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Grade 11Physical Chemistry

1 mole of nitrogen gas 0.8Atm takes 38 seconds to diffuse through a pinhole where is 1 mole of unknown compound of Xenon with fluorine at 1.6 ATM takes 56.26 second to diffuse through the small one then the molecular formula of the compound is

Profile image of Vaibhav barfa
7 Years agoGrade 11
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1 Answer

Profile image of Kapil Khare
7 Years ago
We know that for compounds with molecular mass M1 and M2, diffusion rate r1 and r2 at pressure P1 and P2 respectively, can be written as 
 
r1/r2 = (P1/P2)(M2/M1)1/2
and also r1/r2 = t2/t1
where t1 and t2 are time taken by the gas to diffuse.
 
\implies (P1/P2)(M2/M1)1/2 = t2/t1
 
Let 1st compound be nitrogen gas then M1 = mass of 1mole of nitrogen gas = 28grams
                                                               P1 = 0.8atm
                                                                t1 = 38s
Let 2nd compound be the mixture of xenon and fluorine with M2 = M
                                                                                                P2 = 1.6atm
                                                                                                 t2 = 56.26s
 Then,
                     (0.8/1.6)(M/14)1/2 = 56.26/38
\implies                          (M/14)1/2 = 2.96
\implies                                      M = 245.5grams
Mass of 1 mole of the compound = 245.5 grams
Mass of 1 molecule of the compound = 245.5u
Mass of 1 atom of Xe = 131.5u
Mass of two atoms of Xe = 263u > 245.5u
\implies Two or more atom of Xe is not possible in given compound that means compound have 1 atom of Xe.
Let n atoms of fluorine present in the compounds then,
(mass of 1 atom of Xe) + n(mass of 1 atom of F) = 245.5
\implies                                                 131.5 + 19n = 245.5
\implies                                                                  n = 6
 
\implies Thew compound is XeF6
 

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