To determine the pressure of the gas using the ideal gas law, we will use the formula:
[tex]\[ PV = nRT \][/tex]
Where:
- [tex]\( P \)[/tex] is the pressure in kPa,
- [tex]\( V \)[/tex] is the volume in liters,
- [tex]\( n \)[/tex] is the number of moles,
- [tex]\( R \)[/tex] is the ideal gas constant ([tex]\( 8.314 \frac{L \cdot kPa}{mol \cdot K} \)[/tex]),
- [tex]\( T \)[/tex] is the temperature in Kelvin.
Given the variables in the problem:
- [tex]\( n = 0.540 \)[/tex] moles,
- [tex]\( V = 35.5 \)[/tex] liters,
- [tex]\( T = 223 \)[/tex] Kelvin,
- [tex]\( R = 8.314 \frac{L \cdot kPa}{mol \cdot K} \)[/tex],
We need to solve for [tex]\( P \)[/tex]. The ideal gas law rearranged to solve for [tex]\( P \)[/tex] is:
[tex]\[ P = \frac{nRT}{V} \][/tex]
Substitute the given values into the equation:
[tex]\[ P = \frac{0.540 \, \text{mol} \times 8.314 \frac{L \cdot kPa}{mol \cdot K} \times 223 \, \text{K}}{35.5 \, \text{L}} \][/tex]
Calculate the numerator:
[tex]\[ (0.540 \, \text{mol}) \times (8.314 \frac{L \cdot kPa}{mol \cdot K}) \times (223 \, \text{K}) = 1001.736564 \, \text{kPa} \cdot \text{L} \][/tex]
And then divide by the volume:
[tex]\[ P = \frac{1001.736564 \, \text{kPa} \cdot \text{L}}{35.5 \, \text{L}} \approx 28.202 \, \text{kPa} \][/tex]
Therefore, the pressure of the gas is:
[tex]\[ P \approx 28.2 \, \text{kPa} \][/tex]
So, the correct answer is:
[tex]\[ 28.2 \, \text{kPa} \][/tex]
