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Equilibrium, $$X\rightleftharpoons 2Y$$ and $$Z\rightleftharpoons P+Q$$ are established with $$1$$ mole of Z and Z taken initially in separate vessels with equilibrium pressures of $$1$$ atm and $$36$$ atm respectively. If the degree of dissociations are same. Then $$K_{P2}=nK_{P1}$$. What is the value of n?


Solution

                                      $$ X\rightleftharpoons 2Y   \quad  Z\rightleftharpoons P+Q $$ 
$$Eqlb^m Pressure$$     1 atm   2 atm  36 atm  36 atm

   $$ K_{p1} =\displaystyle \frac{{ P }_{ Y }^{ 2 }}{P_X} \quad ,  K_{p2} =\frac{P_P\times P_Q}{P_Z}$$
$$ K_{p1} =\displaystyle \frac{4}{1}   \quad,  K_{p2}=\frac{36\times36}{36}$$
   $$ K_{p1}=4 \quad,  K_{p2} =36 $$
  $$ \displaystyle \frac{K_{p2}}{k_{p1}} =\frac{36}{4}=9$$
  $$ K_{p2} =9K_{p1} $$                           
    Compare with $$ K_{p2} =nK_{p1}$$
                              $$n=9$$

Chemistry

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