Determine the activation energy in kJ/mol for a first order reaction if its spec

Question

Determine the activation energy in kJ/mol for a first order reaction if its specific rate constant 3.00e-05 s-1 at 350. K and 2.04e+02 s-1 at 510. K Ea= An Arrhenius plot (ln k vs. 1/T) for a second order reaction (2A -> C) produced a straight line with a slope of -7.20e+03 K. What is the value of the Arrhenius pre-exponential if k = 4860 M-1 s-1 at 640 K A= The first order rate constant for a reaction at 530 oC is 2.43e-03 s-1. If the activation energy for the reaction is 220 kJ/mol, what is the rate constant at 630 oC? K=

Explanation / Answer

ln (k'/k) = Ea/R ( 1/T- 1/T' ) Constants: R = 8.314 J/ K.mol (gas constant in joules) R=8.314 X 10^(-3) kJ/ K mol (gas constant in kJ) k' = 23.0 1/M s, T' = 800K k= 1.3 1/M s, T= 700K ln (k'/k) = Ea/R ( 1/T- 1/T' ) (R X ln (k'/k)) / (1/T - T') = Ea Subsitute Ea=(R X ln (k'/k)) / (1/T - T') Ea=(8.314 X 10^(-3) X ln (23.0/1.3)) / (1/700-1/800) Ea= 133.768 kJ/mol 2) What's the rate constant at 730K? Step 1: We need A (preexponential factor) first. Use either Use the relation: k=Ae(-Ea/RT) A=k/(e(-Ea/RT) A=1.3/(-133.768/(8.314X 10^(-3)X700)) A=1.24801 X 10^(10) Step 2: Use the relation: k=Ae(-Ea/RT) (new temperature) k=1.24801 X 10^(10) X e(-133.768/(8.314X 10^(-3)X730)) k=3.34329 1/M.s

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