   Chapter 14, Problem 79GQ

Chapter
Section
Textbook Problem

Egg protein albumin is precipitated when an egg is cooked in boiling (100 °C) water. Ea for this first-order reaction is 52.0 kJ/mol. Estimate the time to prepare a 3-minute egg at an altitude at which water boils at 90 °C.

Interpretation Introduction

Interpretation:

The time required to prepare a 3 minute egg at some height under given temperature conditions should be determined.

Concept introduction:

Rate law: It is generally the rate equation that consists of the reaction rate with the concentration or the pressures of the reactants and constant parameters.

Rate constant: The rate constant for a chemical reaction is the proportionality term in the chemical reaction rate law which gives the relationship between the rate and the concentration of the reactant present in the chemical reaction.

Rate order: The order of each reactant in a reaction is represented by the exponential term of the respective reactant present in the rate law and the overall order of the reaction is the sum of all the exponents of all reactants present in the chemical reaction.  The order of the reaction is directly proportional to the concentration of the reactants.

Arrhenius equation:

• Arrhenius equation is a formula that represents the temperature dependence of reaction rates
• The Arrhenius equation has to be represented as follows

k=AeEa/RTlnk=lnAeEa/RTlnk=(EaR)(1T)+lnA

• Ea represents the activation energy and it’s unit is kJ/mol
• R represents the universal gas constant and it has the value of 8.314 J/K.mol
• T represents the absolute temperature
• A represents the frequency factor or collision frequency
• e represents the base of natural logarithm
•  Arrhenius equation equation was proposed by Svante Arrhenius in 1889.
Explanation

The given condition says that reaction is first order reaction, the temperature and the activation energy data are as follows,

Temperature,T1=100CEa=52.1kJ/molTemperature,T2=90CTime=?

Now, using the Arrhenius equation the required time is determined as follows,

lnk2k1=(EaR)(1T1-1T2)lnk2k1=(52000 J/mol8

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