The experiment requires 1 mg per ml of iron (Fe3+). What mass of iron (III) nitrate hexahydrate (Fe(NO3) - 6H2O) would you need to dissolve in 1 litre to achieve this value?

1 mg/mL of Fe x 1000 mL = 1,000 mg in the L container.

1000 mg Fe^+3 = ? mg Fe(NO3)3*6H2O.
Just convert 1000 mg Fe^+3 to the hexahydrate. That will be
1000 mg Fe^+3 x (1 mol Fe(NO3)3*6H2O/1 mol Fe^+3) x (349.95 g Fe(NO3)3*6H2O/1 mol Fe(NO3)3*6H2O) x (1 mol Fe^+3/55.85) = ??
Check my work.