The catalysts decrease the Ea from 100 K J mol^-1 to 80 K J mol^-1 . At what temperature the rate of reaction in the absence of catalyst at 500 K will be equal to rate of reaction in presence of catalyst.

Apply Arhenius equation.

K = Ae^-Ea/RT

If the two Rates are equal. 

e^-Ea₁/RT₁ = e^-Ea₂/RT₂

Ea₁/T₁ = Ea₂/T2

100/T = 80/500

T = 625 K

Approve if i helped.

the catalyst decreses the Ea from 100 kj mol to 80 kj mol .at what temperature the rate of reaction in absence of catalyst at 500 k will be equal to rate of reaction in presence of catalyst