Considering the Dalton's partial pressure, the partial pressure of nitrogen and oxygen is 3.634 atm and 0.966 atm respectively.
The pressure exerted by a particular gas in a mixture is known as its partial pressure.
So, Dalton's law states that the total pressure of a gas mixture is equal to the sum of the pressures that each gas would exert if it were alone:
[tex]P_{T} =P_{1} +P_{2} +...+P_{n}[/tex]
where n is the amount of gases.
Dalton's partial pressure law can also be expressed in terms of the mole fraction of the gas in the mixture.
The mole fraction is a dimensionless quantity that expresses the ratio of the number of moles of a component to the number of moles of all the components present:
[tex]x_{A} =\frac{n_{A} }{n_{total} }[/tex]
So in a mixture of two or more gases, the partial pressure of gas A can be expressed as:
[tex]P_{A} =x_{A} P_{T}[/tex]
In this case, the mixture contains 5.4 mol of nitrogen and 1.4 mol of oxygen. So, the total number of moles of all the components present is 5.4 moles + 1.4 moles= 6.8 moles.
Then, the mole fraction of each gas can be calculated as:
So, being 4.6 atm the total pressure of the gas mixture, the partial pressure of each gas can be calculated as:
[tex]P_{nitrogen} =x_{nitrogen} P_{T}[/tex]= 0.79× 4.6 atm= 3.634 atm
[tex]P_{oxygen} =x_{oxygen} P_{T}[/tex]= 0.21× 4.6 atm= 0.966 atm
In summary, the partial pressure of nitrogen and oxygen is 3.634 atm and 0.966 atm respectively.
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