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A mixture of N2, O2, and Ar has mole fractions of 0.25, 0.65, and 0.10, respectively. What is the pressure of N2 if the total pressure of the mixture is 3.9 bar?A. 0.67 barB. 1.33 barC. 0.98 barD. 0.39 barE. 2.5 bar

Answer :

Answer:

Partial pressure of nitrogen gas is 0.98 bar.

Explanation:

According to the Dalton's law, the total pressure of the gas is equal to the sum of the partial pressure of the mixture of gases.

[tex]P=p_{N_2}+p_{O_2}+p_{Ar}[/tex]

[tex]p_{N_2}=P\times \chi_{N_2}[/tex]

[tex]p_{O_2}=P\times \chi_{O_2}[/tex]

[tex]p_{Ar}=P\times \chi_{Ar}[/tex]

where,

[tex]P[/tex] = total pressure = 3.9 bar

[tex]p_{N_2}[/tex] = partial pressure of nitrogen gas  

[tex]p_{O_2}[/tex] = partial pressure of oxygen gas  

[tex]p_{Ar}[/tex] = partial pressure of argon gases  

[tex]\chi_{N_2}[/tex] = Mole fraction of nitrogen gas  = 0.25

[tex]\chi_{O_2}[/tex] = Mole fraction of oxygen gas  = 0.65

[tex]\chi_{Ar}[/tex] = Mole fraction of argon gases = 0.10

Partial pressure of nitrogen gas :

[tex]p_{N_2}=P\times \chi_{N_2}=3.9 bar\times 0.25 =0.98 bar[/tex]

Partial pressure of oxygen gas :

[tex]p_{N_2}=P\times \chi_{O_2}=3.9 bar\times 0.65=2.54 bar[/tex]

Partial pressure of argon gas :

[tex]p_{N_2}=P\times \chi_{Ar}=3.9 bar\times 0.10=0.39 bar[/tex]

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