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## 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 seperated from U-238 by flourinating the uranium to form UF

_{6}(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

^{238}UF

_{6}and

^{235}UF

_{6}.

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

[tex]\frac{RateA}{RateB}[/tex] = [tex]\sqrt{\frac{M_B}{M_A}}[/tex]

Where M = molar mass

## The Attempt at a Solution

1) [tex]\frac{RateA}{RateB}[/tex] = .462

M

_{A}= [tex]\frac{M_B}{(.462)^2}[/tex]

M

_{A}= [tex]\frac{28.02}{(.462)^2}[/tex] = 131g

2) Rate A/ M

_{A}= U-238 RateB/ M

_{B}= U-235

[tex]\frac{RateA}{RateB}[/tex] = [tex]\sqrt{\frac{M_B}{M_A}}[/tex]

[tex]\sqrt{\frac{235.054}{238.051}}[/tex]= .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:

[tex]\frac{76s}{155s}[/tex] = [tex]\sqrt{\frac{M_U}{20.18g}}[/tex]

.2404=[tex]\frac{M_U}{20.18}[/tex][tex]\Rightarrow[/tex] 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:

[tex]\frac{76s}{155s}[/tex] = [tex]\sqrt{\frac{20.18g}{M_U}}[/tex]

M

_{U}= [tex]\frac{20.18g}{.2404}[/tex][tex]\Rightarrow[/tex] 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