A reaction takes place in 3 steps with activation energy e1=180kj/mol

1.	A reaction takes place in 3 steps with activation energy e1=180kj/mol e2=80kj/mol and e3=50kj/mol respectively.Overall rate constant of the reaction is k= [k1*k2/k3]^2/3 the activation energy of the reaction will be?
Answer» Answer : The ACTIVATION ENERGY of the reaction is, 140 KJ/mole. Solution : Given, $e_1=180KJ/mole$ $e_2=80KJ/mole$ $e_3=50KJ/mole$ The overall rate of reaction is given, $K=[\frac{K_1\times K_2}{K_3}]^{2/3}$ The expression for Arrhenius rate constant is, $K=Ae^{\frac{-E_a}{RT}}$ Now taking 'ln' on both side, we get $ln(K)=\frac{-E_a}{RT}$ Now the expression for activation energy of the reaction will be, $E_a=\frac{2}{3}[e_1+e_2-e_3]$ Now PUT all the given VALUES in this formula, we get $E_a=\frac{2}{3}[180+80-50]=140KJ/mole$ Therefore, the activation energy of the reaction is, 140 KJ/mole.