Calculating the Molar Mass of an Unknown Gas

[irNewton]

Homework Statement

It takes 16.6 min for a 10.0 mL sample of an unknown gas to effuse through a pinhole. A 10.0 -mL sample of
helium, He, required 5.00 min. What is the molar mass of the unknown gas?

Homework Equations

No idea =/

The Attempt at a Solution

No idea =/
Don't know the relationship between time and volume and moles @__@

 

[Borek]

Check Graham's law.

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methods

 

[Blueshift5]

Hello,

Thank you for your question. To calculate the molar mass of an unknown gas using effusion, we can use the Graham's Law of Effusion, which states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. In other words, the lighter the gas, the faster it will effuse through a pinhole.

In this case, we have two gases - the unknown gas and helium - with known volumes and effusion times. We can set up the following equation:

(rate of unknown gas)/(rate of helium) = √(molar mass of helium)/(molar mass of unknown gas)

We know that the rate of helium is 10.0 mL/5.00 min = 2.00 mL/min. We also know that the rate of the unknown gas is 10.0 mL/16.6 min = 0.602 mL/min. Plugging these values into the equation, we get:

(0.602 mL/min)/(2.00 mL/min) = √(4.00 g/mol)/(molar mass of unknown gas)

Solving for the molar mass of the unknown gas, we get:

molar mass of unknown gas = (4.00 g/mol)/(0.602 mL/min)^2 = 44.9 g/mol

Therefore, the molar mass of the unknown gas is 44.9 g/mol.

I hope this helps! Let me know if you have any further questions.