I believe you mean KO2 reacting with H2O. The reaction is 4KO2+2H2O->4KOH +3O2. The mole ratio O2:KO2 is 3:4. Thus moles of O2 produced = 0.500/4*3 = 0.375 mol.
Vapor pressure refers to the force exerted by vapor or gas molecules above the surface of a liquid. It is inversely related to the concentration of solute particles; an increase in solute concentration results in a decrease in vapor pressure, and vice versa. For (a), it dissociates into two particles. In (b), the total count of particles from dissociation becomes 1 + 2, totaling three. For (c), dissociation yields 1 + 3 for a total of four particles. (d) Since sucrose is a covalent compound, it does not break apart into ions, so it remains as one particle. For (e), dissociation results in 1 + 1, equating to two particles.