To solve for the volume [tex]\( V \)[/tex] of an ideal gas using the ideal gas law [tex]\( PV = nRT \)[/tex], we need to rearrange the equation to solve for [tex]\( V \)[/tex]:
[tex]\[ V = \frac{nRT}{P} \][/tex]
Let's plug in the given values:
- [tex]\( P \)[/tex] (Pressure) = 200 kPa
- [tex]\( n \)[/tex] (Number of moles) = 0.200 mol
- [tex]\( R \)[/tex] (Ideal gas constant) = 8.314 \frac{L \cdot kPa}{mol \cdot K}
- [tex]\( T \)[/tex] (Temperature) = 400 K
Now, substitute these values into the equation:
[tex]\[ V = \frac{0.200 \, \text{mol} \times 8.314 \, \frac{L \cdot kPa}{mol \cdot K} \times 400 \, K}{200 \, kPa} \][/tex]
Perform the multiplication and division:
[tex]\[ V = \frac{0.200 \times 8.314 \times 400}{200} \][/tex]
[tex]\[ V = \frac{665.12}{200} \][/tex]
[tex]\[ V = 3.3256 \, L \][/tex]
Therefore, the volume of the gas is approximately:
[tex]\[ V = 3.33 \, L \][/tex]
So, the correct answer is:
[tex]\[ \boxed{3.33 \, L} \][/tex]
