To determine the number of chlorine molecules in 6.5 moles of chlorine, we should use Avogadro's number, which is approximately [tex]\(6.022 \times 10^{23}\)[/tex] molecules per mole. Here’s a step-by-step approach to solving this problem:
1. Identify the given values:
- Number of moles of chlorine ([tex]\( \text{Cl}_2 \)[/tex]): 6.5 moles
- Avogadro's number: [tex]\(6.022 \times 10^{23}\)[/tex] molecules per mole
2. Compute the total number of chlorine molecules:
- Multiply the number of moles by Avogadro's number:
[tex]\[
\text{Number of molecules} = \text{moles} \times \text{Avogadro's number}
\][/tex]
[tex]\[
\text{Number of molecules} = 6.5 \times 6.022 \times 10^{23}
\][/tex]
3. Calculate the product:
- First, calculate the product of the numerical values:
[tex]\[
6.5 \times 6.022 = 39.143
\][/tex]
- Then, incorporate the power of [tex]\(10\)[/tex]:
[tex]\[
39.143 \times 10^{23}
\][/tex]
4. Express the result in scientific notation:
- To convert [tex]\(39.143 \times 10^{23}\)[/tex] into proper scientific notation ([tex]\(a \times 10^b\)[/tex], where [tex]\(1 \leq a < 10\)[/tex]):
[tex]\[
39.143 = 3.9143 \times 10^1
\][/tex]
- Therefore, multiplying this by [tex]\(10^{23}\)[/tex]:
[tex]\[
3.9143 \times 10^1 \times 10^{23} = 3.9143 \times 10^{24}
\][/tex]
5. Final answer:
- The number of chlorine molecules in 6.5 moles of chlorine is:
[tex]\[
3.9143 \times 10^{24}
\][/tex]
So, the prefix is [tex]\(3.9143\)[/tex] and the exponent is [tex]\(24\)[/tex].
