Answer :
To determine how many oxygen atoms are found in 75.0 grams of sulfuric acid ([tex]\( \text{H}_2\text{SO}_4 \)[/tex]), follow these steps:
1. Find the number of moles of [tex]\( \text{H}_2\text{SO}_4 \)[/tex] in 75.0 grams:
- The molar mass of [tex]\( \text{H}_2\text{SO}_4 \)[/tex] is given as 98.1 g/mol.
- Use the formula:
[tex]\[
\text{Moles of } \text{H}_2\text{SO}_4 = \frac{\text{Mass of } \text{H}_2\text{SO}_4 }{\text{Molar mass of } \text{H}_2\text{SO}_4 }
\][/tex]
- Substituting the values:
[tex]\[
\text{Moles of } \text{H}_2\text{SO}_4 = \frac{75.0 \text{ g}}{98.1 \text{ g/mol}} \approx 0.765 \text{ moles}
\][/tex]
2. Determine the number of oxygen atoms in the moles of [tex]\( \text{H}_2\text{SO}_4 \)[/tex]:
- Each molecule of [tex]\( \text{H}_2\text{SO}_4 \)[/tex] contains 4 oxygen atoms.
- Thus, the number of moles of oxygen atoms is:
[tex]\[
\text{Moles of oxygen atoms} = 4 \times \text{Moles of } \text{H}_2\text{SO}_4
\][/tex]
- Substituting the moles of [tex]\( \text{H}_2\text{SO}_4 \)[/tex]:
[tex]\[
\text{Moles of oxygen atoms} = 4 \times 0.765 \approx 3.06 \text{ moles}
\][/tex]
3. Convert moles of oxygen atoms to the number of atoms:
- Use Avogadro's number, [tex]\( 6.022 \times 10^{23} \)[/tex] atoms/mole, to find the number of oxygen atoms:
[tex]\[
\text{Number of oxygen atoms} = \text{Moles of oxygen atoms} \times 6.022 \times 10^{23}
\][/tex]
- Substituting the moles of oxygen atoms:
[tex]\[
\text{Number of oxygen atoms} \approx 3.06 \times 6.022 \times 10^{23} \approx 1.84 \times 10^{24} \text{ atoms}
\][/tex]
Therefore, there are approximately [tex]\( 1.84 \times 10^{24} \)[/tex] oxygen atoms in 75.0 grams of [tex]\( \text{H}_2\text{SO}_4 \)[/tex]. The correct answer is [tex]\( 1.84 \times 10^{24} \)[/tex].
1. Find the number of moles of [tex]\( \text{H}_2\text{SO}_4 \)[/tex] in 75.0 grams:
- The molar mass of [tex]\( \text{H}_2\text{SO}_4 \)[/tex] is given as 98.1 g/mol.
- Use the formula:
[tex]\[
\text{Moles of } \text{H}_2\text{SO}_4 = \frac{\text{Mass of } \text{H}_2\text{SO}_4 }{\text{Molar mass of } \text{H}_2\text{SO}_4 }
\][/tex]
- Substituting the values:
[tex]\[
\text{Moles of } \text{H}_2\text{SO}_4 = \frac{75.0 \text{ g}}{98.1 \text{ g/mol}} \approx 0.765 \text{ moles}
\][/tex]
2. Determine the number of oxygen atoms in the moles of [tex]\( \text{H}_2\text{SO}_4 \)[/tex]:
- Each molecule of [tex]\( \text{H}_2\text{SO}_4 \)[/tex] contains 4 oxygen atoms.
- Thus, the number of moles of oxygen atoms is:
[tex]\[
\text{Moles of oxygen atoms} = 4 \times \text{Moles of } \text{H}_2\text{SO}_4
\][/tex]
- Substituting the moles of [tex]\( \text{H}_2\text{SO}_4 \)[/tex]:
[tex]\[
\text{Moles of oxygen atoms} = 4 \times 0.765 \approx 3.06 \text{ moles}
\][/tex]
3. Convert moles of oxygen atoms to the number of atoms:
- Use Avogadro's number, [tex]\( 6.022 \times 10^{23} \)[/tex] atoms/mole, to find the number of oxygen atoms:
[tex]\[
\text{Number of oxygen atoms} = \text{Moles of oxygen atoms} \times 6.022 \times 10^{23}
\][/tex]
- Substituting the moles of oxygen atoms:
[tex]\[
\text{Number of oxygen atoms} \approx 3.06 \times 6.022 \times 10^{23} \approx 1.84 \times 10^{24} \text{ atoms}
\][/tex]
Therefore, there are approximately [tex]\( 1.84 \times 10^{24} \)[/tex] oxygen atoms in 75.0 grams of [tex]\( \text{H}_2\text{SO}_4 \)[/tex]. The correct answer is [tex]\( 1.84 \times 10^{24} \)[/tex].
