To determine the number of oxygen atoms in 160 grams of [tex]\(N_2O_3\)[/tex], follow these steps:
1. Calculate the molar mass of [tex]\(N_2O_3\)[/tex]:
[tex]\[
\text{Molar mass of } N_2O_3 = (2 \times 14) + (3 \times 16) = 28 + 48 = 76 \, \text{grams/mol}
\][/tex]
2. Calculate the number of moles of [tex]\(N_2O_3\)[/tex] in 160 grams:
[tex]\[
\text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{160 \, \text{grams}}{76 \, \text{grams/mol}} \approx 2.1052631578947367 \, \text{moles}
\][/tex]
3. Determine the number of molecules of [tex]\(N_2O_3\)[/tex] using Avogadro's number [tex]\(6.02214076 \times 10^{23}\)[/tex] molecules per mole:
[tex]\[
\text{Number of molecules} = \text{moles} \times \text{Avogadro's number} \approx 2.1052631578947367 \, \text{moles} \times 6.02214076 \times 10^{23} = 1.2678191073684209 \times 10^{24} \, \text{molecules}
\][/tex]
4. Calculate the number of oxygen atoms in the given mass:
Each molecule of [tex]\(N_2O_3\)[/tex] contains 3 oxygen atoms. Therefore, the total number of oxygen atoms is:
[tex]\[
\text{Number of oxygen atoms} = \text{number of molecules} \times 3 \approx 1.2678191073684209 \times 10^{24} \times 3 = 3.8034573221052626 \times 10^{24} \, \text{oxygen atoms}
\][/tex]
The correct answer is:
C. [tex]\(3.80 \times 10^{24}\)[/tex]
