One molecule of the antibiotic known as penicillin g has a mass of 5.553*10-22g. what is the molar mass of penicillin g?

Molar mass means the mass of one mole of penicillin.

Now, one mole of penicillin contains 6.022 x 10^23 molecules (That's Avogadro's number).

Therefore:

molar mass of penicillin = mass of 6.022 x 10^23 molecules

molar mass of penicillin = mass of one molecule x 6.022 x 10^23

molar mass of penicillin = 5.553 x 10^-22 x 6.022 x 10^23

= 334.40166 grams