What is the molecular mass of a gas that diffuses through a porous membrane 1.86 times faster than Xe?
To find the molecular mass of a gas that diffuses through a porous membrane 1.86 times faster than Xe, we can use Graham's Law of Diffusion. According to Graham's Law:
Rate 1 / Rate 2 = sqrt(mass 2 / mass 1)
Where Rate 1 and Rate 2 are the rates of diffusion of the two gases, and mass 1 and mass 2 are their respective molecular masses.
Since we want to find the molecular mass of the unknown gas, we can substitute the given values into Graham's Law and solve for mass 2 (unknown gas) as follows:
1.86 (Rate of unknown gas) / 1 (Rate of Xe) = sqrt(mass of Xe / mass 2)
Taking the square of both sides to eliminate the square root:
(1.86)^2 * Rate of unknown gas = (mass of Xe / mass 2)
Simplifying:
3.4596 * Rate of unknown gas = mass of Xe / mass 2
Now, we can rearrange the equation and solve for mass 2:
mass 2 = mass of Xe / (3.4596 * Rate of unknown gas)
To find the molecular mass of Xe, we can look it up in the periodic table. The atomic mass of Xe is approximately 131.29 g/mol.
Now, let's assume the rate of diffusion of Xe is 1 (arbitrary unit).
mass 2 = 131.29 g/mol / (3.4596 * 1.0)
mass 2 ≈ 37.9 g/mol
Therefore, the molecular mass of the unknown gas that diffuses through the porous membrane 1.86 times faster than Xe is approximately 37.9 g/mol.
To find the molecular mass of the gas, we need to use Graham's Law of Effusion, which states that the rate of effusion (or diffusion) of a gas is inversely proportional to the square root of its molar mass.
First, let's assign some variables:
- Rate of effusion/diffusion of the unknown gas: R
- Rate of effusion/diffusion of Xe: X
- Molecular mass of the unknown gas: M
- Molecular mass of Xe: MXe
According to the problem, the unknown gas diffuses 1.86 times faster than Xe. That means:
R/X = 1.86
Now, we can express the rate of effusion using Graham's Law:
R ∝ 1/√M
X ∝ 1/√MXe
By combining these equations, we get:
R/X = √(MXe/M)
Substituting the given value of R/X (1.86) into the equation, we have:
1.86 = √(MXe/M)
To find the molecular mass of the unknown gas (M), we need to isolate the variable M in the equation.
Squaring both sides of the equation, we get:
1.86^2 = MXe/M
Rearranging the equation:
1.86^2 * M = MXe
Now, divide both sides by MXe:
M = (1.86^2) * MXe
Finally, substitute the molecular mass of Xe (MXe) into the equation to obtain the answer. The molecular mass of Xe is 131.29 g/mol. Calculate:
M = (1.86^2) * 131.29 g/mol
The molecular mass of the unknown gas is the calculated value.
I would assume a convenient number for the rate of Xe, say something like 5 L/min. Then rate unknown gas, x, is 1.86*5.
(rate x/rate Xe) = (MM Xe/MM X)
Solve for MM = molar mass X.