Answer:
0.343
Explanation:
Step 1: Given data
Step 2: Calculate the partial pressure of Kr
The total pressure of the mixture is equal to the sum of the partial pressures of the individual gases.
P = pXe + pAr + pKr
pKr = P - pXe - pAr
pKr = 6.70 atm - 1.60 atm - 2.80 atm
pKr = 2.30 atm
Step 3: Calculate the mole fraction of Kr
We will use the following expression.
X(Kr) = pKr/P
X(Kr) = 2.30 atm/6.70 atm
X(Kr) = 0.343
Considering the Dalton's partial pressure, the mole fraction of Kr is 0.34.
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 number of gases.
This relationship is due to the assumption that there are no attractive forces between the gases.
Dalton's partial pressure law can also be expressed in terms of the mole fraction of the gas in the mixture.
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, you know:
So, replacing in the Dalton's partial pressure law:
[tex]P_{T} =P_{Xe} +P_{Ar} +P_{Kr}[/tex]
6.70 atm= 1.60 atm + 2.80 atm + [tex]P_{Kr}[/tex]
6.70 atm- 1.60 atm- 2.80 atm= [tex]P_{Kr}[/tex]
2.30 atm=[tex]P_{Kr}[/tex]
Then: [tex]P_{Kr} =x_{Kr} P_{T}[/tex]
2.30 atm= [tex]x_{Kr}[/tex] 6.70 atm
[tex]x_{Kr}[/tex] =2.30 atm ÷6.70 atm
[tex]x_{Kr}[/tex] = 0.34
In summary, the mole fraction of Kr is 0.34.
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