Martin P. answered • 08/19/22

graduate chemistry work, Doctorate degree, Former College Professor

Using the ideal gas law will not be helpful with this question as **one mole of any representative particle **whether it be an atom, ion, molecule, formula unit, etc. **will always be Avogadro's number of that representative particle. **In the question you are already given that at STP (standard temperature and pressure, zero degrees Celsius and one atmosphere of pressure) **you have one mole of N2 gas**. If you did try to use the ideal gas law, PV=nRT, at STP one mole of an ideal gas equals a volume of 22.4 Liters. If you plugged everything given into the ideal gas law equation to solve for the # of moles of N2 -

(1)(22.4) = (n)(0.0821)(273), then n(number of moles) = **1 mole, **or what you were given originally in the question. So the **key** is the fact that **N2 is a diatomic molecule, or two nitrogen atoms **covalently bonded to form** one** **molecule of N2.** so one mole of N2 gas is **Avogadro's number of molecules**, the number of nitrogen atoms would intuitively be **twice Avogadro's number**. You as well can use dimensional analysis to show this.

1 mole N2 x 6.02 x 10^23 molecules N2 /1 mole N2 = 6.02 x 10^23 (Avogadro's #) of molecules N2

then

6.02 x 10^23 molecules N2 x 2 atoms N/1 molecule N2 = **2 x Avogadro's number of atoms of N**.