Sure! Let's determine how many oxygen atoms are present in one mole of ammonium nitrate ([tex]\(\text{NH}_4\text{NO}_3\)[/tex]).
1. Identify the elements and their amounts in the chemical formula:
Ammonium nitrate ([tex]\(\text{NH}_4\text{NO}_3\)[/tex]) contains:
- 1 nitrogen ([tex]\(\text{N}\)[/tex]) atom from the [tex]\(\text{NH}_4^+\)[/tex] ion
- 4 hydrogen ([tex]\(\text{H}\)[/tex]) atoms from the [tex]\(\text{NH}_4^+\)[/tex] ion
- 1 nitrogen ([tex]\(\text{N}\)[/tex]) atom from the [tex]\(\text{NO}_3^-\)[/tex] ion
- 3 oxygen ([tex]\(\text{O}\)[/tex]) atoms from the [tex]\(\text{NO}_3^-\)[/tex] ion
2. Determine the number of oxygen atoms in each molecule:
Each molecule of [tex]\(\text{NH}_4\text{NO}_3\)[/tex] has 3 oxygen atoms.
3. Use Avogadro's number:
Avogadro's number ([tex]\(N_A\)[/tex]) is approximately [tex]\(6.022 \times 10^{23}\)[/tex], which represents the number of molecules in one mole of a substance.
4. Calculate the number of oxygen atoms in one mole of ammonium nitrate:
- One mole of [tex]\(\text{NH}_4\text{NO}_3\)[/tex] contains [tex]\(6.022 \times 10^{23}\)[/tex] molecules.
- Since each molecule of [tex]\(\text{NH}_4\text{NO}_3\)[/tex] contains 3 oxygen atoms, we multiply the number of molecules by 3 to get the total number of oxygen atoms.
[tex]\[ \text{Number of oxygen atoms} = (6.022 \times 10^{23} \text{ molecules/mole}) \times (3 \text{ oxygen atoms/molecule}) \][/tex]
[tex]\[ \text{Number of oxygen atoms} = 1.8066 \times 10^{24} \text{ oxygen atoms} \][/tex]
So, the number of oxygen atoms present in one mole of ammonium nitrate is [tex]\(1.81 \times 10^{24}\)[/tex] atoms, rounded to three significant figures.
Therefore, the correct answer is:
[tex]\[
\boxed{1.81 \times 10^{24} \text{ atoms}}
\][/tex]
Thus, the correct option is:
D. [tex]\(1.81 \times 10^{24} \text{ atoms}\)[/tex]
