To determine the number of oxygen atoms in 160 grams of [tex]\(N_2O_3\)[/tex], we can follow these steps:
1. Calculate the number of moles of [tex]\(N_2O_3\)[/tex] in the sample:
- The molar mass of [tex]\(N_2O_3\)[/tex] is given as 108 grams per mole.
- Given the mass of the sample is 160 grams.
The number of moles is calculated using the formula:
[tex]\[
\text{moles of } N_2O_3 = \frac{\text{mass of sample}}{\text{molar mass of } N_2O_3}
\][/tex]
Substituting the given values:
[tex]\[
\text{moles of } N_2O_3 = \frac{160 \text{ grams}}{108 \text{ grams/mole}} \approx 1.4814814814814814 \text{ moles}
\][/tex]
2. Determine the number of oxygen atoms per mole of [tex]\(N_2O_3\)[/tex]:
- Each molecule of [tex]\(N_2O_3\)[/tex] contains 3 atoms of oxygen.
3. Calculate the total number of oxygen atoms:
- Avogadro's number, which is the number of molecules (or atoms) in one mole, is [tex]\(6.022 \times 10^{23}\)[/tex].
- To find the total number of oxygen atoms, we multiply the number of moles of [tex]\(N_2O_3\)[/tex] by the number of oxygen atoms per molecule and by Avogadro's number.
Therefore,
[tex]\[
\text{oxygen atoms} = \text{moles of } N_2O_3 \times \text{oxygen atoms per molecule} \times \text{Avogadro's number}
\][/tex]
Substituting the values:
[tex]\[
\text{oxygen atoms} = 1.4814814814814814 \text{ moles} \times 3 \text{ atoms/molecule} \times 6.022 \times 10^{23} \text{ atoms/mole}
\][/tex]
[tex]\[
\text{oxygen atoms} \approx 2.676444444444445 \times 10^{24}
\][/tex]
Given the calculations, the number of oxygen atoms in 160 grams of [tex]\(N_2O_3\)[/tex] is approximately [tex]\(\boxed{2.676 \times 10^{24}}\)[/tex], which does not directly match any of the options provided (A-D). However, this precise answer implies that there may be a typo or a discrepancy in the provided options, or that additional context or rounding considerations are needed.
