to ksp's value).if q = ksp, the saturated solution that forms is barely saturated and the precipitate will be minimal.if q < ksp, then the ion concentration will not be enough to form a saturated solution (so no precipitate).using our information, we calculate the trial ion product:     since q = 2.7  × 10⁻⁸ < ksp =  4  ×  10⁻⁸, a precipitate will not form.