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How many moles are contained in [tex]$3.131 \times 10^{24}$[/tex] particles?

A. [tex]$5.199 \, \text{mol}$[/tex]
B. [tex][tex]$18.85 \, \text{mol}$[/tex][/tex]
C. [tex]$0.5199 \times 10^{23} \, \text{mol}$[/tex]
D. [tex]$1.885 \times 10^{47} \, \text{mol}$[/tex]



Answer :

GinnyAnswer
To determine the number of moles contained in [tex]\(3.131 \times 10^{24}\)[/tex] particles, we need to use Avogadro's number, which is the number of particles in one mole. Avogadro's number is [tex]\(6.022 \times 10^{23}\)[/tex] particles/mole.

Here's a step-by-step solution:

1. Identify the given data:
- Number of particles: [tex]\(3.131 \times 10^{24}\)[/tex]
- Avogadro's number: [tex]\(6.022 \times 10^{23}\)[/tex] particles/mole

2. Set up the formula to convert particles to moles:
[tex]\[ \text{moles} = \frac{\text{particles}}{\text{Avogadro's number}} \][/tex]

3. Substitute the given values into the formula:
[tex]\[ \text{moles} = \frac{3.131 \times 10^{24}}{6.022 \times 10^{23}} \][/tex]

4. Perform the division:
[tex]\[ \text{moles} = 5.199269345732314 \][/tex]

5. Round the answer to an appropriate number of significant figures:
The given data ([tex]\(3.131 \times 10^{24}\)[/tex]) has 4 significant figures, so the number of moles should also be rounded to 4 significant figures:
[tex]\[ \text{moles} \approx 5.199 \][/tex]

Analyzing the options given:
- A. 5.199 mol
- B. 18.85 mol
- C. 0.5199 \times 10^{23} mol
- D. 1.885 \times 10^{47} mol

The correct answer is:
A. 5.199 mol

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