A container holds 1.00 mol O2, and the pressure in the container is 2.00 atm. A student adds 60.0 g of gas Y to the container. The total pressure (of O2 and gas Y) is 3.00 atm.
What is the molar mass of gas Y?
(V and T constant)
Ok so i also was going to ask this question but I THINK i figured it out.
remember that mols and pressure are proportional. if 1 mol of O2 gives 2 atm of pressure, then how many mols of a gas gives 1 atm of pressure? (because the total is three, so we just need to find out how to get that extra atm of pressure). so i set up a proportion. 1mol/2atm=Xmol/1atm and i got .5 so then i set up 60g Y/.5 mol and i got 120. it makes sense but im not sure if this is how it was supposed to be done. i did get the right answer so i hope i helped a little!
Yes, 120 is correct.
I worked it with mole fractions.
XO2 = (PO2/Ptotal) = (2/3)
Xunk = (Punk/Ptotal) = (1/3)
Then for oxygen, (1 mol)
(mol O2/(mol O2 + mol unk) = 2/3
Solve for mole unk, then moles = g/molar mass and solve for molar mass.
Your solution is more esoteric than mine.
To find the molar mass of gas Y, we first need to determine the number of moles of gas Y added to the container.
We know that the initial container holds 1.00 mol O2, and the pressure in the container is 2.00 atm. The total pressure after adding gas Y is 3.00 atm. Since the volume (V) and temperature (T) are constant, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
Since V and T are constant, we can rewrite the equation as:
P1 * n1 = P2 * n2
Where:
P1 = initial pressure
n1 = initial number of moles (1.00 mol for O2)
P2 = final pressure (3.00 atm considering O2 and gas Y)
n2 = final number of moles (unknown)
Rearranging the equation to solve for n2:
n2 = (P1 * n1) / P2
Plugging in the values:
n2 = (2.00 atm * 1.00 mol) / 3.00 atm
n2 = 2.00 mol / 3.00
n2 = 0.666 mol
Now that we know the number of moles of gas Y (n2), we can calculate the molar mass.
The molar mass (M) is given by:
Molar mass = mass / moles
We know that the mass of gas Y is 60.0 g.
Therefore, the molar mass of gas Y is:
Molar mass = 60.0 g / 0.666 mol
Molar mass ≈ 90.09 g/mol
So, the molar mass of gas Y is approximately 90.09 g/mol.