# Thermodynamics & Electrochemical Reactions

Instructor: Amanda Robb

Amanda holds a Masters in Science from Tufts Medical School in Cellular and Molecular Physiology. She has taught high school Biology and Physics for 8 years.

In this lesson, we'll be looking at how the principles of thermodynamics can be applied to electrochemical cells. We'll examine the relationship between the cell potential, free energy and the equilibrium constant for both voltaic and electrolytic cells.

## What Are Electrochemical Reactions?

Many of us spend our days typing away on laptops, or engaged with various apps on our phones. These small pieces of technology all run on batteries, which are powered by electrochemical reactions. An electrochemical reaction is any type of chemical reaction that involves the movement of electrons, which creates electricity.

Electrochemical reactions can be divided into two types: voltaic cells or electrochemical cells. Voltaic cells are the batteries we are most familiar with. They have favorable redox reactions, where electrons are transferred, between different chemicals. The movement of electrons creates electricity. These reactions happen spontaneously. Electrochemical reactions on the other hand run in reverse. Electrical energy must be applied to the cell in order to carry out redox reactions.

Either of these electrochemical reactions are governed by the properties of thermodynamics. Next, we'll look at how the cell potential and equilibrium constant for electrochemical reactions relates to Gibb's free energy.

## What Is Gibb's Free Energy?

The free energy of a system, or Gibb's free energy, is a measure of how much work can be done in a system. It takes into consideration the heat and entropy lost or gained during a chemical reaction. Any reactions with a negative free energy will occur spontaneously, or on their own. Reactions with a positive free energy need energy put into the system in order to occur.

## Standard Cell Potential and Gibbs Free Energy

Since the free energy is a measure of how much work can be done by a system, the free energy can be related to the equation for work done by an electrochemical or voltaic cell:

G=-nFE cell

In this equation the variable n is equal to the number of moles of the electrons flowing, F is Faraday's constant and Ecell is the cell potential. The cell potential is the voltage between two sides of the battery in a reaction. You can think of the cell potential like the energy stored in the battery.

Looking at the relationship between free energy (G) and the cell potential (E cell ), we can see that when the cell potential is positive, the free energy is negative. This means when there is an overall positive cell potential the reaction is spontaneous and will occur without any additional energy input.

Since voltaic cells contain reactions that occur spontaneously, they will always have a positive cell potential. Electrochemical cells on the other hand need energy for the reaction to occur. So, their cell potentials will be negative.

Noticing the relationship between free energy and cell potential also tells us the relationship is proportional. As the cell potential gets bigger, the free energy for the reaction also gets bigger.

## Equilibrium Constant and Gibbs Free Energy

How does the free energy relate to the equilibrium constant for a reaction, k? The equilibrium constant describes the relationship between the concentration of products and reactants when a reaction is in equilibrium. The equilibrium constant can help predict which way a reaction will proceed. If the equilibrium constant is greater than one, the reaction will favor the products. However, if the equilibrium constant is less than one, the reactants will be favored and the reaction will proceed in reverse.

So, how does this relate to free energy? We can recall that the change in free energy is also equal to the gas constant multiplied by the temperature by the natural log of the equilibrium constant, k.

G = -RT*ln(k)

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