A gas mixture contains 0.700 mol of N2, 0.300 mol of H2, and 0.400 mol of CH4. Calculate the pressure of the gas mixture and the partial pressure of each constituent gas if the mixture is in a 8.00 L vessel at 27.00°C

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12-03-2020
Chemistry

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A gas mixture contains 0.700 mol of N2, 0.300 mol of H2, and 0.400 mol of CH4. Calculate the pressure of the gas mixture and the partial pressure of each constituent gas if the mixture is in a 8.00 L vessel at 27.00°C

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anfabba15 anfabba15 · Answer 1 · 2020-03-13T16:12:12+01:00

Answer:

Pressure of the gas mixture: 4.30 atm

Partial pressure N₂ = 2.15 atm

Partial pressure H₂ = 0.91 atm

Partial pressure CH₄ = 1.23 atm

Explanation:

To determine partial pressure we sum the total moles in order to find out the total pressure

We can work with mole fraction

We apply the Ideal Gases Law

0.700 N₂ + 0.300 H₂ + 0.400 CH₄ = 1.4 moles

We replace data → P . V = n . R .T

T° must be at K → 27 °C + 273 = 300 K

P . 8 L = 1.4 mol . 0.082 L.atm/mol.K . 300 K

P = ( 1.4 mol . 0.082 L.atm/mol.K . 300 K) / 8 L = 4.30 atm (Total pressure)

We apply the mol the fraction for the partial pressure

Moles x gas / total moles = partial pressure x gas / total pressure

Mole fraction N₂ → 0.700 /1.4 = 0.5

Partial pressure N₂ = 0.5 . 4.30 atm =2.15 atm

Mole fraction H₂ → 0.300 / 1.4 = 0.21

Partial pressure H₂ = 0.21 . 4.30 atm = 0.91 atm

Mole fraction CH₄ → 0.400 /1.4 = 0.28

Partial pressure CH₄ = 0.28 . 4.30 atm =1.23 atm

Eduard22sly Eduard22sly · Answer 2 · 2021-12-02T14:21:37+01:00

A. The pressure of the gas mixture is 4.31 atm

B. The partial pressure of N₂ is 2.16 atm

C. The partial pressure of H₂ is 0.92 atm

D. The partial pressure of CH₄ is 1.23 atm

A. Determination of the pressure of the gas mixture

Mole of N₂ = 0.7 mole

Mole of H₂ = 0.3 mole

Mole of CH₄ = 0.4 mole

Total mole (n) = 0.7 + 0.3 + 0.4 = 1.4 mole

Volume (V) = 8 L

Temperature (T) = 27 °C = 27 + 273 = 300 K

Gas constant (R) = 0.0821 atm.L/Kmol

Pressure (P) =?

PV = nRT

P × 8 = 1.4 × 0.0821 × 300

P × 8 = 34.482

Divide both side by 8

P = 34.482 / 8

P = 4.31 atm

Thus, the pressure of the gas mixture is 4.31 atm

B. Determination of the partial pressure of N₂

Total mole = 1.4 mole

Total pressure = 4.31 atm

Mole of N₂ = 0.7 mole

Partial pressure of N₂ =?

[tex]partial \: pressure = \frac{mole}{total \: mole} \times total \: pressure \\ \\ = \frac{0.7}{1.4} \times 4.31 \\ \\ [/tex]

Partial pressure of N₂ = 2.16 atm

C. Determination of the partial pressure of H₂

Mole of H₂ = 0.3 mole

Total mole = 1.4 mole

Total pressure = 4.31 atm

Partial pressure of H₂ =?

[tex]partial \: pressure = \frac{mole}{total \: mole} \times total \: pressure \\ \\ = \frac{0.3}{1.4} \times 4.31 \\ \\ [/tex]

Partial pressure of H₂ = 0.92 atm

D. Determination of the partial pressure of CH₄

Partial pressure of N₂ = 2.16 atm

Partial pressure of H₂ = 0.92 atm

Total pressure = 4.31 atm

Partial pressure of CH₄ =?

Partial pressure of CH₄ = Total pressure – (Partial of N₂ + Partial pressure of H₂

Partial pressure of CH₄ = 4.31 – (2.16 + 0.92)

Partial pressure of CH₄ = 1.23 atm

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