A sample of pure `PCl_(5)` was introduced into an evacuted vessel at `473 K`. After equilibrium was attained,concentration of `PCl_(5)` was found to be `0.5xx10^(-1)mol litre^(-1)`. If value of `K_(c)` is `8.3xx10^(-3) mol litre^(-1)`. What are the concentrations of `PCl_(3)` and `Cl_(2)` at equilibrium ?

Explanation

` {:(,PCl_(5)(g),hArr,PCl_(3)(g),+,Cl_(2)(g),), ("At eqm.", 0*5 xx 10^(-1)"mol"L^(-1),,x"mol"L^(-1),,x"mol"L^(-1),("suppose")):}`
` :. K_(c) (x^(2))/(0*5 xx 10^(-1)) = 8*3 xx10^(-3) ("Given")`
or `x^(2) = (8*3 xx 10^(-3))(0*5 xx 10^(-1)) = 4* 15 xx 10^(-4)`
or ` x = sqrt(4*15 xx 10^(-4)) = 2*04 xx 10^(-2) "M" = 0 *02 "M"`
Hence, `[PCl_(3)]_(eq) = [Cl_(2)]_(eq) = 0*02 " M"`