1. Tardigrade
  2. Question
  3. Chemistry
  4. Two solids dissociate as follows A ( s ) leftharpoons B ( g )+ C ( g ) ; K p 1= x atm 2 D ( s ) leftharpoons C ( g )+ E ( g ) ; K P 2= y atm 2 The total pressure when both the solids dissociate simultaneously is :

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Q. Two solids dissociate as follows
$A ( s ) \rightleftharpoons B ( g )+ C ( g ) ; K _{ p _1}= x \,atm { }^2$
$D ( s ) \rightleftharpoons C ( g )+ E ( g ) ; K _{ P _2}= y\, atm { }^2$
The total pressure when both the solids dissociate simultaneously is :

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Solution:

$A(s)\rightleftharpoons \underset{{ P_1}}{ B(g)} + \underset{{ P_1}}{ C(g)}$ $\underset{{ x = P_1 (P_1 + P_2) }}{ K_{P_1} = x = P_{B} . P_{C}}$ ....(1)
$D(s) \rightleftharpoons \underset{{ P_2}}{ C(g)} + \underset{{ P_2}}{ E(g)}$ $\underset{{ y = (P_1 + P_2) (P_2)}}{ K_{P_2} = y = P_{C} . P_{E}}$ ...(2)
Adding (1) and (2)
$x +y = (P_1 + P_2)^2$
Now total pressure
$P_T = P_C + P_B + P_E$
$ = (P_1 + P_2) + P_1 + P_2 = 2 (P_1 + P_2)$
$P_{T} = 2 (\sqrt{x+y}) $