To determine how many moles are in 17.0 grams of [tex]\(H_2O_2\)[/tex], we can follow these steps:
1. Identify the Molar Mass of [tex]\(H_2O_2\)[/tex]:
- The molar mass is the sum of the atomic masses of all atoms in a molecule.
- For [tex]\(H_2O_2\)[/tex]:
- Hydrogen (H): [tex]\(1.01 \, \text{g/mol} \times 2 = 2.02 \, \text{g/mol}\)[/tex]
- Oxygen (O): [tex]\(16.00 \, \text{g/mol} \times 2 = 32.00 \, \text{g/mol}\)[/tex]
- Total molar mass of [tex]\(H_2O_2 = 2.02 \, \text{g/mol} + 32.00 \, \text{g/mol} = 34.02 \, \text{g/mol}\)[/tex]
2. Calculate the Number of Moles:
- Use the formula:
[tex]\[
\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}
\][/tex]
- Plug in the values:
[tex]\[
\text{moles of } H_2O_2 = \frac{17.0 \, \text{g}}{34.02 \, \text{g/mol}} \approx 0.49985 \, \text{mol}
\][/tex]
3. Compare to Multiple-Choice Options:
- The calculated value is approximately [tex]\(0.49985 \, \text{mol}\)[/tex].
- Review the multiple-choice answers to find the closest one:
- [tex]\(0.284 \, \text{mol}\)[/tex]
- [tex]\(0.385 \, \text{mol}\)[/tex]
- [tex]\(0.500 \, \text{mol}\)[/tex]
- [tex]\(0.730 \, \text{mol}\)[/tex]
- The closest value to [tex]\(0.49985 \, \text{mol}\)[/tex] is [tex]\(0.500 \, \text{mol}\)[/tex].
Therefore, the number of moles in 17.0 grams of [tex]\(H_2O_2\)[/tex] is approximately [tex]\(0.500 \, \text{mol}\)[/tex]. The correct answer is:
[tex]\[
0.500 \, \text{mol} \, H_2O_2
\][/tex]
