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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

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

Grade:11

1 Answers

Kapil Khare
80 Points
5 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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