The question is incomplete, here is the complete question:
Consider a mixture of two gases, A and B, confined in a closed vessel. A quantity of a third gas, C, is added to the same vessel at the same temperature. How does the addition of gas C affect the following. The mole fraction of gas B?
A mixture of gases contains 10.25 g of N₂, 2.05 g of H₂, and 7.63 g of NH₃.
<u>Answer:</u> The mole fraction of gas B (hydrogen gas) is 0.557
<u>Explanation:</u>
To calculate the number of moles, we use the equation:
.....(1)
Given mass of nitrogen gas = 10.25 g
Molar mass of nitrogen gas = 28 g/mol
Putting values in equation 1, we get:
![\text{Moles of nitrogen gas}=\frac{10.25g}{28g/mol}=0.366mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20nitrogen%20gas%7D%3D%5Cfrac%7B10.25g%7D%7B28g%2Fmol%7D%3D0.366mol)
Given mass of hydrogen gas = 2.05 g
Molar mass of hydrogen gas = 2 g/mol
Putting values in equation 1, we get:
![\text{Moles of hydrogen gas}=\frac{2.05g}{2g/mol}=1.025mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20hydrogen%20gas%7D%3D%5Cfrac%7B2.05g%7D%7B2g%2Fmol%7D%3D1.025mol)
Given mass of ammonia gas = 7.63 g
Molar mass of ammonia gas = 17 g/mol
Putting values in equation 1, we get:
![\text{Moles of ammonia gas}=\frac{7.63g}{17g/mol}=0.449mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20ammonia%20gas%7D%3D%5Cfrac%7B7.63g%7D%7B17g%2Fmol%7D%3D0.449mol)
Mole fraction of a substance is given by:
![\chi_A=\frac{n_A}{n_A+n_B+n_C}](https://tex.z-dn.net/?f=%5Cchi_A%3D%5Cfrac%7Bn_A%7D%7Bn_A%2Bn_B%2Bn_C%7D)
Moles of gas B (hydrogen gas) = 1.025 moles
Total moles = [0.366 + 1.025 + 0.449] = 1.84 moles
Putting values in above equation, we get:
![\chi_{(H_2)}=\frac{1.025}{1.84}=0.557](https://tex.z-dn.net/?f=%5Cchi_%7B%28H_2%29%7D%3D%5Cfrac%7B1.025%7D%7B1.84%7D%3D0.557)
Hence, the mole fraction of gas B (hydrogen gas) is 0.557