Calculate the t90 (shelf-life) for Phenolax at 60 °C in the presence of 1 M sodium hydroxide assuming the activation energy Ea for the process is 53 kJ/mol. Show all work. Symbolically state the equations you are using defining all variables and constants.
We have Arrhenius equation,
K = AeEa/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 = AeEa/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[Ao] –kt90
At t90, 90 % of the consumption is over.
At t90, Ao = 0.9 [Ao]
t90 = (1/k) x ln[Ao]/[0.9Ao]
t90 = (1/ 1.019 M-1s-1) x ln[Ao]/[0.9Ao]
t90 = (1/ 1.019) x 0.62 = 0.60 seconds
Shelf life of Phenolax = 0.60 seconds
Calculate the t90 (shelf-life) for Phenolax at 60 °C in the presence of 1 M sodium...
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