<u>Answer:</u> The partial pressure of oxygen gas is 2.76 bar
<u>Explanation:</u>
To calculate the number of moles, we use the equation given by ideal gas which follows:
![PV=nRT](https://tex.z-dn.net/?f=PV%3DnRT)
where,
P = pressure of the gas = 5.57 bar
V = Volume of the gas = 2.19 L
T = Temperature of the gas = 298 K
R = Gas constant = ![0.0831\text{ L bar }mol^{-1}K^{-1}](https://tex.z-dn.net/?f=0.0831%5Ctext%7B%20L%20bar%20%7Dmol%5E%7B-1%7DK%5E%7B-1%7D)
n = Total number of moles = ?
Putting values in above equation, we get:
![5.57bar\times 2.19L=n\times 0.0831\text{ L. bar }mol^{-1}K^{-1}\times 298K\\\\n=\frac{5.57\times 2.19}{0.0831\times 298}=0.493mol](https://tex.z-dn.net/?f=5.57bar%5Ctimes%202.19L%3Dn%5Ctimes%200.0831%5Ctext%7B%20L.%20bar%20%7Dmol%5E%7B-1%7DK%5E%7B-1%7D%5Ctimes%20298K%5C%5C%5C%5Cn%3D%5Cfrac%7B5.57%5Ctimes%202.19%7D%7B0.0831%5Ctimes%20298%7D%3D0.493mol)
To calculate the mole fraction of carbon dioxide, we use the equation given by Raoult's law, which is:
........(1)
where,
= partial pressure of carbon dioxide = 0.318 bar
= total pressure = 5.57 bar
= mole fraction of carbon dioxide = ?
Putting values in above equation, we get:
![0.318bar=5.57bar\times \chi_{CO_2}\\\\\chi_{CO_2}=\frac{0.381}{5.57}=0.0571](https://tex.z-dn.net/?f=0.318bar%3D5.57bar%5Ctimes%20%5Cchi_%7BCO_2%7D%5C%5C%5C%5C%5Cchi_%7BCO_2%7D%3D%5Cfrac%7B0.381%7D%7B5.57%7D%3D0.0571)
- 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)
We are given:
Moles of nitrogen gas = 0.221 moles
Mole fraction of nitrogen gas, ![\chi_{N_2}=\frac{0.221}{0.493}=0.448](https://tex.z-dn.net/?f=%5Cchi_%7BN_2%7D%3D%5Cfrac%7B0.221%7D%7B0.493%7D%3D0.448)
Calculating the partial pressure of oxygen gas by using equation 1, we get:
Mole fraction of oxygen gas = (1 - 0.0571 - 0.448) = 0.4949
Total pressure of the system = 5.57 bar
Putting values in equation 1, we get:
![p_{O_2}=5.57bar\times 0.4949\\\\p_{O_2}=2.76bar](https://tex.z-dn.net/?f=p_%7BO_2%7D%3D5.57bar%5Ctimes%200.4949%5C%5C%5C%5Cp_%7BO_2%7D%3D2.76bar)
Hence, the partial pressure of oxygen gas is 2.76 bar