Let's solve the problem step-by-step:
1. Identify the number of nitrogen atoms per molecule of [tex]\( NH_4NO_3 \)[/tex]:
- Ammonium nitrate ([tex]\( NH_4NO_3 \)[/tex]) is composed of the ammonium ion ([tex]\( NH_4^+ \)[/tex]) and the nitrate ion ([tex]\( NO_3^- \)[/tex]).
- The ammonium ion ([tex]\( NH_4^+ \)[/tex]) contains 1 nitrogen atom.
- The nitrate ion ([tex]\( NO_3^- \)[/tex]) also contains 1 nitrogen atom.
- Thus, each molecule of [tex]\( NH_4NO_3 \)[/tex] has a total of [tex]\( 1 \)[/tex] (from [tex]\( NH_4^+ \)[/tex]) + [tex]\( 1 \)[/tex] (from [tex]\( NO_3^- \)[/tex]) = 2 nitrogen atoms.
2. Determine the number of molecules in one mole:
- By definition, one mole of any substance contains Avogadro's number of molecules, which is approximately [tex]\( 6.02 \times 10^{23} \)[/tex] molecules.
3. Calculate the total number of nitrogen atoms in one mole of [tex]\( NH_4NO_3 \)[/tex]:
- Since each molecule of [tex]\( NH_4NO_3 \)[/tex] contains 2 nitrogen atoms, the total number of nitrogen atoms in one mole of [tex]\( NH_4NO_3 \)[/tex] can be calculated by multiplying the number of nitrogen atoms per molecule (2) by Avogadro's number ([tex]\( 6.02 \times 10^{23} \)[/tex]).
- Therefore, the total number of nitrogen atoms in one mole of [tex]\( NH_4NO_3 \)[/tex] is [tex]\( 2 \times 6.02 \times 10^{23} = 1.20 \times 10^{24} \)[/tex].
So, the number of nitrogen atoms present in one mole of [tex]\( NH_4NO_3 \)[/tex] is [tex]\( 1.20 \times 10^{24} \)[/tex] atoms.
The correct answer is:
B. [tex]\( 1.20 \times 10^{24} \)[/tex] atoms.
