For the reaction equilibrium, 2 NOBr(g) 2 NO(g) + Br2(g) . If PBr2 = P/9 at equilibrium and P is total pressure, the ratio of Kp/P is equal to (The ones marked in blue, those steps I couldn't understand , please explain it )



Dear User,
Here the initial pressure of the system is taken as Pinitial. Now,
                               2NOBr          2NO    +   Br2Initial pressure         Pinitial                    0               0At equilibrium         Pinitial(1-2α ) 2Pinitialα      PinitialαHere 2α is used for NOBr because the rate of decomposition is multiplied by the stoicheometric coefficient. Pressure at equilibrium of NO is also multiplied by 2 as the formation of NO is also multiplied by the stoicheometric coeficient.Total pressure at equilibrium, P = Pinitial (1-2α) + 2Pinitialα+ Pinitialαor, P = Pinitial (1+α)Now, we have calculated that Pinitial =89P and Pinitialα = P9   (from the step PBr2= Pinitialα = P9)Therefore, Equilibrium pressure of 2NOBr = Pinitial(1-2α ) = Pinitial - 2 PinitialαSubstituting the values of    Pinitial and Pinitialα, we getEquilibrium pressure of 2NOBr = 89P - 2×P9=69P

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