Respuesta :
Answer:
Volume of the gas at 500 mm Hg pressure is 960 [tex]cm^{3}[/tex]
Explanation:
Let's assume the gas behaves ideally.
According to combined gas law for an ideal gas-
[tex]\frac{P_{1}V_{1}}{T_{1}}=\frac{P_{2}V_{2}}{T_{2}}[/tex]
Where [tex]P_{1}[/tex] and [tex]P_{2}[/tex] are initial and final pressure of the gas respectively. [tex]V_{1}[/tex] and [tex]V_{2}[/tex] are initial and final volume of the gas respectively. [tex]T_{1}[/tex] and [tex]T_{2}[/tex] are initial and final temperature of the gas in kelvin respectively.
Here [tex]T_{1}[/tex] = [tex]T_{2}[/tex], [tex]V_{1}[/tex] = 1200 [tex]cm^{3}[/tex], [tex]P_{1}[/tex] = 400 mm Hg, [tex]P_{2}[/tex] = 500 mm Hg
So, [tex]V_{2}=\frac{P_{1}V_{1}T_{2}}{T_{1}P_{2}}[/tex]
Hence [tex]V_{2}=\frac{400\times 1200}{500}[tex]cm^{3}[/tex]=960 [tex]cm^{3}[/tex][/tex]
Hence volume of the gas at 500 mm Hg pressure is 960 [tex]cm^{3}[/tex]
Considering the Boyle's law, when the pressure is 500 mmHg, the volume is 960 cm³.
The gas laws are a set of chemical and physical laws that allow determining the behavior of gases in a closed system. The parameters evaluated in these laws are pressure, volume, temperature and moles.
Boyle's law is one of the gas laws that states that the pressure of a gas in a closed container is inversely proportional to the volume of the container, when the temperature is constant.
Boyle's law is expressed mathematically as:
P× V = k
That is, the product of pressure and volume is a constant value.
Studying two different states, an initial state 1 and a final state 2, it is satisfied:
P1× V1= P2× V2
In this case, you know:
- P1= 400 mmHg
- V1= 1200 cm³
- P2= 500 mmHg
- V2= ?
Replacing:
400 mmHg× 1200 cm³= 500 mmHg× V2
Solving:
[tex]V2=\frac{400 mmHg x1200 cm^{3} }{500 mmHg}[/tex]
V2=960 cm³
Finally, when the pressure is 500 mmHg, the volume is 960 cm³.
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