`3.00` mol of `PCl_(5)` kept in `1L` closed reaction vessel was allowed to attain equilibrium at `380K`. Calculate composition of the mixture at equlibrium `K_(c)=1.80`

Explanation

`{:(,PCl_(5),hArr,PCl_(3),+,Cl_(2)),("Intial",,,,,),("concentration",3.0,,0,,0):}`
Let x mol per litre of `PCl_(5)` be dissociated,
At equilibrium :
`{:((3-x),,x,x):}`
`K_(c)=[PCl_(5)][Cl_(2)]//[PCl_(5)]`
`1.8=x^(2)//(3-x)`
`x^(2)+1.8x-5.4=0`
`x=[-1.8+-(1.8)^(2)-4-(-5.4)]//2`
`x=[-1.8+-3.24+21.6]//2`
`x=[-1.8+4.98]//2`
`x=[-1.8+4.98]//2=1.59`
`[PCl_(5)]=3.0-x=3-1.59=1.41M`
`[PCl_(3)]=[Cl_(2)]=x=1.59M`