How to do the equation for this While alkenes, like 1-butene shown below, are mo

Question

How to do the equation for this

While alkenes, like 1-butene shown below, are more reactive than their alkane counterparts, there are relatively few modifications that can be achieved via synthetic processes. The formation of 2-chlorobutane is an example of a reaction that is used to activate the alkene for other transformations: The rate of the reaction at 25 degreeC is 1.52 x 10^-5 mol/(Ls). Estimate the activation energy of the reaction if the rate at 105 degreeC is 1.3 x 10^-1 mol/(Ls). 8853 kJ/mol 106 kJ/mol 2.5 kJ/mol 46 kJ/mol

Explanation / Answer

Arrhenius equation can be written as

In (k2/k1) = [Ea/R] [(1/T1) - (1/T2)]

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

Given that

Initial rate of rection k1 = 1.52 x 10-5mol/(Ls)

Final rate of reaction k2 = 1.3 x10-1 mol/(Ls)

Initial temperature T1 = 25oC = 25 + 273 K = 298 K

Final temperature T2 = 105oC = 105 + 273 K = 378 K

Substitute all these velues in eq (1),

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

= (8.314 J/K/mol) [ In (1.3 x10-1 / 1.52 x10-5)] / [(1/298) - (1/378)]

= 106000 J/mol

= 106 kJ/mol

Ea = 106 kJ/mol

Therefore, activation energy of the reaction = 106 kJ/mol

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