A famous Italian scientist named Amedeo Avogadro (not avocado) realized that certain elements were naturally heavier than others, so 1 gram of gold, for instance, had far fewer atoms than 1 gram of lithium. He created a unit of measure, called a mole, which we now know is equal to [tex]6.022*10^{23}[/tex] particles of a substance.
It is defined such that 12 grams of carbon-12 is equal to 1 mole, but we don't actually need to know that. We use the atomic mass units on the periodic table of the elements to get a molar mass in moles per gram.
For instance, nitrogen has an atomic mass of 14.01 amu. This is equivalent to 14.01 grams per mole.
With this information, let's find how many moles are in [tex]1.11 * 10^{24} [/tex] hydrogen molecules.
We use Avogadro's number, which says that
[tex]1 \ mol = 10^{24} \ particles[/tex].
So, making this our conversion factor, we have
[tex]1.11 * 10^{24} \ molecules \ * \ \dfrac{1 \ mol}{6.022 * 10^{23} \ molecules} = \dfrac{1.11*10}{6.022} \ mol \\\\\\ = 1.84 \ mol[/tex]
From the periodic table of the elements, we have
[tex]1.008 \ \dfrac{g \ H}{mol \ H} [/tex].
But, since we have diatomic (molecular) hydrogen, this is actually [tex]H_2[/tex]. So, we double our number.
[tex] \dfrac{2.016 \ g \ H_2}{mol \ H_2} [/tex]
Now, we use this molar mass as our conversion factor to get from moles to grams.
[tex]1.84 \ mol \ H_2 \ * \ \dfrac{2.016 \ g \ H_2}{mol \ H_2} = 3.98 \ g \ H_2[/tex]
