Chemistry Question about gas & temperature

Question

Dear experts,

I would like to know how to solve this problem:

How many nitrogen atoms are present in one mole of nitrogen

gas at the temperature of 0 ° C and at a pressure of 1 atm?

(Actually it asks how many times the Avogadro's number)

I tried the equation of state for ideal gases (P*V = nRT) but

haven't found anything yet...

Answer 1

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.

Answer 2

This is kind of a trick question. The temperature and pressure doesn’t matter. You are given that there is one mole. For every mole of anything, at any temperature or pressure, there is always 1 Avogadro’s number of whatever you have. The issue here is that nitrogen gas always appears as the molecule N₂ which means that although there is one Avogadro’s number of molecules, there is 2 Avogadro’s number of atoms.