Equilibrium

Equilibrium

Question

The equilibrium constants KP1 and KP2 for the reactions X ⇌2Y and Z ⇌ P + Q, respectively are in the ratio of 1 : 9. If the degree of dissociation of X and Z be equal then the ratio of total pressure at these equilibria is

  • 1:1

  • 1:36

  • 1:9

  • 1:3

Answer

A.

1:1

straight X space space rightwards harpoon over leftwards harpoon with space space space space space space space space space space space space space on top space 2 straight Y
stack 1 space with left parenthesis 1 minus straight x right parenthesis below space space space space space space space space space space space 0 with space 2 straight x below
straight k subscript straight p subscript 1 end subscript space equals space fraction numerator left parenthesis 2 straight x right parenthesis squared over denominator left parenthesis 1 minus straight x right parenthesis end fraction open parentheses fraction numerator straight P subscript 1 over denominator 1 plus straight x end fraction close parentheses
straight Z space rightwards harpoon over leftwards harpoon with space on top space space space space space space straight P plus space straight Q
1 with left parenthesis 1 minus straight x right parenthesis below space space space space space space space space space space 0 with straight x below space space space space space space space 0 with straight x below
straight k subscript straight p subscript 2 space equals space end subscript fraction numerator left parenthesis straight x right parenthesis squared over denominator left parenthesis 1 minus straight x right parenthesis end fraction open parentheses fraction numerator straight P subscript 1 over denominator 1 plus straight x end fraction close parentheses to the power of 1
fraction numerator 4 space straight x space straight P subscript 1 over denominator straight P subscript 2 end fraction space equals space 1 over 9 space
rightwards double arrow space straight P subscript 1 over straight P subscript 2 space equals space 1 over 36

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