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Dawn has taught chemistry and forensic courses at the college level for 9 years. She has a PhD in Chemistry and is an author of peer reviewed publications in chemistry.

In this video lesson, we'll study free energy (G) and its relationship to enthalpy, entropy and temperature. You'll also learn why free energy (G) is the single most useful criterion for predicting the spontaneity and direction of a chemical reaction.

What Is Free Energy?

Chemical reactions are all around us. They are even inside our body. In fact, the human body is a mass of thousands of chemical reactions. If you are like me, the one you are really familiar with is eating and digesting, scientifically called cellular respiration. I love this chemical reaction. This is where we eat delicious food that our body breaks down to form the products of carbon dioxide and water. This chemical reaction gives out energy that we can use.

The amount of available energy depends on the type of food we eat and how much potential energy is available in its chemical bonds. If we don't use all the energy given out, then the extra energy is stored by the body as fat. The available energy that allows us to run and do useful work is called Gibbs free energy, or sometimes just Gibbs energy. Put simply, Gibbs free energy is the amount of energy left over after a chemical reaction has taken place. It is important that we have this extra, leftover energy; otherwise, we wouldn't be able to do work.

We can use our understanding of Gibbs free energy as an easy way to predict whether a reaction is spontaneous and calculate how much free energy is available for us to use. Spontaneity is the direction in which the reaction will take place without outside interference. In other words, it doesn't need us to keep putting in work or energy to keep it happening.

The Gibbs free energy equation we will be working with is Delta or change in G is equal to change in enthalpy minus temperature multiplied by the change in entropy. This is a very important equation for you to remember, so be sure to commit it to memory. G equals H minus TS. Use 'Green Eagles Hit Moaning Televisions Suddenly' to help you.

Enthalpy and Entropy Revisited

As we can see from our equation, Gibbs free energy is calculated from the changes in enthalpy and entropy, as well as the temperature at which the reaction is carried out at. Let us quickly remind ourselves about these important thermodynamic quantities.

Enthalpy (H) is a measure of how much energy is released or absorbed during a chemical reaction. Energy, in the form of heat, is released in an exothermic reaction, and the change in enthalpy is negative, -H. On the other hand, energy, in the form of heat, is absorbed in an endothermic reaction, and this time the change in enthalpy is positive, +H.

The second property is the measure of entropy (S), which is a measure of disorder or randomness in the system. In nature, a messy room is far more favored than a neat, ordered room, and when disorder increases, we have +S.

Why Are Reactions Spontaneous?

Now it turns out that for a spontaneous reaction, the sign of Delta G must be negative. Knowing this, what effect does enthalpy and entropy have on spontaneity? Let us first look at enthalpy: an exothermic reaction is more likely to be spontaneous; if Delta H is negative, this makes it more likely that Delta G will also be negative and, therefore, spontaneous. And now, let's look at entropy: if a reaction causes an increase in randomness of the system, it is more likely to be spontaneous; a positive Delta S term will also mean that Delta G is more likely to be negative.

The Effect of Temperature

Got it? Now, if only it were that simple! Let me throw a wrench in the works. We know from everyday experience that water freezes spontaneously, and we recall that solid ice is more ordered than liquid and so the entropy of the system has gone down. The Delta S term is negative, so why is this reaction spontaneous?

I can hear you shouting at the video, but it has to be at freezing temperature for this to happen. And you are absolutely right because this is where the effect of temperature comes in. You can see from the equation that it can have a big effect on the entropy term.

So, now we can see that we cannot simply say that if entropy change is negative, the reaction is always non-spontaneous. It depends. And there are four possible situations a reaction can have, which are summarized in the table below:

Effect of Temperature on Spontaneity of a Reaction

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As you can see from the table, when the signs of enthalpy and entropy are opposite we can say for sure whether the reaction will be spontaneous or not. For a reaction to be spontaneous, the absolute best combination is a negative Delta H and a positive Delta S. Because, remember, a negative Delta G is needed for a reaction to be spontaneous.

Where things get a little tricky is when you have both enthalpy and entropy with the same sign. And here it all depends on the effect on entropy by temperature. When they are both positive, the reaction is only spontaneous at higher temperatures. When they are both negative, the reaction is only spontaneous at lower temperatures. The exact temperature when a reaction becomes spontaneous will vary depending on your reaction. But it can be easily figured out by rearranging the Gibbs free energy equation.

So, now we have learned how to predict when a reaction is likely to be spontaneous, let us do a simple calculation so that we can see if our assumptions are correct. So, my question: If the heat of reaction is -45.0 kJ and the entropy change is -3.50 J/K, will the process be spontaneous or non-spontaneous at 298 K?

So, let us put in the values into our Gibbs free energy equation. The heat of reaction is just another way of saying enthalpy change, so our Delta H is -45.0 kJ, and our Delta S is -0.0035 kJ/K (notice we needed to convert this to kJ so that the units of energy are the same).

Delta G = -45.0 kJ - (298 K)(-0.0035 kJ/K)

= -45.0 kJ + 1.04 kJ

= -44.0 kJ

And because delta G is negative, this process is spontaneous at 298 K. Looking back at our table, we would not have necessarily predicted this - all we know is that it would be spontaneous at relatively low temperatures.

Lesson Summary

In this lesson, we have learned that Gibbs free energy is the energy left over after a reaction has taken place. For a spontaneous reaction, the sign on Delta G must be negative. Gibbs free energy relates enthalpy, entropy and temperature. A spontaneous reaction will always occur when Delta H is negative and Delta S is positive, and a reaction will always be non-spontaneous when Delta H is positive and Delta S is negative. And, finally, temperature has a big role because of the effect on the entropy term.

Learning Outcomes

After this lesson, you should be able to:

Define Gibbs free energy and spontaneity

Identify the Gibbs free energy equation

Recall the role of temperature in the Gibbs free energy equation

Explain how enthalpy, entropy and temperature can be used to predict whether a reaction will be spontaneous or not

The questions below will provide additional practice and understanding of the concepts related to entropy, enthalpy, and free energy. Answers are also provided below to check your answers and understanding.

Questions

1. Which term describes the amount of heat energy transferred (released or absorbed) within a system: entropy, enthalpy or free energy?

2. If Delta G = +44 is the reaction spontaneous?

3. When a system is at equilibrium, what does Delta G equal?

4. Which term describes the degree of randomness or disorder of a system: entropy, enthalpy or free energy?

5. Will entropy increase or decrease as the temperature increases?

6. When the enthalpy is a negative value and entropy is a positive value, what is the sign for the free energy?

7. Will an endothermic reaction result in a positive or negative value for enthalpy?

8. Does entropy increase with the mass of a substance?

Solutions

1. enthalpy

2. No, since Delta G >0 the reaction is not spontaneous.

3. zero

4. entropy

5. Entropy will increase because the higher temperature will increase the energy of the molecules. As a result, the molecules will have more disorder than those at lower temperatures.

6. The free energy is negative.

7. positive

8. yes

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