A certain mixture of helium, He, and krypton, Kr, has a mass of 10.0 g and occupies a volume of 20.0 L at 25.0EC and 1.20 atm. What is the mass of He in the mixture?
Let X = mass He
and Y = mass Kr.
Two equations and two unknowns.
eqn 1 is X + Y = 10
Then use PV = nRT and solve for n = total mols.
equation 2 is
(X/4) + (Y/83.8) = total mols
Solve for X = grams He.
I used the ideal gas law, and I got .980456 moles. then I used the equation to substitute Helium=10.0g -Krypton in the equation (x/4)+(y/83.8)=. 980456 mols for X. With a little bit of algebra, I got 6.38079g of Krypton and 3.61921g of Helium. Thanks you for the help. I wuld of never got the second equation by myself. I think I did this correctly, if not I would really appreciate someone responding.
I went through the calculations quickly and obtained 3.622 which rounds to 3.62 for He. The small difference in our numbers probably comes from my obtaining 0.981 for n. I'm positive you worked it correctly.
To find the mass of helium (He) in the mixture, we need to consider the molar masses of helium and krypton, as well as the partial pressures of the gases.
Step 1: Calculate the number of moles of krypton (Kr):
Given that the total mass of the mixture is 10.0 g and the molar mass of krypton (Kr) is approximately 83.8 g/mol, we can calculate the number of moles of krypton using the formula:
Number of moles (Kr) = Mass of krypton (Kr) / Molar mass of krypton (Kr)
Number of moles (Kr) = 10.0 g / 83.8 g/mol
Step 2: Calculate the number of moles of helium (He):
Since the total number of moles is equal to the sum of moles of helium and krypton, we can subtract the moles of krypton from the total number of moles. To find the total number of moles, we will use the ideal gas law:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in L)
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (in Kelvin)
Rearrange the formula to solve for n:
n = (PV) / (RT)
Convert the given temperature from Celsius to Kelvin:
Temperature (K) = 25.0EC + 273.15 = 298.15 K
Substitute the given values into the formula:
n = (1.20 atm * 20.0 L) / (0.0821 L.atm/mol.K * 298.15 K)
Step 3: Calculate the mass of helium (He):
Since the total mass of the mixture is 10.0 g and the number of moles of helium is equal to the total moles minus the moles of krypton, we can calculate the mass of helium using the formula:
Mass of helium (He) = (Total mass - Mass of krypton) = 10.0 g - (Number of moles (Kr) * Molar mass of krypton (Kr))
Substitute the calculated values from Step 1 and the known molar mass of helium (He) (approximately 4 g/mol) into the formula to find the mass of helium in the mixture.
Note: The molar mass of helium is very small compared to that of krypton, so the error introduced by neglecting the helium atoms' mass in the overall mixture mass calculation is negligible.
Mass of helium (He) = 10.0 g - (Number of moles (Kr) * Molar mass of krypton (Kr))
This calculation will give us the mass of helium in the mixture.