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A certain endothermic reaction: Ararr Pr...

A certain endothermic reaction: `Ararr` Product, `DeltaH=+ve` proceeds in a sequence of three elementary steps with the rate constants `K_(1), K_(2)` and `K_(3)` and each one having energy of activation `E_(a), E_(2)` and `E_(3)` respectively at `25^(@)C`. The observed rate constant for the reaction is equal to `K_(3) sqrt(K_(1)/K_(2)). A_(1), A_(2)` and `A_(3)` are Arrhenius parameters respectively.
For a reversible reaction, `A underset(K_(2))overset(K_(1))(hArr) B, DeltaH=q`, if perexponential factors are same. The correct relation is:

A

(a) `K_(eq)=e^(-q//RT)`

B

(b) Rate of reaction `=(-d[A])/(dt)=K_(1)[A]-K_(2)[B]`

C

(c ) At equilibrium, `K_(1)[A]=K_(2)[B]`

D

(d) Either of these

Text Solution

Verified by Experts

The correct Answer is:
d
`A hArr B`
`(-d[A])/(dt)=K_(1)[A]-K_(2)[B] ,brgt At eq. K_(1)[A]=K_(2)[B]`
and `K_(1)/K_(2)=([B])/([A])=K_(c )`
Also `(Ae^(-E_(a)//RT))/(Ae^(-E_(b)//RT))=K_(c )`
`K_(c )=e^([E_(b)-E_(a)]//RT)=e^(-DeltaH//RT), ( :' E_(a)-E_(b)=DeltaH)`
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