If 1.0 a of current are passing through a wire how many electrons pass through a cross-section of the wire in 1.0 hours?

1 Amp = 1 Coulomb per second

So in one hour, 3600 Coulombs of charge has flowed (is "flowed" a word?) through

1 electron has a charge of approximately (-) 1.6 x 10^-19

So, we just have to divide 3600/1.6x10^-19 = 2.25 x 10^22 electrons