A chemical reaction occurs in three paths having rate constants `k_(1),k_(2)` and `k_(3)` respectively. If `Ea_(1),Ea_(2)` and `E_(a_(3)` are 4,5 and 8kJ respectivel and overall rate constant `k=(k_(1)k_(3))/(k_(2))`. Assuming `A_(av)=(A_(1)A_(3))/(A_(2))` the overall energy of activation in kJ is __________

Answer

7

Explanation

`Aunderset(epsilona=)overset(K)(to)`
`K=A.e^(-Ea//RT),K_(1)=A_(1).e^(-E_(1)//RT),K_(2)=A_(2).e^(-E_(2)//RT),K_(3)=A_(3).e^(-E_(3)//RT)`
Here `K=(K_(1).K_(3))/(K_(2)),A//e^((-Ea//RT))=(A_(1).e^((-E_(1))/(RT))xxA_(3).e^((-E_(3))/(RT)))/(A_(2).e^((-E_(2))/(RT)))impliesA=(A_(1).A_(3))/(A_(2))impliese^((-Ea)/(RT))=e^((-epsilon_(1)-epsilon_(3)+epsilon_(2))/(RT))`
`implies(-Ea)/(RT)=((-epsilon_(1)+epsilon_(2)-epsilon_(3)))/(RT)impliesEa=(epsilon_(1)-epsilon_(2)+epsilon_(3)),epsilon_(a)=(4-5+8)=-1+8=7`