Question

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 1

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.