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During the fermentation of a sample of glucose, the evolved gas had a volume of 0.75 L at 20.0 °C
and 1.01 atm. What is the final volume of this gas at 36.5 °C and 1.0 atm?


Sagot :

Given:

[tex]P_{1} = \text{1.01 atm}[/tex]

[tex]T_{1} = \text{20.0°C + 273.15 = 293.15 K}[/tex]

[tex]V_{1} = \text{0.75 L}[/tex]

[tex]P_{2} = \text{1.0 atm}[/tex]

[tex]T_{2} = \text{36.5°C + 273.15 = 309.65 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{0.75 L} × \frac{\text{1.01 atm}}{\text{1.0 atm}} × \frac{\text{309.65 K}}{\text{293.15 K}}[/tex]

[tex]\boxed{V_{2} = \text{0.80 L}}[/tex]

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