Certainly! Let's solve this problem step-by-step using the ideal gas law equation:
The ideal gas law is given by:
[tex]\[ P V = n R T \][/tex]
where:
- [tex]\( P \)[/tex] is the pressure of the gas.
- [tex]\( V \)[/tex] is the volume of the gas.
- [tex]\( n \)[/tex] is the number of moles of the gas.
- [tex]\( R \)[/tex] is the ideal gas constant.
- [tex]\( T \)[/tex] is the temperature of the gas in Kelvin.
Here are the given values:
- [tex]\( n = 0.540 \)[/tex] moles
- [tex]\( V = 35.5 \)[/tex] liters
- [tex]\( T = 223 \)[/tex] K
- The ideal gas constant, [tex]\( R = 8.314 \frac{L \cdot kPa}{mol \cdot K} \)[/tex]
We need to find the pressure [tex]\( P \)[/tex].
Rearrange the ideal gas law equation to solve for [tex]\( P \)[/tex]:
[tex]\[ P = \frac{n R T}{V} \][/tex]
Substitute the given values into the equation:
[tex]\[ P = \frac{0.540 \times 8.314 \times 223}{35.5} \][/tex]
Calculate the numerator:
[tex]\[ 0.540 \times 8.314 \times 223 = 1003.24892 \][/tex]
Calculate the pressure [tex]\( P \)[/tex]:
[tex]\[ P = \frac{1003.24892}{35.5} \approx 28.202024788732395 \, kPa \][/tex]
Rounded to one decimal place, the pressure is:
[tex]\[ P \approx 28.2 \, kPa \][/tex]
Thus, the pressure of the gas is:
[tex]\[ \boxed{28.2 \, kPa} \][/tex]
