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500.0 liters of a gas in a flexible-walled container are prepared at 700.0 mmHg and 200.0°C The gas is placed into a tank under high pressure When the tank cools to 20.0°C. the pressure of the gas is 30.0 mmHg What is the volume of the gas?

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Sagot :

Given:

[tex]P_{1} = \text{700.0 mmHg}[/tex]

[tex]T_{1} = \text{200.0°C + 273.15 = 473.15 K}[/tex]

[tex]V_{1} = \text{500.0 L}[/tex]

[tex]P_{2} = \text{30.0 mmHg}[/tex]

[tex]T_{2} = \text{20.0°C + 273 = 293.15 K}[/tex]

Unknown:

[tex]V_{2}[/tex]

Solution:

[tex]\frac{P_{1}V_{1}}{T_{1}} = \frac{P_{2}V_{2}}{T_{2}}[/tex]

[tex]V_{2} = V_{1} × \frac{P_{1}}{P_{2}} × \frac{T_{2}}{T_{1}}[/tex]

[tex]V_{2} = \text{500.0 L} × \frac{\text{700.0 mmHg}}{\text{30.0 mmHg}} × \frac{\text{293.15 K}}{\text{473.15 K}}[/tex]

[tex]\boxed{V_{2} = \text{7228 L}}[/tex]

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