Question

In the S_N1 reaction of 2-chloro-2-methylpropane with water at different temperatures, the following reaction rate constants were obtained: 17°C, 0.0052 s^-1; 30°C, 0.0202 s^-1; 42°C, 0.0608 s^-1. Calculate the half-life of this reaction at 41°C.

Answer 1

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

where T1 = 17C = 17 + 273 = 290 K ,

T2 = 30C = 30 + 273 = 303 K , k1 = 0.0052 s-1 , k2 = 0.0202 s-1

we calclate Ea

ln ( 0.0202/0.0052) = ( Ea / 8.314J/molKI) ( 1/290 - 1/303)

Ea = 76260 J/mol

now we use T2 = 41 C = 41 + 273 K = 314 K and find k2

ln ( k2 / 0.0052) = ( 76260 / 8.314) ( 1/290 - 1/314)

ln ( k2 / 0.0052) = 2.4175

k2 / 0.0052 = exp ( 2.4175)

k2 = 0.0052 x exp ( 2.4175)

= 0.0583 s-1

half life = 0.693 / k = 0.693 / ( 0.0583s-1)

= 11.9 second