In my chemistry book it says that the mass of one molecule of H_2SO_4 is 1.63*10^(-22) g. Could you explain how they get this?

Hello! Yes we can:)
All atoms of each type have their specific masses. They are known, particularly in grams per mole. By the definition, one mole of any set of particles contains fixed number of particles, called Avogadro number. It is denoted N_A and is equal to about 6 * 10^(23).
The mass of one mole of hydrogen H is about 1 (g)/(mol), the mass of one mole of sulfur S is about 32 (g)/(mol) and the mass of one mole of oxygen O is about 16 (g)/(mol).
Therefore the mass of one mole of sulfuric acid H_2SO_4 is about 2*1 + 32 + 4*16 = 98 (g)/(mol). Finally, one molecule of sulfuric acid has the mass about 98/N_A approx 98/(6*10^(23)) approx 16.3*10^(-23)=1.63*10^(-22) (g). So your book says the truth.