A mixture contains 5.0 g of He, 1.0 g of Ar, and 3.5 g of Ne. Calculate the volume of this mixture at STP. Calculate the partial pressure of each gas in the mixture at STP.
To calculate the volume of the mixture at standard temperature and pressure (STP), we need to know the molar masses of the gases. The molar mass of a gas can be determined by summing the atomic masses of its constituent elements, which can be found on the periodic table.
The molar masses of the gases are as follows:
- Helium (He): 4.00 g/mol
- Argon (Ar): 39.95 g/mol
- Neon (Ne): 20.18 g/mol
To calculate the moles of each gas, we divide the mass of each gas by its molar mass using the formula:
moles = mass / molar mass
For He:
moles of He = 5.0 g / 4.00 g/mol = 1.25 mol
For Ar:
moles of Ar = 1.0 g / 39.95 g/mol ≈ 0.0250 mol
For Ne:
moles of Ne = 3.5 g / 20.18 g/mol ≈ 0.173 mol
To calculate the total volume of the mixture, we can use the ideal gas law, which states that the volume of a gas is directly proportional to the number of moles of the gas. At STP, one mole of any gas occupies 22.4 liters.
Therefore, the volume of the mixture at STP is:
volume of mixture = (moles of He + moles of Ar + moles of Ne) * 22.4 L/mol
volume of mixture = (1.25 mol + 0.0250 mol + 0.173 mol) * 22.4 L/mol ≈ 32.84 L (rounded to two decimal places)
To calculate the partial pressure of each gas in the mixture at STP, we can use Dalton's law of partial pressures. According to Dalton's law, the total pressure of a gas mixture is the sum of the individual pressures of each gas.
At STP, the total pressure is 1 atmosphere (atm).
Therefore, the partial pressure of each gas in the mixture is:
partial pressure = (moles of gas / total moles of gas) * total pressure
For He:
partial pressure of He = (moles of He / total moles of gas) * total pressure
partial pressure of He = (1.25 mol / (1.25 mol + 0.0250 mol + 0.173 mol)) * 1 atm ≈ 0.89 atm (rounded to two decimal places)
For Ar:
partial pressure of Ar = (moles of Ar / total moles of gas) * total pressure
partial pressure of Ar = (0.0250 mol / (1.25 mol + 0.0250 mol + 0.173 mol)) * 1 atm ≈ 0.01 atm (rounded to two decimal places)
For Ne:
partial pressure of Ne = (moles of Ne / total moles of gas) * total pressure
partial pressure of Ne = (0.173 mol / (1.25 mol + 0.0250 mol + 0.173 mol)) * 1 atm ≈ 0.11 atm (rounded to two decimal places)
Therefore, the partial pressures of each gas in the mixture at STP are approximately:
He: 0.89 atm
Ar: 0.01 atm
Ne: 0.11 atm
Convert grams of each to mols. mol = grams/molar mass. Then use PV = nRT and total n to find volume at STP.
Then use PV = nRT and the volume you found to determine the partial pressure of each gas.