To find the number of molecules of oxygen gas in a gas cylinder containing exactly 1 mole of [tex]\( O_2 \)[/tex], we should use Avogadro's number. Avogadro's number provides the number of atoms or molecules in one mole of a substance.
Avogadro's number is approximately [tex]\( 6.02 \times 10^{23} \)[/tex]. This means that one mole of any substance, including oxygen gas, contains approximately [tex]\( 6.02 \times 10^{23} \)[/tex] molecules.
Since the question states that the cylinder contains exactly 1 mole of oxygen gas ([tex]\( O_2 \)[/tex]), the number of [tex]\( O_2 \)[/tex] molecules in the cylinder is simply Avogadro's number:
[tex]\[
\text{Number of molecules} = 6.02 \times 10^{23}
\][/tex]
Thus, the correct answer is:
[tex]\[
6.02 \times 10^{23} \text{ molecules}
\][/tex]
Therefore, the answer is:
[tex]\[
\boxed{6.02 \times 10^{23} \text{ molecules}}
\][/tex]
