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Question

A sample of hydrogen fluoride gas (only HF molecules) is collected in a vessel and left for some time. Then, a constant molar mass of the sample is experimentally determined as 34 g mol−1. Assume that this abnormal molar mass is due to dimerization as well as trimerization of some HF molecules (no molecules in any other polymeric forms) and the mole ratio of monomeric and trimeric forms of hydrogen fluoride molecules present is 4 : 1. What percentage of hydrogen fluoride molecules is dimerized?

A
50
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B
58.8
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C
76.47
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D
17.65
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Solution

The correct option is B 58.8
According to the question:
Initial concentration of HF = a
Dimerised concentration of HF = x and Trimerised concentration of HF = y
Reaction for the dimerisation of HF
2HF H2F2
a(2x+3y) x
Reaction for the trimerisation of HF
3HF H3F3
a(3y+2x) y
From question, y(a(2x+3y))=14 … (1)
and a(2x+3y)+x+(y×34) = a×20 … (2)
Where 34 g mol1 = molar mass of sample and 20 g mol1 = molar mass of HF
From (1) and (2): a=17y=175×x

Percentage of HF molecules dimerized
= 2xa×100 = 58.82%


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