What is the density(g/L) of a gas mixture that contains 27.0% Fe and 73.0% He by volume at 714 mm Hg and 27.5 degrees Centigrade?
To calculate the density of a gas mixture, you need to use the ideal gas law, which states:
PV = nRT
Where:
- P is the pressure of the gas (in this case, 714 mm Hg)
- V is the volume of the gas (which is not given)
- n is the number of moles of the gas
- R is the ideal gas constant (0.0821 L.atm/mol.K)
- T is the temperature in Kelvin (which needs to be converted from Celsius)
To calculate the number of moles (n) and volume (V) of each gas in the mixture, you can use Dalton's Law of Partial Pressures and the ideal gas law.
Dalton's Law of Partial Pressures states:
Pt = P1 + P2
Where Pt is the total pressure of the gas mixture and P1, P2, etc., are the partial pressures of each component.
Using this information, here are the steps to calculate the density of the gas mixture:
Step 1: Convert the temperature from Celsius to Kelvin.
T(K) = T(C) + 273.15
T(K) = 27.5 + 273.15 = 300.65 K
Step 2: Calculate the partial pressures of each gas component.
P1 = (27.0/100) * Pt
P2 = (73.0/100) * Pt
Step 3: Calculate the number of moles of each gas using the ideal gas law.
n1 = (P1 * V) / (R * T)
n2 = (P2 * V) / (R * T)
Step 4: Calculate the total number of moles of the gas mixture.
ntotal = n1 + n2
Step 5: Calculate the volume of the gas mixture.
V = (ntotal * R * T) / Pt
Step 6: Calculate the density of the gas mixture.
Density = (ntotal * Molar mass of gas mixture) / V
To calculate the molar mass of the gas mixture, you need to know the molar mass of Fe and He. The molar mass of Fe is 55.845 g/mol, and the molar mass of He is 4.00 g/mol.
Molar mass of gas mixture = (0.27 * 55.845) + (0.73 * 4.00) g/mol
Finally, substitute all the values into the density formula to get the density of the gas mixture in g/L.