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# For a chemical reaction at 27°C, the activation energy is 600 R. The ratio of the rate constants at 327°C to that of at 27°C will be (A) 2 (B) 40 (C) e (D) e2

Saurabh Koranglekar
one year ago
Dear student

Regards
Vikas TU
14149 Points
one year ago
The ratio of rate constants at 327° C to that at 27° C is e.
Given-
Activation energy of the chemical reaction = 600 R
Initial temperature (T₁) = 27° C = 300 K
Final temperature (T₂) = 327° C = 600 K
From the Arrhenius equation we can find out the ratio of rate constants -
ln ( K₂/K₁)  = Ea / R (1/T₁ - 1/T₂) ,
where Ea is the activation energy, R is the universal gas constant, K₁ is the rate constant at temperature T₁, and K₂ is the rate constant at temperature T₂.
Now by putting the values we get -
ln ( K₂/K₁) = 600 R/R ( 1/300 - 1/600)
ln ( K₂/K₁)  = 600 ( 2-1/600)
ln ( K₂/K₁)  = 1
So,  K₂/K₁ = e¹ = e
Hence ratio of rate constants is e .