To determine how many moles of [tex]\( O_2 \)[/tex] are in a container with a volume of 67 liters at Standard Temperature and Pressure (STP), we can use the concept of molar volume.
At STP, the molar volume of any ideal gas is 22.4 liters per mole. This means that one mole of an ideal gas occupies 22.4 liters.
Given:
- Volume of the gas, [tex]\( V = 67 \)[/tex] liters
- Molar volume at STP, [tex]\( V_m = 22.4 \)[/tex] liters/mole
To find the number of moles of oxygen gas ([tex]\( O_2 \)[/tex]), we use the formula:
[tex]\[ \text{Number of moles} = \frac{\text{Volume of gas}}{\text{Molar volume at STP}} \][/tex]
Substituting the given values:
[tex]\[ \text{Number of moles of } O_2 = \frac{67 \text{ liters}}{22.4 \text{ liters/mole}} \][/tex]
Performing the division:
[tex]\[ \text{Number of moles of } O_2 \approx 2.991071428571429 \][/tex]
Therefore, there are approximately 2.991 moles of [tex]\( O_2 \)[/tex] in a container with a volume of 67 liters at STP.
