For the following three reaction (i), (ii) and (iii), equilibrium constants are given (i) CO_((g))+H_(2)O_((g))iffCO_(2(g))+H_(2(g)),K_(1) (ii) CH_(4(g))+H_(2)O_((g))iffCO_((g))+3H_(2(g)),K_(2) (iii) CH_(4(g))+2H_(2)O_((g))iffCO_(2(g))+4H_(2(g)),K_(3) Which of the following relations is correct?

For the following three reaction (i), (ii) and (iii), equilibrium cons

1.	For the following three reaction (i), (ii) and (iii), equilibrium constants are given (i) CO_((g))+H_(2)O_((g))iffCO_(2(g))+H_(2(g)),K_(1) (ii) CH_(4(g))+H_(2)O_((g))iffCO_((g))+3H_(2(g)),K_(2) (iii) CH_(4(g))+2H_(2)O_((g))iffCO_(2(g))+4H_(2(g)),K_(3) Which of the following relations is correct?
Answer» `K_(3)K_(2)^(3)=K_(1)^(2)` `K_(1)sqrt(K_(2))=K_(3)` `K_(2)K_(3)=K_(1)` `K_(3)=K_(1)K_(2)` Solution :`CO_((g))+H_(2)O_((g))iffCO_(2(g))+H_(2(g))` `K_(1)=([CO_(2)][H_(2)])/([CO][H_(2)O])""...(i)` `CH_(4(g))+H_(2)O_((g))iffCO_((g))+3H_(2(g))` `K_(2)=([CO][H_(2)]^(3))/([CH_(4)][H_(2)O])""...(ii)` `CH_(4(g))+2H_(2)O_((g))iffCO_(2(g))+4H_(2(g))` `K_(3)=([CO_(2)][H_(2)]^(4))/([CH_(4)][H_(2)O]^(2))""...(iii)` From EQUATIONS (i), (ii) and (iii) , `K_(3)=K_(1)xxK_(2)`