Rates of Effusion: Homework Questions & Solutions

[Agent M27]

Homework Statement

So this isn't just one problem but it is a question as to why it is done one way for two instances and then the opposite way for a third problem. Here it goes.

1) An unknown gas effuses at a rate that is .462 times that of nitrogen gas (at the same temperature). Calculate the molar mass of the unknown gas in g/mol.

2) Uranium-235 can be separated from U-238 by flourinating the uranium to form UF₆ (which is a gas) and then taking advantage of the different effusion rates for compounds containing the two isotopes. Calculate the ratio of effusion rates for ²³⁸UF₆ and ²³⁵UF₆.

3) A sample of neon effuses from a container in 76 seconds. The same amount of an unknown noble gas requires 155 seconds. Identify the gas.

Homework Equations

$$\frac{RateA}{RateB}$$ = $$\sqrt{\frac{M_B}{M_A}}$$

Where M = molar mass

The Attempt at a Solution

1) $$\frac{RateA}{RateB}$$ = .462

M_A = $$\frac{M_B}{(.462)^2}$$

M_A = $$\frac{28.02}{(.462)^2}$$ = 131g


2) Rate A/ M_A = U-238 RateB/ M_B = U-235

$$\frac{RateA}{RateB}$$ = $$\sqrt{\frac{M_B}{M_A}}$$

$$\sqrt{\frac{235.054}{238.051}}$$= .9934

3) This is the one where I am confused on why it was carried out in the way as follows:
If I was to follow the format as shown above, where rateA is over rateB and then on the other side they switch positions, I arrive at a terribly incorrect answer:

$$\frac{76s}{155s}$$ = $$\sqrt{\frac{M_U}{20.18g}}$$

.2404=$$\frac{M_U}{20.18}$$$$\Rightarrow$$ 4.85g which is the incorrect answer.

The only way I can arrive at the correct answer is when rate A is in the same postion on both sides for example:

$$\frac{76s}{155s}$$ = $$\sqrt{\frac{20.18g}{M_U}}$$

M_U = $$\frac{20.18g}{.2404}$$$$\Rightarrow$$ 83.9g

Which points to Krypton and that happens to be the correct answer. I realize this is a long question and I have the answer, but I want to make sure I am not missing something in the formatting and why it appears to change between problems. Thanks in advance.

Joe

 

[epenguin]

You have just got momentarily confused into thinking the bigger number meant faster, but as it is time taken the bigger number means slower, so in your you first attempt you put it upside down. The ratio of atomic masses is close to 4 and Kr is clearly the answer they want.

(You might object that "effuses from a container in 76 seconds" is a pretty vague statement, but whatever it is it is the same for both and Kr is the answer they want. )