Answer :
To determine how many oxygen molecules are present in 113.97 liters of oxygen gas at STP (Standard Temperature and Pressure), we can follow these steps:
1. Identify the volume of the gas and standard molar volume at STP:
- Volume of oxygen: 113.97 liters.
- Standard molar volume of an ideal gas at STP: 22.4 liters per mole.
2. Calculate the number of moles of oxygen:
- The number of moles of a gas is calculated by dividing the volume of the gas by the standard molar volume.
[tex]\[ \text{Moles of oxygen} = \frac{\text{Volume of oxygen}}{\text{Standard molar volume}} = \frac{113.97 \text{ liters}}{22.4 \text{ liters/mole}} = 5.087946428571429 \text{ moles} \][/tex]
3. Use Avogadro's number to find the number of molecules:
- Avogadro's number is \(6.022 \times 10^{23}\), which represents the number of molecules in one mole of a substance.
[tex]\[ \text{Number of molecules} = \text{Moles of oxygen} \times \text{Avogadro's number} = 5.087946428571429 \text{ moles} \times 6.022 \times 10^{23} \, \text{molecules/mole} \][/tex]
4. Calculate the total number of molecules:
- This multiplication gives:
[tex]\[ 5.087946428571429 \text{ moles} \times 6.022 \times 10^{23} = 3.0639613392857147 \times 10^{24} \text{ molecules} \][/tex]
Thus, the number of oxygen molecules present in 113.97 liters of oxygen gas at STP is approximately \( 3.064 \times 10^{24} \).
The correct answer is:
C. [tex]\( 3.064 \times 10^{24} \)[/tex]
1. Identify the volume of the gas and standard molar volume at STP:
- Volume of oxygen: 113.97 liters.
- Standard molar volume of an ideal gas at STP: 22.4 liters per mole.
2. Calculate the number of moles of oxygen:
- The number of moles of a gas is calculated by dividing the volume of the gas by the standard molar volume.
[tex]\[ \text{Moles of oxygen} = \frac{\text{Volume of oxygen}}{\text{Standard molar volume}} = \frac{113.97 \text{ liters}}{22.4 \text{ liters/mole}} = 5.087946428571429 \text{ moles} \][/tex]
3. Use Avogadro's number to find the number of molecules:
- Avogadro's number is \(6.022 \times 10^{23}\), which represents the number of molecules in one mole of a substance.
[tex]\[ \text{Number of molecules} = \text{Moles of oxygen} \times \text{Avogadro's number} = 5.087946428571429 \text{ moles} \times 6.022 \times 10^{23} \, \text{molecules/mole} \][/tex]
4. Calculate the total number of molecules:
- This multiplication gives:
[tex]\[ 5.087946428571429 \text{ moles} \times 6.022 \times 10^{23} = 3.0639613392857147 \times 10^{24} \text{ molecules} \][/tex]
Thus, the number of oxygen molecules present in 113.97 liters of oxygen gas at STP is approximately \( 3.064 \times 10^{24} \).
The correct answer is:
C. [tex]\( 3.064 \times 10^{24} \)[/tex]
