I am having trouble interpreting a few of your questions, so I've rewritten a couple the way I think you meant them (revisions are in BOLD.)
per grams in 3.01 x 1022 molecules of nitric acid?
A mole of Nitric acid contains 6.02x1023 molecules, and has a mass equal to it's molar mass, 63.0 g/mole. We can use this as a conversion factor:
(63.0 g HNO3/6.02x1023
molecules HNO 3) x (3.01 x 1022 molecules HNO 3) = 3.16 g HNO3
What is the volume of 2.408 x 1024 molecules of oxygen?
(2.408 x 1024 molecules)/(6.02x1023 molecules/mole) = 4.01 moles O2. Since we are not told the pressure or temperature, we'll assume it is STP, and then we know that one mole of any gas occupies 22.4 liters.
(4.01 moles O2)x(22.4 liters/mole O2) = 9.7 liters
How Many Molecules are in 112 dm3 of Hydrochloride?
Should we assume this is a gas? My answer depends on it, otherwise we would need a density.
1 dm = 10 cm
1 dm3 = 1000 cm3
1 cm3 = 1 ml
112 dm3 = 112 ml, or 0.112 liters
liters)x(1 mole/22.4 liters) = 0.005 moles
moles x(6.01x1023 molecules/ mole) = 3.01x1021 molecules HCl
How many grams in 134.4 dm3 of sulfur trioxide
Convert cubic dm into liters, as in the above example. Use 1 mole/22.4L to obtain the moles of SO3 . Once you have moles, multiply that by the molar mass SO3 (g/mole).
I hope this helps,