A tank holds a mixture of oxygen and nitrogen gases. If the partial pressure of oxygen is 3.3 atm and the mole fraction of N2 gas X(N2) = 0.78, what are the total pressure in the tank and the partial pressure of N2?
XN2 = 0.78 from the problem so XO2 = 1.00-0.78 = 0.22
pO2 = 3.3 atm = XO2*Ptotal. Solve for Ptotal.
Then pN2 = XN2*Ptotal. Solve for pN2.
Post your work if you get stuck.
To find the total pressure in the tank, we need to use Dalton's Law of Partial Pressure, which states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each component gas.
In this case, we have the partial pressure of oxygen (PO2) given as 3.3 atm. Let's assume that the total pressure in the tank is Ptotal. According to Dalton's Law, the total pressure can be expressed as:
Ptotal = PO2 + PN2
Next, we have the mole fraction of nitrogen gas (X(N2)) given as 0.78. The mole fraction is the ratio of the number of moles of a component gas to the total number of moles in the mixture.
Since we only have two gases in the mixture (oxygen and nitrogen), the mole fraction of oxygen (X(O2)) can be calculated as:
X(O2) = 1 - X(N2)
= 1 - 0.78
= 0.22
Now, we can use the partial pressure equation to find the partial pressure of nitrogen gas (PN2):
PN2 = X(N2) * Ptotal
Substituting the given values, we get:
PN2 = 0.78 * Ptotal
To solve for Ptotal, we can substitute the value of PN2 into the equation for Ptotal we derived earlier:
Ptotal = PO2 + PN2
= 3.3 + (0.78 * Ptotal)
Now, we can solve this equation for Ptotal:
Ptotal - 0.78 * Ptotal = 3.3
(1 - 0.78) * Ptotal = 3.3
0.22 * Ptotal = 3.3
Ptotal = 3.3 / 0.22
Ptotal = 15 atm
Finally, substitute the value of Ptotal into the equation for PN2 to find the partial pressure of nitrogen gas:
PN2 = 0.78 * Ptotal
= 0.78 * 15
= 11.7 atm
Therefore, the total pressure in the tank is 15 atm and the partial pressure of nitrogen gas is 11.7 atm.