Find the number of molecules of 100.0 g of N2

Answer 1

First we will need to convert from mass into a unit that represents a count, that is, the number of particles. The mole is an accessible unit, since the periodic table provides us conversion factors in the form of atomic masses. We can then use Avogadro's number to convert from moles to number of molecules.

First determine the molar mass of nitrogen:

Molar Mass of Nitrogen = 2 * Atomic Mass Nitrogen Atom = 2 (14.01 g / mol N) = 28.02 g / mol N₂

Next use this molar mass to convert mass of nitrogen gas into moles:

100.0g N₂ * (1 mol N₂/ 28.02 g N₂) = 100.0 / 28.02 g N₂ (mol N₂/ g N₂) = 3.569 mol N₂

Now we can convert from moles to number of molecules. Recall that moles are simply a count. Moles are something like a dozen. If you have a dozen of something, you have twelve of it, regardless of what it is. The same goes for moles. The word "mole" is like the label, like the word "dozen". That label is associated with a specific count. Avogadro's number is the actual number associated with the label "mole". As 12 is to dozen, 6.022 * 10²³ is to moles. Since the mole is just a count, when you write moles, you also write the identity of what you are counting (eg mol N₂). You could just as easily say a mole of eggs.

So let's apply that. We know that we have 3.569 moles of nitrogen gas. That means we must have Avogadro's number worth of molecules of nitrogen gas. In equation form:

3.569 mol N₂ * (6.022 * 10^{23 .}molecules of N₂ / 1 mol N₂) = 2.149 * 10²⁴ molecules of N₂

Remember to report your number in appropriate scientific notation. (Do not report as 21.49 * 10²³ molecules of N₂. This is avoided, by convention, to prevent confusion.)