Question

How many carbon atoms are contained in each of the following number of moles:

(a) 3.70 mol; (b) 8.20 mol?
Report answer using three significant figures.
(a) ___× 10_____ atoms

Answer 1

To find the number of carbon atoms in 3.70 mol and 8.20 mol, multiply the moles by Avogadro's number (6.022 × 10^23 atoms/mol) and round to three significant figures giving 2.23 × 10^24 atoms and 4.94 × 10^24 atoms respectively.

Step-by-step explanation:

To calculate the number of carbon atoms contained in a given number of moles, we use Avogadro's number (6.022 × 1023 atoms/mol) as a conversion factor. Avogadro's number provides the link between the molar amount and the number of entities (atoms, molecules).

For part (a) 3.70 moles of carbon atoms, the calculation is as follows:

1. Multiply the number of moles by Avogadro's number: 3.70 moles × 6.022 × 1023 atoms/mole.
2. This gives us the number of carbon atoms: 2.22814 × 1024 atoms.
3. However, we need to round this value to three significant figures, resulting in 2.23 × 1024 atoms (answer to a).

For part (b) 8.20 moles of carbon atoms, the calculation is as follows:

1. Multiply the number of moles by Avogadro's number: 8.20 moles × 6.022 × 1023 atoms/mole.
2. This gives us the number of carbon atoms: 4.93804 × 1024 atoms.
3. Again, rounding this value to three significant figures gives us 4.94 × 1024 atoms (answer to b).

Notice that we are rounding off to three significant figures since Avogadro's number itself is given with three significant figures.