Sure, let's work through the problem step by step:
1. Understand the Problem:
We need to calculate the number of moles of [tex]\( \text{O}_2 \)[/tex] gas when given a certain number of molecules. Specifically, we are given [tex]\( 7.11 \times 10^{24} \)[/tex] molecules of [tex]\( \text{O}_2 \)[/tex].
2. Recall Key Information:
To convert from molecules to moles, we use Avogadro's number. Avogadro's number is [tex]\( 6.022 \times 10^{23} \)[/tex], which is the number of molecules in one mole of any substance.
3. Set Up the Conversion:
We use the relationship:
[tex]\[
\text{Number of moles} = \frac{\text{Number of molecules}}{\text{Avogadro's number}}
\][/tex]
Plugging in the given values:
[tex]\[
\text{Number of moles of } \text{O}_2 = \frac{7.11 \times 10^{24} \text{ molecules}}{6.022 \times 10^{23} \text{ molecules per mole}}
\][/tex]
4. Perform the Calculation:
Dividing the number of molecules by Avogadro's number gives us the number of moles:
[tex]\[
\text{Number of moles of } \text{O}_2 = 11.806708734639654 \text{ moles}
\][/tex]
Thus, the number of moles of [tex]\( 7.11 \times 10^{24} \)[/tex] molecules of [tex]\( \text{O}_2 \)[/tex] gas is approximately [tex]\( 11.807 \)[/tex] moles.
