A gaseous mixture of O2 and N2 contains 30.8 % nitrogen by mass. What is the partial pressure of oxygen in the mixture if the total pressure is 365 mmHg?
First you have to find the moles of O2 and N2. To do this you must assume that this is a 100g sample. Therefore, 30.8g of nitrogen. Now you can find the moles of nitrogen by dividing this mass by nitrogen's molar mass:
30.8g/(14.01g/mol x 2) = 1.10moles N2
Next you can find the moles of oxygen by subracting 100 by the mass of nitrogen.
100-30.8g N2 = 69.2g O2
Now you can find the moles of oxygen:
69.2g/(16.0g/mol x 2) = 2.16moles O2
You can find the mole fraction of oxygen by using the equation :
O2=moles of component/total moles in mixture
=2.16moles/(2.16moles + 1.10moles)
=0.659
Lastly, you can find your partial pressure by multiplying the mole fraction of oxygen that you just found by the total pressure given in the question.
P1=O × Ptotal
=0.659 x 365mmHg
=240mmHg
Hope this helps!! :)
Well, it seems like this gaseous mixture is quite "nitr-oh-my-gosh"! Let's take a closer look at the problem to find a solution that will have you breathing easy.
First, we need to determine the partial pressure of oxygen in the mixture. Since we know that the total pressure is 365 mmHg, we can subtract the partial pressure of nitrogen from this value to find the partial pressure of oxygen.
Now, the partial pressure of nitrogen can be calculated by multiplying the percent of nitrogen in the mixture by the total pressure. So, 30.8% of 365 mmHg gives us the partial pressure of nitrogen.
Once we have the partial pressure of nitrogen, we can subtract it from the total pressure to find the partial pressure of oxygen. And voila, we'll have our answer!
But don't worry, I won't leave you hanging. Let me do the math for you. Calculate the partial pressure of oxygen by subtracting the partial pressure of nitrogen from the total pressure.
To find the partial pressure of oxygen in the mixture, we first need to calculate the mass percent of oxygen in the mixture.
1. Calculate the mass percent of nitrogen:
Mass percent of nitrogen = 30.8 %
2. Calculate the mass percent of oxygen:
Mass percent of oxygen = 100% - 30.8%
= 69.2%
3. Convert the mass percent of oxygen to a decimal:
Decimal of oxygen percentage = 69.2% / 100
= 0.692
4. Calculate the mass of oxygen present in the mixture:
Mass of oxygen = Mass percent of oxygen * Total mass of the mixture
5. Let's assume the total mass of the mixture is 100 grams:
Mass of oxygen = 0.692 * 100 g
= 69.2 g
6. Calculate the mole ratio of oxygen to nitrogen:
Mole ratio of oxygen to nitrogen = (Mass of oxygen / Molar mass of oxygen) / (Mass of nitrogen / Molar mass of nitrogen)
7. The molar mass of oxygen (O2) is 32 g/mol and the molar mass of nitrogen (N2) is 28 g/mol.
Mole ratio of oxygen to nitrogen = (69.2 g / 32 g/mol) / (30.8 g / 28 g/mol)
8. Simplify the equation to find the mole ratio:
Mole ratio of oxygen to nitrogen = (69.2 / 32) / (30.8 / 28)
= 2.1625
9. Calculate the total number of moles of gas in the mixture:
Total moles of gas = Moles of oxygen + Moles of nitrogen
10. The moles of oxygen can be calculated using the mole ratio of oxygen to nitrogen:
Moles of oxygen = Mole ratio of oxygen to nitrogen / (1 + Mole ratio of oxygen to nitrogen)
11. Substitute the known values into the equation:
Moles of oxygen = 2.1625 / (1 + 2.1625)
= 2.1625 / 3.1625
12. Calculate the partial pressure of oxygen using Dalton's Law of Partial Pressure:
Partial pressure of oxygen = Moles of oxygen / Total moles of gas * Total pressure
13. Substitute the known values into the equation:
Partial pressure of oxygen = (2.1625 / 3.1625) * 365 mmHg
14. Calculate the partial pressure of oxygen:
Partial pressure of oxygen = 248.522 mmHg
Therefore, the partial pressure of oxygen in the mixture is approximately 248.522 mmHg.
To find the partial pressure of oxygen in the mixture, we need to use the mole fraction of oxygen and the total pressure. First, calculate the mole fraction of nitrogen (X_N2) in the mixture.
Mole fraction (X) of a component = Moles of the component / Total moles
Since we know that the mixture contains 30.8% nitrogen by mass, we can assume a 100 g sample of the mixture. Therefore, the mass of nitrogen in the mixture is 30.8 g.
Next, we need to find the mole fraction of nitrogen.
Molar mass of nitrogen (N2) = 28 g/mol
Moles of nitrogen (N2) = (mass of nitrogen) / (molar mass of nitrogen) = 30.8 g / 28 g/mol = 1.1 mol
Similarly, calculate the mole fraction of oxygen (X_O2) in the mixture. Since the total mass of the mixture is 100 g and the mass of nitrogen is 30.8 g, the mass of oxygen in the mixture is 100 g - 30.8 g = 69.2 g.
Molar mass of oxygen (O2) = 32 g/mol
Moles of oxygen (O2) = (mass of oxygen) / (molar mass of oxygen) = 69.2 g / 32 g/mol = 2.16 mol
Now, calculate the mole fraction of oxygen:
X_O2 = (moles of oxygen) / (moles of oxygen + moles of nitrogen) = 2.16 mol / (2.16 mol + 1.1 mol) = 0.662
The mole fraction of oxygen in the mixture is 0.662.
Next, we can use Dalton's Law of partial pressures to find the partial pressure of oxygen (P_O2).
Dalton's Law of partial pressures states that the total pressure of a gaseous mixture is the sum of the partial pressures of each component.
P_O2 = X_O2 * Total pressure
P_O2 = 0.662 * 365 mmHg = 241.13 mmHg
Therefore, the partial pressure of oxygen in the mixture is 241.13 mmHg.