<u>Answer:</u> The mass percent of nitrogen gas and hydrogen gas is 91.41 % and 8.59 % respectively.
<u>Explanation:</u>
To calculate the number of moles, we use the equation given by ideal gas equation:
PV = nRT
where,
P = Pressure of the gaseous mixture = 1.00 atm
V = Volume of the gaseous mixture = 24.62 L
n = number of moles of the gaseous mixture = ?
R = Gas constant = ![0.0821\text{ L atm }mol^{-1}K^{-1}](https://tex.z-dn.net/?f=0.0821%5Ctext%7B%20L%20atm%20%7Dmol%5E%7B-1%7DK%5E%7B-1%7D)
T = Temperature of the gaseous mixture = 300 K
Putting values in above equation, we get:
![1.00atm\times 24.62L=n_{mix}\times 0.0821\text{ L atm }mol^{-1}K^{-1}\times 300K\\\\n_{mix}=\frac{1.00\times 24.62}{0.0821\times 300}=0.9996mol](https://tex.z-dn.net/?f=1.00atm%5Ctimes%2024.62L%3Dn_%7Bmix%7D%5Ctimes%200.0821%5Ctext%7B%20L%20atm%20%7Dmol%5E%7B-1%7DK%5E%7B-1%7D%5Ctimes%20300K%5C%5C%5C%5Cn_%7Bmix%7D%3D%5Cfrac%7B1.00%5Ctimes%2024.62%7D%7B0.0821%5Ctimes%20300%7D%3D0.9996mol)
We are given:
Total mass of the mixture = 13.22 grams
Let the mass of nitrogen gas be 'x' grams and that of hydrogen gas be '(13.22 - x)' grams
To calculate the number of moles, we use the equation:
![\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}](https://tex.z-dn.net/?f=%5Ctext%7BNumber%20of%20moles%7D%3D%5Cfrac%7B%5Ctext%7BGiven%20mass%7D%7D%7B%5Ctext%7BMolar%20mass%7D%7D)
<u>For nitrogen gas:</u>
Molar mass of nitrogen gas = 28 g/mol
![\text{Moles of nitrogen gas}=\frac{x}{28}mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20nitrogen%20gas%7D%3D%5Cfrac%7Bx%7D%7B28%7Dmol)
<u>For hydrogen gas:</u>
Molar mass of hydrogen gas = 2 g/mol
![\text{Moles of hydrogen gas}=\frac{(13.22-x)}{2}mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20hydrogen%20gas%7D%3D%5Cfrac%7B%2813.22-x%29%7D%7B2%7Dmol)
Equating the moles of the individual gases to the moles of mixture:
![0.9996=\frac{x}{28}+\frac{(13.22-x)}{2}\\\\x=12.084g](https://tex.z-dn.net/?f=0.9996%3D%5Cfrac%7Bx%7D%7B28%7D%2B%5Cfrac%7B%2813.22-x%29%7D%7B2%7D%5C%5C%5C%5Cx%3D12.084g)
To calculate the mass percentage of substance in mixture we use the equation:
![\text{Mass percent of substance}=\frac{\text{Mass of substance}}{\text{Mass of mixture}}\times 100](https://tex.z-dn.net/?f=%5Ctext%7BMass%20percent%20of%20substance%7D%3D%5Cfrac%7B%5Ctext%7BMass%20of%20substance%7D%7D%7B%5Ctext%7BMass%20of%20mixture%7D%7D%5Ctimes%20100)
Mass of the mixture = 13.22 g
Mass of nitrogen gas = x = 12.084 g
Putting values in above equation, we get:
![\text{Mass percent of nitrogen gas}=\frac{12.084g}{13.22g}\times 100=91.41\%](https://tex.z-dn.net/?f=%5Ctext%7BMass%20percent%20of%20nitrogen%20gas%7D%3D%5Cfrac%7B12.084g%7D%7B13.22g%7D%5Ctimes%20100%3D91.41%5C%25)
Mass of hydrogen gas = (13.22 - x) = (13.22 - 12.084) g = 1.136 g
Putting values in above equation, we get:
![\text{Mass percent of hydrogen gas}=\frac{1.136g}{13.22g}\times 100=8.59\%](https://tex.z-dn.net/?f=%5Ctext%7BMass%20percent%20of%20hydrogen%20gas%7D%3D%5Cfrac%7B1.136g%7D%7B13.22g%7D%5Ctimes%20100%3D8.59%5C%25)
Hence, the mass percent of nitrogen gas and hydrogen gas is 91.41 % and 8.59 % respectively.