What is the magnitude?

Question

A particular first-order reaction has a rate constant of 1.35 × 10² s^-1 at 25.0°C. What is the magnitude of k at 35.0°C if E_a = 55.5 kJ/mol?

Answer 1

For this, you can use the Arrhenius equation:

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

k1 =1.35x10² s^-1

k2 = ?

Ea = 55.5 kJ/mol

R = 8.314 J/Kmol = 0.008314 kJ/Kmol

T1 = 25 + 273 = 298K

T2 = 35 + 273 = 308K

ln (k2/1.35x10²) = -55.5 / 0.008314 (1/308 - 1/298)

ln (k2/1.35x10²) = -6675 (0.00325 - 0.00336)

ln (k2/1.35x10²) = 0.734

k2 (k@35ºC) = 2.81x10² s^-1 (check the math to be sure)