(a)
Interpretation:
The time taken by the given thermal decomposition reaction of mercuric oxide to produce
Concept introduction:
The rate law for second order reaction is represented as,
This represents the case in which identical reactants are present. In the second order kinetics,
Where,
•
•
•
Answer to Problem 20.23E
The time taken by the given thermal decomposition reaction of mercuric oxide to produce
The amount of time taken in second order kinetics to produce the same amount of gas is higher than that of the first order kinetics.
Explanation of Solution
It is given that the thermal decomposition of mercuric oxide follows second order kinetics and the rate constant is
The initial amount of
The number of moles of
Where,
•
•
•
•
•
Substitute the values of pressure, volume, gas constant and temperature in the above formula.
Thus, the number of moles of
The amount of
The molar mass of
Substitute the number of moles and molar mass of
The amount of
The amount of
Thus, the amount of
The rate law for the given second order reaction is given by,
Where,
•
•
•
Substitute the values of initial amount, amount at time
Under the assumption of standard temperature and pressure, units cancel out such that the equation becomes,
Thus, the time taken by the given thermal decomposition reaction of mercuric oxide to produce
On comparison of the time taken by first order kinetics and second order kinetics, it is observed that the amount of time taken in second order kinetics to produce the same amount of gas is higher than the first order kinetics.
The time taken by the given thermal decomposition reaction of mercuric oxide to produce
The amount of time taken in second order kinetics to produce the same amount of gas is higher than the first order kinetics.
(b)
Interpretation:
The time taken by the given thermal decomposition reaction of mercuric oxide to produce
Concept introduction:
The rate law for second order reaction is represented as,
This represents the case in which identical reactants are presents. In the second order kinetics rate of the reaction is proportional to the square of concentration of the reactant. The integrated rate law for second order reaction is represented as,
Where,
•
•
•
Answer to Problem 20.23E
The time taken by the given thermal decomposition reaction of mercuric oxide to produce
The amount of time taken in second order kinetics to produce the same amount of gas is higher than that of the first order kinetics.
Explanation of Solution
It is given that the thermal decomposition of mercuric oxide follows second order kinetics and the rate constant is
The initial amount of
The number of moles of
Where,
•
•
•
•
•
Substitute the values of pressure, volume, gas constant and temperature in the above formula.
Thus, the number of moles of
The amount of
The molar mass of
Substitute the number of moles and molar mass of
The amount of
The amount of
Thus, the amount of
The rate law for the given second order reaction is given by,
Where,
•
•
•
Substitute the values of initial amount, amount at time
Under the assumption of standard temperature and pressure, units cancel out such that the equation becomes,
Thus, the time taken by the given thermal decomposition reaction of mercuric oxide to produce
On comparison of the time taken by first order kinetics and second order kinetics, it is observed that the amount of time taken in second order kinetics to produce the same amount of gas is higher than that of the first order kinetics.
The time taken by the given thermal decomposition reaction of mercuric oxide to produce
The amount of time taken in second order kinetics to produce the same amount of gas is higher than that of the first order kinetics.
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Chapter 20 Solutions
Student Solutions Manual for Ball's Physical Chemistry, 2nd
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