A heliox deep-sea diving mixture contains 2.0 g of oxygen to every 98.0 g of helium.What is the partial pressure of oxygen when this mixture is delivered at a total pressure of 8.9atm ?
To find the partial pressure of oxygen in the heliox mixture, we need to use the Dalton's Law of Partial Pressures, which states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each component gas.
In this case, we are given the total pressure of the mixture as 8.9 atm. Let's assume that the partial pressure of oxygen is represented by P(O2).
According to the given information, there are 2.0 g of oxygen for every 98.0 g of helium in the mixture. To calculate the mole fraction of oxygen (X(O2)) in the mixture, we need to convert the mass of each gas into moles.
Moles of Oxygen (n(O2)) = Mass of Oxygen (m(O2)) / Molar Mass of Oxygen (M(O2))
= 2.0 g / 32.0 g/mol (Molar Mass of Oxygen)
= 0.0625 mol
Moles of Helium (n(He)) = Mass of Helium (m(He)) / Molar Mass of Helium (M(He))
= 98.0 g / 4.0 g/mol (Molar Mass of Helium)
= 24.5 mol
Now, we can calculate the mole fraction of oxygen:
X(O2) = n(O2) / (n(O2) + n(He))
= 0.0625 mol / (0.0625 mol + 24.5 mol)
≈ 0.00255
The mole fraction can be used to find the partial pressure of oxygen. We know that the total pressure of the mixture is 8.9 atm. So, the partial pressure of oxygen (P(O2)) can be calculated using the formula:
P(O2) = X(O2) * Total Pressure
= 0.00255 * 8.9 atm
≈ 0.0227 atm
Therefore, the partial pressure of oxygen in the heliox mixture is approximately 0.0227 atm.
To find the partial pressure of oxygen in the heliox deep-sea diving mixture, we can use Dalton's Law of Partial Pressures. According to Dalton's Law, the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases.
The first step is to calculate the moles of oxygen and helium in the mixture.
1. Calculate the moles of oxygen:
The molar mass of oxygen (O2) is 32.0 g/mol.
Moles of oxygen = Mass of oxygen / Molar mass of oxygen
Moles of oxygen = 2.0 g / 32.0 g/mol
Moles of oxygen = 0.0625 mol
2. Calculate the moles of helium:
The molar mass of helium (He) is 4.0 g/mol.
Moles of helium = Mass of helium / Molar mass of helium
Moles of helium = 98.0 g / 4.0 g/mol
Moles of helium = 24.5 mol
Now, we can calculate the partial pressure of oxygen using Dalton's Law.
3. Calculate the partial pressure of oxygen:
The total pressure of the mixture is given as 8.9 atm.
According to Dalton's Law, the partial pressure of oxygen (PO2) is given by:
PO2 = (Moles of oxygen / Total moles of gas) * Total pressure
Total moles of gas = Moles of oxygen + Moles of helium
Total moles of gas = 0.0625 mol + 24.5 mol
Total moles of gas = 24.5625 mol (rounded to four decimal places)
PO2 = (0.0625 mol / 24.5625 mol) * 8.9 atm
PO2 = 0.002548 atm (rounded to four decimal places)
Therefore, the partial pressure of oxygen in the heliox deep-sea diving mixture is approximately 0.0025 atm.