A gaseous mixture of O2 and N2 contains 35.8% nitrogen by mass. What is the partial pressure of oxygen in the mixture if the total pressure is 565 mmHg?
Can you calculate the mole fraction of O2 and N2? Then partial pressure O2 = XO2*Po.
That's partial pressure O2 = mole fraction O2 * 565 mm.
To find the partial pressure of oxygen in the mixture, we need to know the partial pressure of nitrogen and the total pressure. We are given that the total pressure is 565 mmHg.
To determine the partial pressure of nitrogen, we first need to calculate its mole fraction in the mixture. The mole fraction of a component is the ratio of the moles of that component to the total moles of the mixture.
Let's assume we have 100 grams of the gaseous mixture. Since the mass percent of nitrogen is given as 35.8%, we know that there are 35.8 grams of nitrogen in the mixture.
Now, let's determine the number of moles of nitrogen. We do this by dividing the mass of nitrogen by its molar mass. The molar mass of nitrogen (N2) is approximately 28 grams/mol.
Number of moles of nitrogen = mass of nitrogen / molar mass of nitrogen
= 35.8 g / 28 g/mol
≈ 1.28 mol
Next, let's calculate the number of moles of oxygen. Since the total mass of the mixture is 100 grams, the mass of oxygen can be determined by subtracting the mass of nitrogen from the total mass.
Mass of oxygen = total mass - mass of nitrogen
= 100 g - 35.8 g
= 64.2 g
Now, let's calculate the number of moles of oxygen. We divide the mass of oxygen by its molar mass (O2 has a molar mass of approximately 32 grams/mol):
Number of moles of oxygen = mass of oxygen / molar mass of oxygen
= 64.2 g / 32 g/mol
= 2.01 mol
Finally, we can find the mole fraction of nitrogen in the mixture:
Mole fraction of nitrogen = moles of nitrogen / (moles of nitrogen + moles of oxygen)
= 1.28 mol / (1.28 mol + 2.01 mol)
≈ 0.39
The mole fraction of nitrogen in the mixture is approximately 0.39.
Now, to determine the partial pressure of oxygen (PO2), we need to use Dalton's Law of Partial Pressures, which states that the total pressure of a mixture of ideal gases is equal to the sum of the partial pressures of the individual gases.
We can calculate the partial pressure of oxygen using the equation:
PO2 = XO2 * PT
where XO2 is the mole fraction of oxygen in the mixture and PT is the total pressure.
The mole fraction of oxygen is given by:
XO2 = 1 - mole fraction of nitrogen
= 1 - 0.39
= 0.61
Now, we can substitute the values into the equation:
PO2 = 0.61 * 565 mmHg
≈ 345 mmHg
Thus, the partial pressure of oxygen in the gaseous mixture is approximately 345 mmHg.