The acid catalysed hydrolysis of an organic compound 'A' at 303 K has a time for half change of 100 minute when carried out in a buffer solution at pH=5 and 10 minute when carried out at pH=4. Both times of half change are independent of the initial concentration of A. If the rate constant 'K' is given by (-d[A])/(dt) = K[A]^(X)[H]^(Y). The value of 'y' is

The acid catalysed hydrolysis of an organic compound 'A' at 303 K has

1.	The acid catalysed hydrolysis of an organic compound 'A' at 303 K has a time for half change of 100 minute when carried out in a buffer solution at pH=5 and 10 minute when carried out at pH=4. Both times of half change are independent of the initial concentration of A. If the rate constant 'K' is given by (-d[A])/(dt) = K[A]^(X)[H]^(Y). The value of 'y' is
Answer» Solution :The rate equation is `(-d[A])/(dt) = K[A]^(x)[H^(+)]^(Y)` During any EXPERIMENT, ph is constant, hence `(-d[A])/(dt) = K[A]^(y)` where `K^(.) =K[H^(.)]^(y)` Given that - life is independent of the INITIAL concentration of A, hence x=1. Consequently K. is a first ORDER rate constant is given by `K.= (0.693)/t_(1//2)`, therefore, `((t_(1//2))_(2))/(t_(1//2))_(2) = K_(2)^(.)/K_(1)^(.) = (K[H^(+)]_(2)^(1))/(K[H^(+)]_(1)^(y)) = [H^(+)]_(2)^(y)/[H^(+)]_(1)^(y)` `100/10 =(10^(-4))/(10^(-6)) RARR y=1`