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The atomic mass of potassium is 39.1. What is the mass of [tex]$6.02 \times 10^{23}$[/tex] atoms of potassium?

A. [tex]\quad 39.1 \, \text{mg}[/tex]
B. [tex]\quad 39.10[/tex]
C. [tex]\quad 39.1 \, \text{kg}[/tex]
D. [tex]\quad 6.02 \times 30.1 \, \text{mg}[/tex]
E. [tex]\quad 6.02 \times 39.10[/tex]

Answer :

To find the mass of [tex]\(6.02 \times 10^{23}\)[/tex] atoms of potassium, we need to use the relationship between atomic mass and Avogadro's number. Here's a step-by-step solution:

1. Understand the Concept:
- The atomic mass of potassium is given as 39.1 atomic mass units (amu).
- Avogadro’s number ([tex]\(6.022 \times 10^{23}\)[/tex]) indicates the number of atoms in one mole of any substance.
- The atomic mass in amu is numerically equal to the mass of one mole of atoms in grams.

2. Relate Atomic Mass to Mass in Grams:
- Since the atomic mass of potassium is 39.1 amu, this means one mole (i.e., [tex]\(6.022 \times 10^{23}\)[/tex] atoms) of potassium has a mass of 39.1 grams.

3. Apply the Concept:
- Given [tex]\(6.02 \times 10^{23}\)[/tex] atoms, which is approximately one mole, the mass of these atoms in grams will be the same as the atomic mass in grams.

4. Conclusion:
- Therefore, the mass of [tex]\(6.02 \times 10^{23}\)[/tex] atoms of potassium is 39.1 grams.

So, the correct answer is:

B. [tex]\(39.1\)[/tex] (which represents grams).

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