Answer :
Approximately 0.098 moles of oxygen will occupy a volume of 2.5 liters at 97.6 kPa and 25.0°C by using the ideal gas law formula and converting the temperature to Kelvin.
To determine how many moles of oxygen will occupy a volume of 2.5 liters at 97.6 kPa and 25.0°C, we can use the ideal gas law, which is represented by the equation:
- PV = nRT
Where:
- P = Pressure in kPa,
- V = Volume in liters,
- n = Number of moles,
- R = Ideal gas constant (8.314 L·kPa/(mol·K)),
- T = Temperature in Kelvin.
First, converting the temperature from °C to K:
- T(K) = 25.0°C + 273.15 = 298.15 K
Then, rearranging the ideal gas law to solve for number of moles:
- [tex]n = \frac{PV} {RT}[/tex]
Now, substitute in the given values:
- [tex]n = \frac{97.6 \, \text{kPa} \times 2.5 \, \text{L}}{8.314 \, \frac{\text{L} \cdot \text{kPa}}{\text{mol} \cdot \text{K}} \times 298.15 \, \text{K}}[/tex]
Simplify the equation:
- [tex]n = \frac{244 \, \text{kPa} \cdot \text{L}}{2480.2651 \, \frac{\text{L} \cdot \text{kPa}}{\text{mol} \cdot \text{K}}}[/tex]
- [tex]n \approx 0.098 \, \text{moles}[/tex]
Therefore, approximately 0.098 moles of oxygen will occupy a volume of 2.5 liters at 97.6 kPa and 25.0°C.