Let's solve the problem step-by-step to determine how many grams of hydrogen are in 5.00 grams of [tex]\( \text{C}_{12}\text{H}_{10}\text{O} \)[/tex].
1. Determine the molar masses of each element:
- Carbon (C): 12.01 g/mol
- Hydrogen (H): 1.008 g/mol
- Oxygen (O): 16.00 g/mol
2. Calculate the molar mass of [tex]\( \text{C}_{12}\text{H}_{10}\text{O} \)[/tex]:
- The molecular formula [tex]\( \text{C}_{12}\text{H}_{10}\text{O} \)[/tex] implies:
[tex]\[
12 \times \text{molar mass of C} + 10 \times \text{molar mass of H} + 1 \times \text{molar mass of O}
\][/tex]
- Plugging in the values:
[tex]\[
(12 \times 12.01) + (10 \times 1.008) + (16.00) = 144.12 + 10.08 + 16.00 = 170.20 \, \text{g/mol}
\][/tex]
3. Calculate the moles of [tex]\( \text{C}_{12}\text{H}_{10}\text{O} \)[/tex] in 5.00 g:
- Use the formula:
[tex]\[
\text{moles} = \frac{\text{mass}}{\text{molar mass}}
\][/tex]
- Plugging in the given mass and the calculated molar mass:
[tex]\[
\text{moles of } \text{C}_{12}\text{H}_{10}\text{O} = \frac{5.00}{170.20} \approx 0.02938 \, \text{mol}
\][/tex]
4. Determine the grams of hydrogen in the sample:
- Each molecule of [tex]\( \text{C}_{12}\text{H}_{10}\text{O} \)[/tex] contains 10 moles of hydrogen atoms.
- Therefore, the moles of hydrogen in the sample is:
[tex]\[
\text{moles of H} = \text{moles of } \text{C}_{12}\text{H}_{10}\text{O} \times 10 = 0.02938 \times 10 = 0.2938 \, \text{mol}
\][/tex]
- Now, convert moles of hydrogen to grams using the molar mass of hydrogen:
[tex]\[
\text{grams of H} = \text{moles of H} \times \text{molar mass of H} = 0.2938 \times 1.008 = 0.29612 \, \text{g}
\][/tex]
So, there are approximately 0.296 grams of hydrogen in 5.00 grams of [tex]\( \text{C}_{12}\text{H}_{10}\text{O} \)[/tex].
