Answer:
The final volume of the sample of gas is 36.287 liters.
Explanation:
Let suppose that sample of gas is a closed system, that is, a system with no mass interactions with surroundings, and gas is represented by the equation of state for ideal gases, which is described below:
(1)
Where:
- Pressure, in atmospheres.
- Volume, in liters.
- Molar quantity, in moles.
- Temperature, in Kelvin.
- Ideal gas constant, in atmosphere-liters per mole-Kelvin.
As we know that sample of gas experiments an isobaric process, we can determine the final volume by the following relationship:
(2)
Where:
- Initial volume, in liters.
- Final volume, in liters.
- Initial temperature, in Kelvin.
- Final temperature, in Kelvin.
If we know that
,
and
, then the final volume of the gas is:
![V_{2} = V_{1}\cdot \left(\frac{T_{2}}{T_{1}} \right)](https://tex.z-dn.net/?f=V_%7B2%7D%20%3D%20V_%7B1%7D%5Ccdot%20%5Cleft%28%5Cfrac%7BT_%7B2%7D%7D%7BT_%7B1%7D%7D%20%5Cright%29)
![V_{2} = 33\,L \times \frac{320.15\,K}{291.15\,K}](https://tex.z-dn.net/?f=V_%7B2%7D%20%3D%2033%5C%2CL%20%5Ctimes%20%5Cfrac%7B320.15%5C%2CK%7D%7B291.15%5C%2CK%7D)
![V_{2} = 36.287\,L](https://tex.z-dn.net/?f=V_%7B2%7D%20%3D%2036.287%5C%2CL)
The final volume of the sample of gas is 36.287 liters.