Answer:
The new volume of the gas is 0.332 liters.
Explanation:
Let suppose that argon behaves ideally, the equation of state of the ideal gas is:
![P\cdot V = n \cdot R_{u}\cdot T](https://tex.z-dn.net/?f=P%5Ccdot%20V%20%3D%20n%20%5Ccdot%20R_%7Bu%7D%5Ccdot%20T)
Where:
- Pressure, measured in torr.
- Volume, measured in liters.
- Molar quantity, measured in moles.
- Temperature, measured in kelvins.
- Ideal gas constant, measured in
.
Since gas sample is a closed system experimenting a heating process, that is, molar quantity remains constant, the following relationship is derived from the equation of state described above:
![\frac{P_{o}\cdot V_{o}}{T_{o}} = \frac{P_{f}\cdot V_{f}}{T_{f}}](https://tex.z-dn.net/?f=%5Cfrac%7BP_%7Bo%7D%5Ccdot%20V_%7Bo%7D%7D%7BT_%7Bo%7D%7D%20%3D%20%5Cfrac%7BP_%7Bf%7D%5Ccdot%20V_%7Bf%7D%7D%7BT_%7Bf%7D%7D)
Where:
,
- Initial and final pressures, measured in torr.
,
- Initial and final volumes, measured in liters.
,
- Initial and final temperatures, measured in kelvins.
Now, the final volume of the gas is found:
![V_{f} = \left(\frac{T_{f}}{T_{o}}\right)\cdot \left(\frac{P_{o}}{P_{f}} \right)\cdot V_{o}](https://tex.z-dn.net/?f=V_%7Bf%7D%20%3D%20%5Cleft%28%5Cfrac%7BT_%7Bf%7D%7D%7BT_%7Bo%7D%7D%5Cright%29%5Ccdot%20%5Cleft%28%5Cfrac%7BP_%7Bo%7D%7D%7BP_%7Bf%7D%7D%20%5Cright%29%5Ccdot%20V_%7Bo%7D)
If
,
,
,
and
, the new volume of the gas is:
![V_{f} = \left(\frac{429.15\,K}{286.15\,K} \right)\cdot \left(\frac{568\,torr}{897\,torr} \right)\cdot 0.35\,L](https://tex.z-dn.net/?f=V_%7Bf%7D%20%3D%20%5Cleft%28%5Cfrac%7B429.15%5C%2CK%7D%7B286.15%5C%2CK%7D%20%5Cright%29%5Ccdot%20%5Cleft%28%5Cfrac%7B568%5C%2Ctorr%7D%7B897%5C%2Ctorr%7D%20%5Cright%29%5Ccdot%200.35%5C%2CL)
![V_{f} = 0.332\,L](https://tex.z-dn.net/?f=V_%7Bf%7D%20%3D%200.332%5C%2CL)
The new volume of the gas is 0.332 liters.