Egg protein albumin is precipitated when an egg is cooked in boiling (100°C) wat

Question

Egg protein albumin is precipitated when an egg is cooked in boiling (100°C) water. The Activation Energy for this reaction is 52 kJ/mol. Estimate the time needed to prepare a 3-minute egg at an altitude at which water boils at 90°C (that is, an egg that is cooked as thoroughly as it would have been after 3 minutes of cooking at 100 °C). Assume the reaction is first order in egg (or albumin). Hint: begin by writing out both the first order integrated rate law and the Arrhenius equation. Consider how time will change if the rate constant is changing with temperature.

Explanation / Answer

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

T1 is 100 °C = 373 K,

k1 = 1/(3 min) = 0.333 min-1 ,

and

T2 is 90 °C = 363 K.

Ln( k2/ 0.333 min^-1 )= 52 kJ/mol / 8.314x10^-3 kJ/(molK (1/ 363 k -------1/373 k )

Ln( k2/ 0.333 min^-1 )= -6.255x10^3 K/(molK (0.00007385 * 1/ k )

Ln( k2/ 0.333 min^-1 )= - 0.4619

k2/ 0.333 min^-1 )=e^ - 0.4619  

k2 =0.63

k2 = (0.333 min^-1 ) (0.63) = 0.21 min^-1

t = 1/k = 1/(0.21 min^-1) = 4.8 minutes

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