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Answer :
Certainly! To determine how many atoms of carbon are present in 6.00 grams of carbon, follow these steps:
1. Find the Molar Mass of Carbon:
- The molar mass of carbon is approximately 12.01 grams per mole. This is the mass of one mole of carbon atoms.
2. Calculate the Moles of Carbon:
- To find the number of moles of carbon in 6.00 grams, use the formula:
[tex]\[
\text{moles of carbon} = \frac{\text{grams of carbon}}{\text{molar mass of carbon}}
\][/tex]
- Plug in the values:
[tex]\[
\text{moles of carbon} = \frac{6.00 \, \text{grams}}{12.01 \, \text{grams/mole}} \approx 0.4996 \, \text{moles}
\][/tex]
3. Use Avogadro's Number to Find the Number of Atoms:
- Avogadro's number tells us that there are approximately [tex]\(6.022 \times 10^{23}\)[/tex] atoms in one mole of any substance.
- To find the number of atoms, multiply the number of moles of carbon by Avogadro's number:
[tex]\[
\text{atoms of carbon} = \text{moles of carbon} \times \text{Avogadro's number}
\][/tex]
- Substitute the values:
[tex]\[
\text{atoms of carbon} = 0.4996 \, \text{moles} \times 6.022 \times 10^{23} \, \text{atoms/mole} \approx 3.01 \times 10^{23} \, \text{atoms}
\][/tex]
Therefore, in 6.00 grams of carbon, there are approximately [tex]\(3.01 \times 10^{23}\)[/tex] carbon atoms.
1. Find the Molar Mass of Carbon:
- The molar mass of carbon is approximately 12.01 grams per mole. This is the mass of one mole of carbon atoms.
2. Calculate the Moles of Carbon:
- To find the number of moles of carbon in 6.00 grams, use the formula:
[tex]\[
\text{moles of carbon} = \frac{\text{grams of carbon}}{\text{molar mass of carbon}}
\][/tex]
- Plug in the values:
[tex]\[
\text{moles of carbon} = \frac{6.00 \, \text{grams}}{12.01 \, \text{grams/mole}} \approx 0.4996 \, \text{moles}
\][/tex]
3. Use Avogadro's Number to Find the Number of Atoms:
- Avogadro's number tells us that there are approximately [tex]\(6.022 \times 10^{23}\)[/tex] atoms in one mole of any substance.
- To find the number of atoms, multiply the number of moles of carbon by Avogadro's number:
[tex]\[
\text{atoms of carbon} = \text{moles of carbon} \times \text{Avogadro's number}
\][/tex]
- Substitute the values:
[tex]\[
\text{atoms of carbon} = 0.4996 \, \text{moles} \times 6.022 \times 10^{23} \, \text{atoms/mole} \approx 3.01 \times 10^{23} \, \text{atoms}
\][/tex]
Therefore, in 6.00 grams of carbon, there are approximately [tex]\(3.01 \times 10^{23}\)[/tex] carbon atoms.
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