Concept explainers
The zinc-air battery shows much promise for electric cars because it is lightweight and rechargeable:
The net transformation is
Interpretation:
The half-reaction, the standard emf of battery, the emf under actual operating conditions, the energy density, and the volume of air essential to supply the battery every second is to be calculated.
Concept introduction:
The Nernst equation is the reduction potential of an electrochemical reaction to the standard electrode potential, temperature, and activities of the chemical species undergoing oxidation and reduction.
The Nernst equation is an important equation of electrochemistry. The equation is
Here,
The standard free energy change is the difference of the sum of standard free energy change of products and the sum of standard free energy change of reactants.
Answer to Problem 126AP
Solution:
(a)
The half-reaction is as follows:
The standard emf of battery is
(b)
The emf is
(c)
The energy density of Zn is
(d)
The volume of air essential to supply the battery every second is
Explanation of Solution
Given information: The given reaction is as follows:
The current is
a) The half-reaction at zinc-air electrode and the standard emf of the battery.
The half-reaction is as follows:
The standard emf is calculated with the help of
Here,
The standard free energy changes for the formation of
Substitute the values of standard Gibbs energy of formation of reactants and products in the equation above,
Thus, the standard free energy change
The standard emf of battery is calculated as follows:
Here,
Substitute the values of
Therefore, the standard emf of battery is
b) The emf under actual operating conditions when the partial pressure of oxygen is
The Nernst equation is as follows:
Substitute the values of
Therefore, the emf is
c) The energy density of zinc electrode.
The maximum energy obtained from the reaction is the free energy. The energy density of the zinc electrode is calculated with the help of free energy.
The energy density of the zinc electrode is calculated as follows:
Substitute the values of free energy
Therefore, the energy density is
d) The volume of air would need to be supplied to the battery every second.
The number of moles can be calculated with the help of charge as follows:
Here,
Substitute the values in the equation above:
Therefore, the number of moles is
In the balanced reaction,
Therefore, the number of moles of oxygen reduced by
The volume of oxygen at
Here,
Substitute the values of pressure, moles, temperature, and gas constant in the equation above,
Therefore, the volume of oxygen is
As the air is
The volume of air essential to supply the battery every second is calculated as follows:
Therefore, the volume of air essential to supply the battery every second is
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Chapter 19 Solutions
Chemistry
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