Chemistry Effusion Homework: Calculate Molar Mass of Unknown Gas

[hockeyfghts5]

Homework Statement

One percent of a measured amount of chlorine gas escapes through a tiny hole in 33 sec. One percent of a unknown gas escapes under the same conditions in 75.2 sec. Calculate the molar mass of the unknown gas in g/mol.

I can't seem to figure out how to do this so if some one could help i would be very appreciated.

 

[epenguin]

By now I have to say this. Sometimes students come here with intriguing problems that are not trivial to solve, sometimes they come and have got something confused which others here can help get straightened out, and so on, a variety of problems. But I do have to wonder at those who come here with perfectly standard problems that cannot have arisen out of the blue and say they have no idea where to start. Where to start is probably in a very recent lesson or book chapter. Have you had a recent lesson or where you are in a textbook mentioning effusion or anything sounding like that? Involving movement of gases from somewhere to somewhere else?

And failing that, do you know the equipartition principle? That the average translational kinetic energy per molecule of two gases under the same conditions will be the same? Then do you know the formula for kinetic energy? Put these ideas together. If you manage to get a convincing answer out of this then do not rest content with it but revise the underlying principles like kinetic energy and equipartition which will then fix in your mind.

 

[Blueshift5]

To calculate the molar mass of the unknown gas, we can use the Graham's Law of Effusion. This law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. In other words, lighter gases will effuse faster than heavier gases.

Using this information, we can set up a proportion:

(rate of effusion of chlorine gas) / (rate of effusion of unknown gas) = √(molar mass of unknown gas) / √(molar mass of chlorine gas)

Plugging in the given values, we get:

(1/33) / (1/75.2) = √(molar mass of unknown gas) / √(35.45 g/mol)

Simplifying, we get:

(75.2/33) = √(molar mass of unknown gas) / √(35.45)

Solving for the unknown molar mass, we get:

√(molar mass of unknown gas) = (75.2/33) √(35.45)

molar mass of unknown gas = (75.2/33) √(35.45)^2

molar mass of unknown gas = 85.7 g/mol

Therefore, the molar mass of the unknown gas is approximately 85.7 g/mol.