Given
Mass of K2O2 = 1.0 g
Molar mass of K2O2 = 110.0 g/mol
Calculate the # moles of K2O2
# moles = mass of K2O2/molar mass
= 1.0 g/110.0 g.mol-1 = 0.0091 moles
1 mole of K2O2 contains 2*6.023*10^23 atoms of oxygen
Therefore, 0.0091 moles of K2O2 will correspond to:
= 0.0091 moles * 2* 6.023*10^23 atoms/1 mole
= 1.096 * 10^24 atoms of oxygen