The rate constant for the reaction 2 C (g) -> D (g) is #0.231 s^-1# at 2°C and #11.6 s^-1# at 77°C. What is the the value of A in the Arrhenius equation?

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Answer 1 · 2018-05-17T01:12:04

Consider,

#2C (g) rightleftharpoons D(g)#, where

#k_1 = 0.231"M"^-1"s"^-1# at #T_1 = 275.15"K"#, and

#k_2 = 11.6"M"^-1"s"^-1# at #T_2 = 350.15"K"#

Recall the Arrhenius equation,

#k = Ae^((-E_"a")/(RT))" " (1)#

#=>lnk = lnA -E_"a"/(RT)#

If we make two equations with each set of parameters and subtract them, we arrive at,

#ln(k_2/k_1) = -E_"a"/R(1/T_2 - 1/T_1) " " (2)#

Let's derive the activation energy of the reaction from your data,

#=> E_"a" = (R * ln(k_1/k_2))/(1/T_2 - 1/T_1) approx 41.8"kJ"#

With all of this data, we can calculate the frequency factor using #(1)# and either set of conditions. Hence,

#=> A = k/(e^((-E_"a")/(RT))) approx 2.00*10^7"M"^-1"s"^-1#