Find out the value of `K_(c )` for each of the following equilibrium from the value of `K_(p)`:
a. `2NOCl(g) hArr 2NO(g)+Cl_(2)(g), K_(p)=1.8xx10^(-2)` at `500 K`
b. `CaCO_(3)(s) hArr CaO(s)+CO_(2)(g), K_(p)=167` at `1073 K`

Explanation

`K_(p) " and "K_(c)` are related to each other as `K_(p) =K_(c) (RT)^(Delta ng)`
The value of `K_(c)` can be calculated as follows:
`(a)" " 2NOCI(g) hArr 2NO (g) +CI_(2)(g)`
`K_(p) =1.8 xx 10^(-2) atm.`
`Delta^(ng) =3-2 =1, R =0.0821 " litre atm " K^(-1) mol^(-1) , T =500 K`
`:. " " K_(c) =(K_(p))/((RT)^(Deltang))=((1.8xx10^(-2) atm))/((0.0821 L " atm " K^(-1) mol^(-1) xx 500 K^(1))`
`=4.4 xx 10^(-4) mol L^(-1)`
`(b) " " CaCO_(3)(s)hArr CaO (s) +CO_(2)(g)`
`K_(p) = 167 atm Delta^(ng) =1-0 =1`
`R= 0.0821 " litre atm " K^(-1) mol^(-1) , T = 1073 K`
`K_(c) (K_(p))/((RT)^(Deltang))= ((167 atm))/((0.0821 L atm K^(-1) mol^(-1) xx 1073K)^(-1))=1.9 " mol"^(-1)L`