1. Determine the molar ratio of hydrogen atoms to H2SO4 molecules.
From the chemical formula H2SO4, we can see that there are 2 hydrogen atoms for every one H2SO4 molecule.
2. Calculate the total number of H2SO4 molecules in 0.09 moles.
Number of H2SO4 molecules = 0.09 moles * (6.022 x 10^23 molecules/mole) = 5.42 x 10^22 molecules
3. Multiply the number of H2SO4 molecules by the molar ratio of hydrogen atoms to H2SO4 molecules.
Number of hydrogen atoms = 5.42 x 10^22 molecules * 2 hydrogen atoms/molecule = 1.08 x 10^23 hydrogen atoms.
Therefore, there are approximately 1.08 x 10^23 hydrogen atoms in 0.09 moles of H2SO4.