Question

Calculate the t₉₀ (shelf-life) for Phenolax at 60 °C in the presence of 1 M sodium hydroxide assuming the activation energy E_a for the process is 53 kJ/mol. Show all work. Symbolically state the equations you are using defining all variables and constants.

Answer 1

We have Arrhenius equation,

K = Ae^Ea/RT

Where, A is the collision frequency, Ea is the activation energy, R is the gas constant and T is the temperature in Kelvin

Here, Temperature = 60 ^oC = 333.15 K

Ea = 61 kJ/mol

Assume collision frequency as 1

K = Ae^Ea/RT = e^{[(53 kJ/mol)/(8.314 J/Kmol x 333.15 K)]} = 1.019 M^-1s^-1

We have, first order rate law,

ln[A] = ln[A_o] –kt₉₀

At t₉₀, 90 % of the consumption is over.

At t₉₀, A_o = 0.9 [A_o]

t₉₀ = (1/k) x ln[A_o]/[0.9A_o]

t₉₀ = (1/ 1.019 M^-1s^-1) x ln[A_o]/[0.9A_o]

t₉₀ = (1/ 1.019) x 0.62 = 0.60 seconds

Shelf life of Phenolax = 0.60 seconds