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The Arrhenius equation shows the relationship between the rate constant k and th

ID: 1008206 • Letter: T

Question

The Arrhenius equation shows the relationship between the rate constant k and the temperature T in kelvins and is typically written as k = Ae^-Ea/RT where R is the gas constant (8.314 J/mol middot K), A is a constant called the frequency factor, and E_a is the activation energy for the reaction. However, a more practical form of this equation is ln k2/k1 = E_a/R (1/T_1 - 1/T_2) which is mathematically equivalent to ln k1/k2 = E_a/R (1/T_2 - 1/T_1) where k_1 and k_2 are the rate constants for a single reaction at two different absolute temperatures (T_1 and T_2). The activation energy of a certain reaction is 43.6 kJ/mol. At 20 degree C, the rate constant is 0.0170s^-1. At what temperature in degrees Celsius would this reaction go twice as fast? Express your answer with the appropriate units. Given that the initial rate constant is 0.0170s^-1 at an initial temperature of 20 degree C, what would the rate constant be at a temperature of 200. degree C for the same reaction described in ? Express your answer with the appropriate units.

Explanation / Answer

logK2/K1   = Ea/2.303R [1/T1-1/T2]

        K1   = 0.017Sce-1         T1 = 20C0 = 20+273 = 293K

       K2   = 2*0.017sec-1        T2 =

       Ea   = 43.6kj/mole = 43600joule/mole

       R   = 8.314j/mole-k

logK2/K1   = Ea/2.303R [1/T1-1/T2]

log2*0.017/0.017 = 43600/2.303*8.314 [1/293 -1/T2]

0.3020                = 2277 [0.00341-1/T2]

0.3020/2277        =    [0.00341-1/T2]

0.000132           = 0.00314-1/T2

0.000132-0.00314    = -1/T2

-0.003008               = -1/T2

          T2                  = 332.5K    = 332.5-273 = 59.5C0

2.

logK2/K1   = Ea/2.303R [1/T1-1/T2]

        K1   = 0.017Sce-1         T1 = 20C0 = 20+273 = 293K

       K2   =        T2 = 200C0   = 200+273 = 473K

       Ea   = 43.6kj/mole = 43600joule/mole

logK2/K1   = Ea/2.303R [1/T1-1/T2]

logK2/0.017    = 43600/2.303*8.314 [ 1/293- 1/473]

logK2/0.017   = 2277 [0.00341-0.00211]

logK2/0.017   = 2.9601

   K2/0.017    = 102.9601

K2/0.017    = 912.22

   K2             = 912.22*0.017   = 15.5Sec-1   >>> answer