A student has a 2.66 L bottle that contains a mixture of O2 , N2 , and CO2 with a total pressure of 4.50 bar at 298 K . She knows that the mixture contains 0.297 mol N2 and that the partial pressure of CO2 is 0.269 bar . Calculate the partial pressure of O2 .

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priya678 priya678 · Answer 1 · 2020-04-25T18:16:32+02:00

Answer:

The partial pressure of [tex]O_{2} = 1.455[/tex] bar.

Explanation:

Given:

Volume [tex]V = 2.66[/tex] L

Total pressure [tex]P_{} = 4.50[/tex] bar

Temperature of system [tex]T = 298[/tex] K

Moles of nitrogen [tex]n = 0.297[/tex] mole

Partial pressure [tex]P_{co_{2} } = 0.269[/tex] bar

From ideal gas equation,

[tex]PV = nRT[/tex]

Where [tex]R = 8.314 \times 10^{-2} \frac{L .bar}{K.mol}[/tex] = gas constant

First finding partial pressure of nitrogen

[tex]P_{N_{2} } = \frac{nRT}{V}[/tex]

[tex]P_{N_{2} } = \frac{0.297\times 8.314 \times 10^{-2} \times 298}{2.66}[/tex]

[tex]P_{N_{2} } = 2.766[/tex] bar

We know, total pressure is given by

[tex]P = P_{O_{2} } + P_{N_{2} } + P_{CO_{2} }[/tex]

[tex]P_{O_{2} } = 4.50 - 0.269 - 2.776[/tex]

[tex]P_{O_{2} } =1.455[/tex] bar

Therefore, the partial pressure of [tex]O_{2} = 1.455[/tex] bar.