… weighs one gram … An amount of hydrogen weighing the same amount has exactly one mole of atoms in it.
Not only was this never true - the sentence would have to have say “An amount of carbon-12 atoms weighing 12 times this amount has exactly 1 mole atoms in it” (far less elegant) – but not even this is true any longer after the fuckup in redefining the mole in 2019, after which all these relations between amount of substance and mass are only approximate.