A mixture of gases contains 0.65 mol of N2, 0.70 mol of O2, and 0.90 mol of He.
What is the partial pressure of each gas (in atm and in torr) in a 25.0 L cylinder at 340 K?
What is total pressure?
I know you:
Use mols each gas in PV = nRT and solve for p.
Then Ptotal = pN2 + pO2 + pHe
So do the steps.
You are correct! To find the partial pressure of each gas in the mixture, you can use the ideal gas law equation, which is PV = nRT. Let's go step by step to calculate the partial pressure for each gas.
Step 1: Calculate the partial pressure of nitrogen gas (N2):
Given: nN2 = 0.65 mol, V = 25.0 L, T = 340 K, and R = 0.0821 atm·L/mol·K (gas constant)
Plug these values into the ideal gas law equation:
pN2 = (nN2 * R * T) / V
= (0.65 mol * 0.0821 atm·L/mol·K * 340 K) / 25.0 L
≈ 3.53 atm
To convert this value to torr, use the conversion factor 1 atm = 760 torr:
pN2 = 3.53 atm * 760 torr/atm
≈ 2682 torr
So the partial pressure of nitrogen gas (N2) is approximately 3.53 atm or 2682 torr.
Step 2: Calculate the partial pressure of oxygen gas (O2):
Given: nO2 = 0.70 mol, V = 25.0 L, T = 340 K, and R = 0.0821 atm·L/mol·K (gas constant)
Using the ideal gas law equation:
pO2 = (nO2 * R * T) / V
= (0.70 mol * 0.0821 atm·L/mol·K * 340 K) / 25.0 L
≈ 4.78 atm
To convert this value to torr:
pO2 = 4.78 atm * 760 torr/atm
≈ 3633 torr
So the partial pressure of oxygen gas (O2) is approximately 4.78 atm or 3633 torr.
Step 3: Calculate the partial pressure of helium gas (He):
Given: nHe = 0.90 mol, V = 25.0 L, T = 340 K, and R = 0.0821 atm·L/mol·K (gas constant)
Using the ideal gas law equation:
pHe = (nHe * R * T) / V
= (0.90 mol * 0.0821 atm·L/mol·K * 340 K) / 25.0 L
≈ 9.00 atm
To convert this value to torr:
pHe = 9.00 atm * 760 torr/atm
≈ 6840 torr
So the partial pressure of helium gas (He) is approximately 9.00 atm or 6840 torr.
Step 4: Calculate the total pressure (Ptotal):
To calculate the total pressure, you need to add up the partial pressures of each gas:
Ptotal = pN2 + pO2 + pHe
= 3.53 atm + 4.78 atm + 9.00 atm
≈ 17.31 atm
To convert this value to torr:
Ptotal = 17.31 atm * 760 torr/atm
≈ 13160 torr
So the total pressure is approximately 17.31 atm or 13160 torr.