To determine the number of molecules in 6.0 moles of methane (CH₄), we use Avogadro's number, which is [tex]\(6.022 \times 10^{23}\)[/tex] molecules per mole. Here's the step-by-step solution:
1. Determine the given values:
- Moles of methane: [tex]\(6.0 \text{ moles}\)[/tex]
- Avogadro's number: [tex]\(6.022 \times 10^{23} \text{ molecules/mole}\)[/tex]
2. Set up the calculation for the number of molecules:
[tex]\[
\text{Number of molecules} = \text{moles of methane} \times \text{Avogadro's number}
\][/tex]
3. Plug in the values:
[tex]\[
\text{Number of molecules} = 6.0 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mole}
\][/tex]
4. Perform the multiplication:
[tex]\[
\text{Number of molecules} = 36.132 \times 10^{23} \text{ molecules}
\][/tex]
5. Express the result in scientific notation with the coefficient between 1 and 10:
[tex]\[
36.132 \times 10^{23} \text{ molecules} = 3.6132 \times 10^{24} \text{ molecules}
\][/tex]
6. Round to the correct number of significant figures:
Given that 6.0 moles has two significant figures, we should round our answer to two significant figures:
[tex]\[
3.6132 \times 10^{24} \approx 3.6 \times 10^{24}
\][/tex]
Final Answer:
[tex]\[
\boxed{3.6 \times 10^{24}}
\][/tex]
Upon extracting the coefficient and exponent, the number of molecules in 6.0 moles of methane (CH₄) is [tex]\(3.6 \times 10^{24}\)[/tex].
