A gaseous mixture of O2 (MM = 32 g/mol) and N2 (MM = 28.02 g/mol) contains 35.8% nitrogen by mass. What is the partial pressure of oxygen in the mixture, if the total pressure is 788.0 mmHg?
Take 100 g sample: 35.8 g is N2 and 61.2 g is O2.
moles N2 = g/molar mass = 35.8/28.02 = 1.28 (rounded)
moles O2 = 61.2/32 = 1.91
total mols = 1.28 + 1.91 = 3.19
XO2 = mole fraction O2 = 1.91/3.19 = 0.599
Then pO2 = XO2*Ptotal = 0.599*788 = ?
To find the partial pressure of oxygen in the mixture, we first need to determine the partial pressure of nitrogen.
Given that the gaseous mixture contains 35.8% nitrogen by mass, we can assume that the remaining mass percentage is oxygen (since we are only dealing with O2 and N2 in this mixture). Therefore, the mass percentage of oxygen is 100% - 35.8% = 64.2%.
Now, let's assume we have 100 grams of the mixture. The mass of nitrogen in the mixture would be 35.8 grams (since it accounts for 35.8% of the total mass), and the mass of oxygen would be 64.2 grams (since it accounts for 64.2% of the total mass).
Next, we need to calculate the number of moles for each gas. We can use the following equation:
Number of moles = Mass of substance / Molar mass
Number of moles of nitrogen (N2) = 35.8 g / 28.02 g/mol = 1.28 mol
Number of moles of oxygen (O2) = 64.2 g / 32 g/mol = 2.01 mol
Now that we have the number of moles for each gas, we can determine the mole fraction for nitrogen and oxygen:
Mole fraction of nitrogen (XN2) = Number of moles of nitrogen / Total number of moles of all gases
Mole fraction of nitrogen (XO2) = Number of moles of oxygen / Total number of moles of all gases
Mole fraction of nitrogen (XN2) = 1.28 mol / (1.28 mol + 2.01 mol) = 0.389
Mole fraction of oxygen (XO2) = 2.01 mol / (1.28 mol + 2.01 mol) = 0.611
The mole fraction of a gas is directly proportional to its partial pressure. Therefore, we can use the mole fractions to calculate the partial pressure of each gas.
Partial pressure of nitrogen (PN2) = Mole fraction of nitrogen * Total pressure
Partial pressure of nitrogen (PN2) = 0.389 * 788.0 mmHg = 306.43 mmHg
Partial pressure of oxygen (PO2) = Mole fraction of oxygen * Total pressure
Partial pressure of oxygen (PO2) = 0.611 * 788.0 mmHg = 481.57 mmHg
Therefore, the partial pressure of oxygen in the mixture is approximately 481.57 mmHg.