To determine the number of [tex]\( \text{C}_{70} \)[/tex] molecules that can be made from one mole of carbon atoms, you need to follow these steps:
1. Understand the Concepts:
- The Avogadro constant represents the number of atoms or molecules contained in one mole of a substance.
- In one mole of carbon atoms, there are [tex]\( 6.02 \times 10^{23} \)[/tex] carbon atoms.
- For each molecule of [tex]\( \text{C}_{70} \)[/tex], there are 70 carbon atoms.
2. Determine the Number of [tex]\( \text{C}_{70} \)[/tex] Molecules per Mole of Carbon Atoms:
- You can find the number of [tex]\( \text{C}_{70} \)[/tex] molecules by dividing the total number of carbon atoms in one mole (Avogadro constant) by the number of carbon atoms in one [tex]\( \text{C}_{70} \)[/tex] molecule.
3. Perform the Calculation:
- The Avogadro constant is [tex]\( 6.02 \times 10^{23} \)[/tex] atoms per mole.
- Each [tex]\( \text{C}_{70} \)[/tex] molecule contains 70 carbon atoms.
Using the formula:
[tex]\[
\text{Number of} \, \text{C}_{70} \, \text{molecules} = \frac{\text{Number of carbon atoms in one mole}}{\text{Number of carbon atoms per} \, \text{C}_{70} \, \text{molecule}}
\][/tex]
Substituting the known values:
[tex]\[
\text{Number of} \, \text{C}_{70} \, \text{molecules} = \frac{6.02 \times 10^{23}}{70}
\][/tex]
Simplifying this:
[tex]\[
\text{Number of} \, \text{C}_{70} \, \text{molecules} \approx 8.6 \times 10^{21}
\][/tex]
4. Conclusion:
- The number of [tex]\( \text{C}_{70} \)[/tex] molecules that can be made from one mole of carbon atoms is approximately [tex]\( 8.6 \times 10^{21} \)[/tex] molecules.
So, from one mole of carbon atoms, you can make approximately [tex]\( 8.6 \times 10^{21} \)[/tex] molecules of [tex]\( \text{C}_{70} \)[/tex].
