(e) Calculate the number of [tex]C_{70}[/tex] molecules that can be made from one mole of carbon atoms.

Given:
The Avogadro constant [tex]= 6.02 \times 10^{23}[/tex] per mole.



Answer :

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].