i. The initial pressure of `PCl_(5)` present in one litre vessel at `200 K` is `2` atm. At equilibrium the pressure increases to `3` atm with temperature increasing to `250`. The percentage dissociation of `PCl_(5)` at equilibrium is

Options

A. `30%`
B. `60%`
C. `0.2%`
D. `20%`

Answer

D

Explanation

i. First method:
Pressure at `200 K=2 "atm"`
Pressure at `250 K=P "atm"`
Using relation,
`P_(1)/T_(1)=P_(2)/T_(2)rArr P/250=2/200`
`:. P=2.5 "atm"`
`{:(,PCl_(5),hArr,PCl_(3),+,Cl_(2)),("Initial",a,,0,,0),("At equilibrium",a-alpha,,alpha,,alpha),("Total moles" =a+alpha,,,,,):}`
`("Intial mole")/("moles at equilibrium")= (("Intial pressure after"),("change of temperature"))/("Equilibrium pressure")`
`(a)/(a+alpha)=2.5/3 rArr alpha=1/5 a`
Therefore, `%` of `PCl_(5)` dissociated `=alpha/axx100`
`=a/(5xxa)xx100=20%`
Secondethod:
Using relation:
`alpha=(T_(2)P_(2)-T_(2)P_(1))/(T_(2)P_(1))`
`=(200xx3-250xx2)/(250xx2)=(600-500)/(500)`
`alpha=1/5`
`% "of" alpha=1/5xx100=20%`