To find out how many moles are equivalent to [tex]\(5.44 \times 10^{28}\)[/tex] atoms of chromium, we'll use Avogadro's number. Avogadro's number, [tex]\(6.022 \times 10^{23}\)[/tex], tells us how many atoms or molecules are in one mole of a substance.
Here's a step-by-step breakdown:
1. Given Data:
- Number of chromium atoms: [tex]\(5.44 \times 10^{28}\)[/tex]
- Avogadro's number: [tex]\(6.022 \times 10^{23}\)[/tex]
2. Formula:
The number of moles ([tex]\(n\)[/tex]) is calculated using the formula:
[tex]\[
n = \frac{\text{Number of atoms}}{\text{Avogadro's number}}
\][/tex]
3. Substitute the given values into the formula:
[tex]\[
n = \frac{5.44 \times 10^{28}}{6.022 \times 10^{23}}
\][/tex]
4. Perform the division:
[tex]\[
n = \frac{5.44}{6.022} \times 10^{28 - 23}
\][/tex]
5. Simplify the expression:
[tex]\[
n \approx 0.90335 \times 10^5
\][/tex]
6. Convert to scientific notation:
[tex]\[
n \approx 9.0335 \times 10^4
\][/tex]
Therefore, [tex]\(5.44 \times 10^{28}\)[/tex] atoms of chromium are approximately equivalent to [tex]\(9.0335 \times 10^4\)[/tex] moles of chromium.
