Question

The rate of the elementary reaction I + CH4HI + CH3 has been studied as a...

The rate of the elementary reaction I + CH4HI + CH3 has been studied as a function of temperature between 830 and 1022 K. The following data were obtained for the rate constant k:

temperature K

830 322

894 1.34 x 10^3

958 4.63 x 10^3

1022 1.37 x 10^4

Calculate the activation energy of this reaction in kJ/mol.  Please show all work (all steps and algebra conversions) Thank you

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Answer #1

A/C Arrhenius equation -

k = Ae^(-Ea/RT)

where,

k = rate constant; A = frequency factor; Ea = activation energy; R = ideal gas constant; T = temperature
Let k1 and k2 be the rate constants determined at T1 and T2, respectively, then we have two equations

 ln k1 = lnA - Ea/(R T1)
 ln k2 = lnA - Ea/(R T2) or,

ln k1/k2 = - Ea/R ( 1/T2 -1/T1)

Ea = T1T2 R /T2-T1 ln k2/k1

Ea = 830K x 1022K x 8.314 J/K-mol / 1022K- 830K ln1.37x10^4/322

Ea=7052433.64 /192 ln42.5466= 36731.4252 x 3.7505=137761.2102J/mol =137.76121KJ/mol

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