<u>Answer:</u> The mole fraction of Helium is 0.978 and that of oxygen gas is 0.022
<u>Explanation:</u>
To calculate the number of moles, we use the equation:
.....(1)
Given mass of helium = 23 g
Molar mass of helium = 4 g/mol
Putting values in equation 1, we get:
![\text{Moles of helium}=\frac{23g}{4g/mol}=5.75mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20helium%7D%3D%5Cfrac%7B23g%7D%7B4g%2Fmol%7D%3D5.75mol)
Given mass of oxygen gas = 4.14 g
Molar mass of oxygen gas = 32 g/mol
Putting values in equation 1, we get:
![\text{Moles of oxygen gas}=\frac{4.14g}{32g/mol}=0.129mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20oxygen%20gas%7D%3D%5Cfrac%7B4.14g%7D%7B32g%2Fmol%7D%3D0.129mol)
Mole fraction of a substance is given by:
![\chi_A=\frac{n_A}{n_A+n_B}](https://tex.z-dn.net/?f=%5Cchi_A%3D%5Cfrac%7Bn_A%7D%7Bn_A%2Bn_B%7D)
Moles of helium = 5.75 moles
Total moles = [5.75 + 0.129] = 5.879 moles
Putting values in above equation, we get:
![\chi_{(He)}=\frac{5.75}{5.879}=0.978](https://tex.z-dn.net/?f=%5Cchi_%7B%28He%29%7D%3D%5Cfrac%7B5.75%7D%7B5.879%7D%3D0.978)
Moles of oxygen gas = 0.129 moles
Total moles = [5.75 + 0.129] = 5.879 moles
Putting values in above equation, we get:
![\chi_{(O_2)}=\frac{0.129}{5.879}=0.022](https://tex.z-dn.net/?f=%5Cchi_%7B%28O_2%29%7D%3D%5Cfrac%7B0.129%7D%7B5.879%7D%3D0.022)
Hence, the mole fraction of Helium is 0.978 and that of oxygen gas is 0.022