Establish the relation between `K_(p) and K_(c)` for the following reactions: `aA+bBhArrlL+mM` [where the terms have their usual significance].

Explanation

`K_(c)=([L]^(l)xx[M]^(m))/([A]^(a)xx[B]^(b)),` where `[A],[B],[L] and [M]` are molar concentrations of A,B,L and M at equilibrium.
`K_(p)=(p_(L)^(l)xxp_(M)^(m))/(p_(A)^(a)xxp_(B)^(b))`, where `p_(A),p_(B),p_(L) and p_(M)` are the partial pressures of A,B,L and M respectively at equilibrium.
Now, `p_(A)=[A]RT,p_(B)=[B]RT,p_(L)[L]RT and p_(M)=[M]RT`. putting the values of `p_(A),p_(B),p_(L) and p_(M)` in the expressions of `K_(p)`, we have-
`K_(p)=([L]^(l)xx[M]^(m))/([A]^(a)[B]^(b))xx(RT)^((l+m)-(a+b))`
or, `K_(p)=K_(c)xx(RT)^((l+m)-(a+b))`