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The rate of effusion of unknown gas X is foundto be about 2.6 times that of SF6 gas...

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precious531 | Student, Grade 10 | (Level 2) eNoter

Posted September 15, 2012 at 6:25 PM via web

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The rate of effusion of unknown gas X is found
to be about 2.6 times that of SF6 gas (MW
= 146 g/mol)..

at the same conditions of tem-
perature and pressure. What is the molecular
weight of gas X?
Answer in units of g/mol

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valentin68 | College Teacher | (Level 3) Associate Educator

Posted October 5, 2013 at 10:53 AM (Answer #1)

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Effusion is a process of mass transport that happens when a gas escapes through the pores of a solid materia (or through a small opening)l. Is is similar to the diffusion process in that both diffusion and effusion rates depends on the speed of gas molecules (in diffusion, molecules of a gas become mixed with molecules of a second gas because of their thermal agitation).  At the same temperature (the same thermal agitation or speed of molecules) we can say that bigger molecules escapes slower than smaller molecules.

It has been experimentally determined that the rate of effusion of a gas is inversely proportional  to the square root of the molecular mass `M` of the gas (to the square root of molecules mass `m`)

`R =C*1/sqrt(M)`

With the data in text we have

`2.6= R_X/R_(SF6)= sqrt(M_(SF6)/M_X)`

`M_X =146/2.6^2 =21.6 g/(mol)`

The molecular mass of gas X is 21.6 g/mol.

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