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What is the mass of [tex]6.02 \times 10^{24}[/tex] molecules of hydrogen, [tex]H_2[/tex]?

Given:
- Molar mass of [tex]H_2 = 2.02 \, \text{g/mol}[/tex]
- 1 mole [tex]= 6.02 \times 10^{23}[/tex] molecules

A. [tex]2.98 \times 10^{24} \, \text{g} \, H_2[/tex]
B. [tex]1.22 \times 10^{25} \, \text{g} \, H_2[/tex]
C. [tex]10.0 \, \text{g} \, H_2[/tex]
D. [tex]20.2 \, \text{g} \, H_2[/tex]



Answer :

GinnyAnswer
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]

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