(a)
Interpretation:
The activation energy for the isomerization reaction is to be predicted.
Concept introduction:
A small packet of energy is known as quanta. Light is emitted in the form of quanta or photons. The Planck’s law gives the relation between the energy and wavelength, frequency and wavenumber.
Answer to Problem 20.68E
The activation energy for the isomerization reaction is
Explanation of Solution
The given isomerization reaction is,
It is given that the wavelength of least energetic photon is
To calculate the activation energy of given isomerization reaction the formula used is,
Where,
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•
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•
Substitute the values of Planck’s constant, speed of light and wavelength of photon in the given formula.
Thus, the energy for theleast energetic photon is
Thus, the activation energy for the isomerization reaction is
The activation energy for the isomerization reaction is
(b)
Interpretation:
The value of pre-exponential factor for the given isomerization reaction is to be calculated.
Concept introduction:
The Arrhenius equation gives the temperature dependence of reaction rates.
Where,
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•
•
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•
The pre-exponential factor is also known as the frequency factor or the steric factor.
Answer to Problem 20.68E
The value of pre-exponential factor is
Explanation of Solution
The rate constant for the given isomerization reaction is
The Arrhenius equation can be used for the calculation of activation energy. The Arrhenius equation is,
Where,
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•
•
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•
Conversion of temperature in Celsius to Kelvin is done by the formula,
Substitute the temperature
Thus, the given temperature in Kelvin is
Substitute the values of activation energy, gas constant, rate constant and temperature.
The above equation if further solved to obtain the value of pre-exponential factor as shown below.
The value of pre-exponential factor is
The value of pre-exponential factor is
(c)
Interpretation:
The value of the rate constant at
Concept introduction:
The Arrhenius equation gives the temperature dependence of reaction rates.
Where,
•
•
•
•
•
The pre-exponential factor is also known as the frequency factor or the steric factor.
Answer to Problem 20.68E
The value of the rate constant at
Explanation of Solution
It is given that the rate constant at
The form of Arrhenius equation used to calculate the rate constant at different temperature is,
Where,
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•
•
•
Conversion of temperature in Celsius to Kelvin is done by the formula,
Substitute the temperature
Thus, the temperature
Substitute the values of activation energy, temperatures, the rate constant at
Take inverse of logarithm on both sides of equation to solve for the value of rate constant at
Thus, the value of rate constant at
The value of the rate constant at
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Chapter 20 Solutions
Physical Chemistry