To determine the partial pressure of argon in the jar using the provided conditions, we apply the Ideal Gas Law equation:
[tex]\[ PV = nRT \][/tex]
Where:
- [tex]\( P \)[/tex] is the partial pressure of the gas,
- [tex]\( V \)[/tex] is the volume,
- [tex]\( n \)[/tex] is the number of moles,
- [tex]\( R \)[/tex] is the ideal gas constant, and
- [tex]\( T \)[/tex] is the temperature in Kelvin.
From the problem, we have:
- Volume, [tex]\( V = 25.0 \)[/tex] liters,
- Number of moles of argon, [tex]\( n = 0.0104 \)[/tex] moles,
- Temperature, [tex]\( T = 273 \)[/tex] Kelvin,
- Ideal gas constant, [tex]\( R = 8.314 \)[/tex] L[tex]\(\cdot\)[/tex]kPa/(mol[tex]\(\cdot\)[/tex]K).
We need to find the partial pressure of argon, [tex]\( P \)[/tex].
Rearranging the Ideal Gas Law to solve for [tex]\( P \)[/tex]:
[tex]\[ P = \frac{nRT}{V} \][/tex]
Plugging in the given values:
[tex]\[ P = \frac{0.0104 \times 8.314 \times 273}{25.0} \][/tex]
First, calculate the numerator:
[tex]\[ 0.0104 \times 8.314 = 0.0864656 \][/tex]
[tex]\[ 0.0864656 \times 273 = 23.6151136 \][/tex]
Then, calculate the pressure:
[tex]\[ P = \frac{23.6151136}{25.0} \approx 0.944 \][/tex]
Therefore, the partial pressure of argon in the jar is approximately [tex]\( 0.944 \)[/tex] kilopascals when rounded to three significant figures.
