One theory of rate constants for bimolecular gas phase react

One theory of rate constants for bimolecular gas phase reactions is “Collision Theory”. The collision theory form for the rate constant is: k equals C square root of T e to the power of minus fraction numerator E subscript o over denominator R T end fraction end exponent, where C is a constant, and Eo is the threshold energy for reaction. Using an expression you can develop relating Eo to the Arrhenius Activation Energy, Ea, you can show that if the collision theory threshold energy is Eo = 50. kJ/mol, then at 300 oC, the Arrhenius Activation, Ea, is approximately:

Solution

Ans:

Arrhenius Activation Energy, Ea=1/2*RT+Eo

where Eo is the threshold energy,T is absoulute temperature,R is universal gas constant+ 8.314 j/mole/k

given Eo = 50. kJ/mol, t=300 c

T=300+273=573K , Arrhenius Activation, Ea=0.5*8.314*573+50

=2431.96   kJ/mol.