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Prove alpha=sqrt((K(p)/(P+K(p)))) for ...

Prove `alpha=sqrt((K_(p)/(P+K_(p))))` for
`PCl_(5) hArr PCl_(3)+Cl_(2)`
where `alpha` is the degree of dissociation at temperature when equilibrium constant is `K_(p)`.

Text Solution

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`P_(PCI_(5)) =(P(1-x))/((1+x)) : P_(PCI _(3)) =(P(x))/((1+x)) , P_(CI_(2)) =(P(x))/((1+x))`
Applying Law of Chemical equilibrium.
`K_(p) =(P_(PCI_(3))xxPCI_(2))/(P_(PCI_(5)))=((P(x))/((1+x))xx(P(x))/((1+x)))/((P(1+x))/(1+x))`
`K_(p) =(Px^(2))/(1+x^(2)) , x^(2)P =K_(P) -K_(p)x^(2) , x^(2) (P +K_(p)) =K_(p)`
`" or "" " x^(2) =(k_(p))/((P +K_(p))) :. x =((K_(p))/(P+K_(p)))^(1//2)`
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