To find the mass of [tex]\(6.02 \times 10^{24}\)[/tex] molecules of hydrogen ([tex]\(H_2\)[/tex]), we need to carry out a series of steps involving the mole concept and the molar mass.
### Step-by-Step Solution:
1. Determine the number of moles of [tex]\(H_2\)[/tex]:
- 1 mole of any substance contains [tex]\(6.02 \times 10^{23}\)[/tex] molecules (Avogadro's number).
- We have [tex]\(6.02 \times 10^{24}\)[/tex] molecules of [tex]\(H_2\)[/tex].
[tex]\[
\text{Number of moles} = \frac{\text{Number of molecules}}{\text{Avogadro's number}} = \frac{6.02 \times 10^{24}}{6.02 \times 10^{23}}
\][/tex]
Simplifying this fraction, we get:
[tex]\[
\text{Number of moles} = 10
\][/tex]
2. Calculate the mass of [tex]\(10\)[/tex] moles of [tex]\(H_2\)[/tex]:
- The molar mass of [tex]\(H_2\)[/tex] is [tex]\(2.02 \, \text{g/mol}\)[/tex].
Using the formula:
[tex]\[
\text{Mass} = \text{Number of moles} \times \text{Molar mass}
\][/tex]
We plug in the values:
[tex]\[
\text{Mass} = 10 \, \text{moles} \times 2.02 \, \text{g/mol} = 20.2 \, \text{g}
\][/tex]
### Conclusion:
The mass of [tex]\(6.02 \times 10^{24}\)[/tex] molecules of hydrogen ([tex]\(H_2\)[/tex]) is [tex]\(20.2 \, \text{g}\)[/tex].
Thus, the correct answer is:
D. [tex]\(20.2 \, \text{g} \, H_2\)[/tex]
