Respuesta :
Answer: The mole fraction of Helium is 0.978 and that of oxygen gas is 0.022
Explanation:
To calculate the number of moles, we use the equation:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex] .....(1)
- For helium:
Given mass of helium = 23 g
Molar mass of helium = 4 g/mol
Putting values in equation 1, we get:
[tex]\text{Moles of helium}=\frac{23g}{4g/mol}=5.75mol[/tex]
- For oxygen gas:
Given mass of oxygen gas = 4.14 g
Molar mass of oxygen gas = 32 g/mol
Putting values in equation 1, we get:
[tex]\text{Moles of oxygen gas}=\frac{4.14g}{32g/mol}=0.129mol[/tex]
Mole fraction of a substance is given by:
[tex]\chi_A=\frac{n_A}{n_A+n_B}[/tex]
- For helium:
Moles of helium = 5.75 moles
Total moles = [5.75 + 0.129] = 5.879 moles
Putting values in above equation, we get:
[tex]\chi_{(He)}=\frac{5.75}{5.879}=0.978[/tex]
- For oxygen gas:
Moles of oxygen gas = 0.129 moles
Total moles = [5.75 + 0.129] = 5.879 moles
Putting values in above equation, we get:
[tex]\chi_{(O_2)}=\frac{0.129}{5.879}=0.022[/tex]
Hence, the mole fraction of Helium is 0.978 and that of oxygen gas is 0.022
Considering the definition of mole fraction and molar mass, the mole fraction of He and O₂ in the mixture is 0.978 and 0.022 respectively.
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.
The mole fraction of a gas in a gas mixture is given by:
[tex]x_{A} =\frac{n_{A} }{n_{T} }[/tex]
This fraction will always be less than 1.
On the other side, the molar mass is the amount of mass that a substance contains in one mole. This is:
[tex]molar mass=\frac{mass}{number of moles}[/tex]
Then, the number of moles can be calculated as:
[tex]number of moles=\frac{mass}{molar mass}[/tex]
In this case, you know:
- Mass of helium = 23 g
- Molar mass of helium = 4 g/mol
- Mass of oxygen gas = 4.14 g
- Molar mass of oxygen gas = 32 g/mol
So, the number of moles of each gas can be calculated as:
- Helium: [tex]number of moles of helium=\frac{23 g}{4 \frac{g}{mole} }= 5.75 moles[/tex]
- Oxygen: [tex]number of moles of oxygen=\frac{4.14 g}{32 \frac{g}{mole} }= 0.129 moles[/tex]
Being the total moles of moles 5.879 moles (5.75 moles of helium + 0.129 moles of oxygen), the mole fraction of each gas can be calculated as:
- [tex]x_{He} =\frac{n_{He} }{n_{T} }=\frac{5.75 moles}{5.879 moles} =[/tex] 0.978
- [tex]x_{O_{2} } =\frac{n_{O_{2} } }{n_{T} }=\frac{0.129 moles}{5.879 moles} =[/tex] 0.022
Finally, the mole fraction of He and O₂ in the mixture is 0.978 and 0.022 respectively.
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