What mass of electrons would be required to just neutralize the charge of 1.0 grams of protons?

mass of 1 proton x #protons = 1 gram.

Look up mass of 1 proton (in grams) and solve for # protons. You will need the same number of electrons to balance the charge. So how much will those weigh?
They will weigh
mass of 1 electron (in grams) x # electrons (same as number of protons) = mass of those electrons.