A closed vessel of volume 2.50 dm3 contains 100g of nitrogen (N2) and 100g of carbon dioxide (CO2) at 25 C. What are the partial pressures and mole fractions of each gas?
mols N2 = grams/molar mass = ?
mols CO2 = grams/molar mass = ?
Use PV = nRT, substitute EACH (mols N2 and mols CO2 separately) and find pressure of each.
You can find X two ways.
1. total mols = mols N2+mols CO2.
XN2 = mols N2/total mols
XCO2 = mols CO2/total mols.
2. Ptotal = pN2 + pCO2
XN2 = mols N2*Ptotal
XCO2 = mols CO2*Ptotal
Post your work if you get stuck.
To calculate the partial pressures and mole fractions of each gas, we need to know the total pressure and the mole fractions of nitrogen and carbon dioxide.
Step 1: Convert the volume of the vessel to liters.
Given volume = 2.50 dm^3
1 dm^3 = 1 liter.
So, the volume of the vessel = 2.50 liters.
Step 2: Calculate the total moles of nitrogen and carbon dioxide.
To find the moles, we can use the formula:
moles = mass / molar mass.
The molar mass of nitrogen (N2) = 2 * atomic mass of nitrogen.
The atomic mass of nitrogen = 14.01 g/mol.
So, the molar mass of nitrogen = 2 * 14.01 g/mol = 28.02 g/mol.
For nitrogen:
moles of nitrogen = 100 g / 28.02 g/mol.
The molar mass of carbon dioxide (CO2) = atomic mass of carbon + 2 * atomic mass of oxygen.
The atomic mass of carbon = 12.01 g/mol.
The atomic mass of oxygen = 16.00 g/mol.
So, the molar mass of carbon dioxide = 12.01 g/mol + 2 * 16.00 g/mol = 44.01 g/mol.
For carbon dioxide:
moles of carbon dioxide = 100 g / 44.01 g/mol.
Step 3: Calculate the mole fractions of nitrogen and carbon dioxide.
The mole fraction of a gas is given by the formula:
mole fraction = moles of the gas / total moles of all gases.
For nitrogen:
mole fraction of nitrogen = moles of nitrogen / (moles of nitrogen + moles of carbon dioxide).
For carbon dioxide:
mole fraction of carbon dioxide = moles of carbon dioxide / (moles of nitrogen + moles of carbon dioxide).
Step 4: Calculate the partial pressures of nitrogen and carbon dioxide.
The partial pressure of a gas is given by the formula:
partial pressure = mole fraction of the gas * total pressure.
Given that the total pressure is not provided, we cannot calculate the partial pressures unless we know the total pressure.
Therefore, we can find the mole fractions of each gas, but without the total pressure, we cannot calculate the partial pressures.