A reaction takes place in three steps with individual rate constant and activation energy,
`{:(,"Rate constant","Activation energy"),("Step 1",k_(1),E_(a_(1))=180kJ //"mol"),("Step2", k_(2),E_(a_(2))=180kJ //"mol"),("Step3",k_(3),E_(a_(3))=180kJ //"mol"):}`
oveall rate constant, `k=((k_(1)k_(2))/(k_(3)))^(2//3)` overall activation energy of the reaction will be :

Options

A. 140 kJ/mol
B. 150 kJ/mol
C. 130 kJ/mol
D. 120 kJ/mol

Answer

A

Explanation

`Ae^(-E_(a)//RT)=[(Ae^(-E_(a_(1))//RT)xxAe^(-E_(a_(2))//RT))/(Ae^(-E_(a_(3))//RT))]^(2//3)`
`=[Ae^((-E_(a_(1))-E_(a_(2))+E_(a_(3)))//RT)]^(2//3)`
`E_(a)=(2)/(3)[E_(a_(1))+E_(a_(2))-E_(a_(3))]`
`=(2)/(3)[180+80-50]=140 ` kJ/mol