4.5 g of PCl5 on vapourisation occupied a volume of 1700 mL at 1 atmosphere pressure and 227 °C temperature. Its degree of dissociation is

Options

A. 0.0921
B. 0.0091
C. 0.921
D. None of these

Answer

C

Explanation

Let the degree of dissociation be `alpha`, then
`PCl_(5)toPCl_(3)+Cl_(2)`
`(1-alpha)" "alpha" "alpha`
(M) Molecular weight of `PCl_(5)` = 31 + 5 `xx` 35.5 = 208.5
Total number of molecules before dissociation= 1
Total number of molecules after dissociation
`=1-alpha+alpha+alpha=1+alpha`
Thus each gram mole changes to (1 + a) gram-mole.
Thus `PV=W/M(1+alpha)RT`
( V = volume after dissociation)
or `1xx1700/1000=(4.5)/(208.5)(1+alpha)RT` [1700ml`=1700/1000L`]
or `alpha=0.921`
`therefore%` age dissociation =92.1%