The values of $$Kp1$$ and $$Kp2$$ for the reactionsX ⇌ Y $$+$$ Z (i)and$$ A ⇌ $$2B$$ $$(ii)are$$ in the ratio of $$9$$ : $$1$$. If the degree of dissociation of X and A be equal, then total pressure at equilibrium $$(i) and (ii) are in the ratio

Question

The values of $$Kp1$$  and $$Kp2$$ for the reactionsX  ⇌   Y $$+$$ Z          (i)and$$ A  ⇌   $$2B$$         $$(ii)are$$ in the ratio of $$9$$ : $$1$$. If the degree of dissociation of X and A be equal, then total pressure at equilibrium $$(i) and (ii) are in the ratio

Infinity Learn · Accepted Answer

In equation,        X  ⇌   Y $$+$$ ZInitial moles         $$1$$           $$0$$       $$0At$$ equilibrium    $$1-$$α     α      αWhere α $$=$$ degree of dissociationTotal number of moles $$=$$ $$1$$ $$-$$ α $$+$$ α $$+$$ α $$=$$ (1$$ $$+$$ α$$)px$$ $$=$$ $$1-$$α$$1+$$α$$p1$$ py $$=$$ α$$1+$$α$$p1$$ pz $$=$$ α$$1+$$α$$p1$$ $$Kp1$$ $$=$$ py  $$pzpx=$$ α$$1+$$α$$p1$$  ×     α$$1+$$α$$p1$$ $$1-$$α$$1+$$α$$p1$$       $$=$$  α$$1+$$α$$2p11-$$α$$1+$$α$$=$$α$$2(1+$$α$$)(1-$$α$$)P1$$ ……… $$(i)For$$ equation,     A  ⇌   $$2BInitial$$ moles       $$1$$            $$0At$$ equilibrium $$1-$$α      $$2$$αTotal number of moles at equilibrium   $$(1$$ $$+$$ α$$)pB$$ $$=$$ $$2$$α$$1+$$α$$p2$$ pB $$=$$ $$1-$$α$$1+$$α$$p2$$ $$Kp2$$ $$=$$  $$pB2pA$$  $$=$$   $$2$$α$$1+$$α$$p221-$$α$$1+$$α$$p2$$ $$=$$ $$2$$α$$1+$$α$$2p21-$$α$$1+$$α$$=4$$α$$2(1+$$α$$)(1-$$α$$)P2Eq$$. $$(i) $$/$$ $$(ii)Kp1Kp2$$ $$=$$ α$$2$$  × $$p1$$ $$4$$α$$2$$  × $$p2$$ $$91$$  $$=$$  $$p14p2$$ $$p1p2$$ $$=$$ $$361$$  $$=$$ $$36$$ : $$1$$

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