The question requires us to calculate the mass of N2O4 where there are one million atoms of oxygen (O).
First, we need to keep in mind that each molecule of N2O4 contains four oxygen atoms.
To calculate the value required, we can use the Avogadro's constant, 6.02 x 10^23 mol^-1, which is the proportionality factor that relates the number of constituent particles (molecules, atoms or ions) in a sample with the amount of substance in that sample.
Using the Avogadro's number means that we can estabilsh the following relation:
1 mol of N2O4 ---------- 6.02 x 10^23 molecules of N2O4
Now, considering the number of atoms in one molecule of N2O4, how many molecules we would need to achieve one million oxygen atoms?
1 molecule N2O4 -------------- 4 oxygen atoms
x ------------- 1.000 x 10^6 oxygen atoms
Solving for x, we see that we would need 2.500 x 10^5 molecules of N2O4.
Next, we can apply the relation estabilshed with the Avogadro's number and calculate how many moles of N2O4 we would need:
1 mol of N2O4 ---------- 6.02 x 10^23 molecules of N2O4
y --------- 2.500 x 10^5 molecules of N2O4
Solving for y, we have that 2.500 x 10^5 molecules of N2O4 corresponds to 4.153 x 10^-19 moles of this molecule.
At last, we can use the molar mass of N2O4 to calculate the mass required, as we already have the amount of this molecule in number of moles.
First, we calculate the molar mass of N2O4 knowing that the atomic mass of nitrogen is 14.00 u and oxygen is 15.99 u:
molar mass N2O4 = (2 * 14.00) + (4 * 15.99) = 91.96 g/mol
Next, we use the molar mass (91.96 g/mol) and the number of moles calculated (4.153 x 10^-19 moles) to obtain the mass of N2O4 in which there are one million atoms of oxygen:
1 mol N2O4 ------------------------ 91.96 g N2O4
4.153 x 10^-19 mol N2O4 ----- y
Solving for y, we have that in 3.819 x 10^-17 g of N2O4, there are 1.000 x 10^6 atoms of oxygen.