Temperature Coefficient: Temperature Coeffiecient of EMF , Gibb’s Free Energy , Thermodynamics of Galvanic Cell, Practice Problems and FAQs:

Which device do you use for online classes tablet/mobile phone/laptop/pc?

Well, whatever the device you use, one thing is common in all device that is heating. If we perform some heavy task then definitely our deice will heat up.

Do you think heating influences the performance of your device?

Yes, you must have noticed that when your device heat up, system starts lagging and doesn’t perform with full efficiency.

It indicates that heating has an active role in conduction of electricity.

Let’s find out how it influences the parameters of an electrochemical cell.

Table of content

Temperature Co-effiecient of EMF (T.C)P
Gibb’s Free Energy (G)
Entropy Change in Cell
Enthalpy Change for a Cell
Thermodynamics of Galvanic Cell
Practice Problems
Frequently Asked Questions (FAQs)

Temperature Coefficient of EMF

A temperature coefficient explains how a particular change in temperature affects a physical property's relative change.

Gibbs Helmholtz law is used to calculate the temperature coefficient of the cell's emf. The emf value decreases as the temperature rises. Internal resistance is also affected by temperature. The resistance decreases as the temperature rises, and the resistance rises as the temperature falls.

In simple terms we can define it as the rate of change of EMF with temperature at constant pressure P.

Mathematically,

For single electrode,

For a cell,

Gibb’s Free Energy

Gibbs free energy, known variously as Gibbs function, Gibbs energy, free enthalpy, is a measure of the maximum amount of work done obtainable in a thermodynamic process. It is denoted by a symbol 'G'. It has a unIts of energy in Joules or calories.

Josiah Willard Gibbs, an American scientist, was trying to understand the conditions for spontaneity of processes. Gibbs free energy is the available energy of a thermodynamic process to do work.

Mathematically,

For single electrode,

For a cell,

For a cell at standard condition that is at 298K and 1 atm pressure,

Entropy Change in Cell

Entropy is typically referred to as a measurement of a system's randomness or disorder. In the year 1850, a German physicist by the name of Rudolf Clausius first proposed this idea.

The microscopic specifics of a system are not taken into account from a thermodynamics perspective on entropy. The behaviour of a system is instead described in terms of thermodynamic parameters as temperature, pressure, entropy, and heat capacity using the concept of entropy.

Mathematically,

Or,

Enthalpy Change for a Cell

Enthalpy is the measurement of energy in a thermodynamic system. The quantity of enthalpy equals to the total content of heat of a system, equivalent to the system’s internal energy plus the product of volume and pressure.

From thermodynamics,

Workdone by the Cell

Maximum Work Done by the Cell

Equilibrium Constant of a Cell

As we know at equilibrium of a cell,

Reaction quotient is defined as the ratio of the activity of the products raised to the power of their stoichiometry to the activity of reactants raised to the power of their stoichiometry.

Reaction Quotient For a general electrochemical reaction,

Q = =

Thermodynamics of Galvanic Cell

We know that in thermodynamics we can identify whether a reaction is spontaneous or not on the basis of the value of Gibbs free energy. Thermodynamics of galvanic cell depends upon the Gibbs free energy of a cell reaction and cell potential.

If there’s a decrease in Gibbs free energy then it is a spontaneous reaction. Whereas if there’s a increase in Gibbs free energy, it will be a non-spontaneous reaction.
When cell potential of cell is negative, the reaction becomes nonspontaneous whereas when the value of cell potential is positive, the reaction becomes spontaneous.

During working of a galvanic cell work done is the product of charge passing through the cell and the potential difference between the electrodes.

1 mole of electron

Standard Cell Potential and Equilibrium Constant

The relationship can be derived from the below equation

We know that from thermodynamics,

At 298 k

Practice Problems

Q.1 Gibbs free energy change for a single electrode can be represented as

Answer: (A)
Gibbs free energy change for a single electrode is

For a cell it is,

For a cell at standard condition the value of Gibbs free energy is

Q2. Equilibrium constant for the below reaction reaction is . what is the standard potential of a cell in which the reaction takes place?

Solution:

Given:

To calculate n let’s write this equation in terms of redox reaction

At cathode:

At anode:

Here

Now,

Q3. Calculate standard Gibbs free energy change and equilibrium constant at 298K for the below cell reaction. If . write the formula of the cell?

Solution:

Given:

We can see the value of is greater than the value of

Thus it implies that has a greater reduction potential. Hence, will reduce and work as a cathode and will oxidize and work as anode.

Formula of the cell :

Q4. Which of the following expression is true for temperature coefficient of the emf of a cell with entropy?

Answer: (A)

Mathematically,

Or,

Frequently Asked Questions (FAQs)

Q1. Why Gibbs free energy change is an extensive property?

Answer: The size or amount of the matter affects some attributes of it, like its length, mass, volume, weight, and so forth. These properties are referred to as extensive properties of matter, and as the size or amount of the matter changes, so does the value of these properties. Let's say we have two identical boxes, one with a four-liter capacity and the other with a ten-liter capacity. A ten-litre box will hold more material when compared to a four-litre box.

Let’s consider a reaction

No. of electrons involved is 2

Hence,

Now if we increase the quantity of reactant

No. of electrons involved is 4

We can see clearly that even if after changing the value of , remains same. Which means is independent of quantity of substance.

Hence, EMF of a cell is an intensive property.

Q2. Can we have a negative valued EMF for a cell?

Answer: A galvanic or voltaic cell's electromotive force (EMF) is the maximum potential difference between two electrodes. The reaction is reversible if the cell potential is negative.

Q3. From where do we generate EMF in a cell?

Answer: Because there is a charge flow in the cell, battery, and generator. As a result, we can conclude that an emf can be generated in any of the three sources. As a result, the cell, battery, and generator are the sources of emf.

Q4. A reaction is said to be spontaneous if :

a.
b.
c.
d. Both (B) & (C)

Answer: (D)

Solution: If there’s a decrease in Gibbs free energy then it is a spontaneous reaction. Whereas if there’s a increase in Gibbs free energy, it will be a non-spontaneous reaction. When cell potential of cell is negative, the reaction becomes nonspontaneous whereas when the value of cell potential is positive, the reaction becomes spontaneous.

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