JEE Main202523 Jan 2025Evening ShiftChemistryChemical EquilibriumActual
Consider the reaction X ₂ Y ( ~g )= X ₂( ~g )+ 1 2 Y ₂( ~g ) The equation representing correct relationship between the degree of dissociation (x) of X ₂ Y ( g ) with its equilibrium constant Kp is ______ . Assume x to be very very small.
Options
- Ax= [3] 2 Kp p
- Bx= [3] 2 Kp ^2 p
- Cx= [3] Kp p
- Dx= [3] K p 2 p
Correct answer
B. x= [3] 2 Kp ^2 p
Step-by-step solution
aligned & 1 ~mol & X ₂ Y ( g ) x X X ₂( ~g )+ 1 2 Y ₂( ~g ) & x 2 & P_ x ₂ y & = 1- x 1+ x 2 p & P_ x₂ = x 1+ x 2 p aligned aligned & P_ y₂ = x / 2 1+ x 2 p K_p= & ( x 1+ x 2 p ) ( x 2 (1+ x 2 ) p )^ 1 / 2 ( 1-x 1+ x 2 ) p & K_p= ( x 1-x ) ( x 2 (1+ x 2 ) )^ 1 / 2 p^ 1 / 2 aligned x to be very small aligned & K_p= x^ 3 / 2 2^ (1 / 2) p^ 1 / 2 & x^ 3 / 2 = K_p 2^ 1 / 2 p^ 1 / 2 & x^3= K_p^2 2 p & x= ( K_p^2 2 p )^ 1 / 3 aligned