Question

-(a) A certain first-order reaction has a rate constant of 2.75 × 10^–2 s^–1 at 20 °C. What is the value of k at 60 °C if E_a = 75.5 kJ/mol?

(b) Another first-order reaction also has a rate constant of 2.75 × 10^–2 s^–1 at 20 °C. What is the value of k at 60 °C if E_a = 125 kJ/mol?

(c) What assumptions do you need to make in order to calculate answers for parts (a) and (b)?

Answer 1

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

with,

k1 = 2.75 x 10^-2 s-1

k2 = rate constant at 6- oC = ?

T1 = 20 + 273 = 293 K

T2 = 60 + 273 = 333 K

Ea = 75.5 kJ/mol

R = gas constant

we get,

ln(k2/2.75 x 10^-2) = 75500/8.314[1/293 - 1/333]

k2 at 60 oC = 1.14 s-1

(b) Again using the same equation and taking values from above,

ln(k2/2.75 x 10^-2) = 125000/8.314[1/293 - 1/333]

k2 at 60 oC = 13.07 s-1

(c) We have used Arrhenius equation in both (a) and (b) case. The ssumption is to be made that the rate constant would be higher at higher temperature.