Calculate half life when given half life at a different temperature, and the activation energy

Question

the half life of a first order reaction at 283.15 kelvin is 2.5 minutes. The activation energy is 66.0 kJ/mol. Calculate the half life or the reaction at 298.15 kelvin.

Answer 1

For a first order reaction, the half life = t_1/2 = 0.693/k

2.5 min = 0.693/k

k = 0.2772 min^-1 at 283.15K

Now, calculate k2 at 298.15K using the Arrhenius equation:

ln(k₁/k₂) = Ea/R(1/T₂ -1/T₁)  

ln(k₁/k₂) = 66.0/8.314 (1/298.15 - 1/283.15)

Solve for k₂ and the use t_1/2 = 0.693/k₂ to find the new half life