Would penicillin be expected to have an equal ability to kill both Gram-positive and Gram-negative bacteria? Why or why not?

No, due to the difference in Peptidoglycan layer

Explanation:

Since the mode of operation of the drug penicillin is to prevent the proper build-up of peptidoglycan in the cell wall of bacteria and bursting up its cell wall, Penicillin would have greater effect in killing Gram-negative bacteria with thin layer of peptidoglycan in their cell wall, unlike Gram-positive bacteria with a thick layer of peptidoglycan in their cell wall.