To determine the number of moles of chlorine in [tex]\(6.67 \times 10^{40}\)[/tex] chlorine molecules, we need to use Avogadro's number, which is approximately [tex]\(6.02214076 \times 10^{23}\)[/tex] molecules per mole. Here is the detailed step-by-step approach:
1. Identify the given values:
- Number of chlorine molecules: [tex]\(6.67 \times 10^{40}\)[/tex]
- Avogadro's number: [tex]\(6.02214076 \times 10^{23}\)[/tex] molecules per mole
2. Calculate the number of moles:
The number of moles can be calculated by dividing the number of molecules by Avogadro's number:
[tex]\[
\text{Number of moles} = \frac{6.67 \times 10^{40} \text{ molecules}}{6.02214076 \times 10^{23} \text{ molecules/mole}}
\][/tex]
3. Perform the division:
- Divide the coefficients: [tex]\( \frac{6.67}{6.02214076} \approx 1.11 \)[/tex]
- Subtract the exponents: [tex]\( 10^{40} \div 10^{23} = 10^{(40-23)} = 10^{17} \)[/tex]
This gives us:
[tex]\[
\text{Number of moles} \approx 1.11 \times 10^{17}
\][/tex]
4. Ensure the result is in proper scientific notation:
The prefix (or coefficient) is between 1 and 10, which it is in this case. Thus, our result remains [tex]\(1.11\)[/tex].
5. Write the final answer:
The number of moles of chlorine in [tex]\(6.67 \times 10^{40}\)[/tex] chlorine molecules is:
[tex]\[
1.11 \times 10^{17}
\][/tex]
This means there are [tex]\(1.11 \times 10^{17}\)[/tex] moles of chlorine.
