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### Course: AP®︎/College Chemistry > Unit 9

Lesson 2: Gibbs free energy and thermodynamic favorability# Introduction to Gibbs free energy

The standard Gibbs free energy change, Δ

*G*°, indicates the thermodynamic favorability of a physical or chemical process. When Δ*G*° < 0, the process is thermodynamically favored. For a given process, the value of Δ*G*° can be calculated directly from the values of Δ*H*° and Δ*S*° using the following equation: Δ*G*° = Δ*H*° -*T*Δ*S*°. Created by Jay.## Want to join the conversation?

- How is the Gibbs free energy of a system different from its enthalpy? What different usages or significances would they have?(2 votes)
- Enthalpy is essentially the amount of heat lost or gained by a reaction. Gibbs free energy takes into account enthalpy and entropy of a reaction.

Hope that helps.(5 votes)

- What does the number in ΔG mean? For example, what is the difference between a ΔG value of -50 KJ/(mol rxn) vs -500 KJ/(mol rxn)?(1 vote)
- G stands for Gibbs free energy, and so ΔG stands for the change in Gibbs free energy. Change in Gibbs free energy is a measure of how spontaneous a process like a chemical reaction is. Spontaneity meaning a process progresses naturally without the need of outside work or energy to move it along.

The change in Gibbs free energy is also related to the change in the universe’s entropy at a specific temperature because of a certain process. Specifically, the formula is: ΔG = -TΔSuniv, where T is temperature and ΔSuniv is the change in the universe’s entropy. And according to the second law of thermodynamics, if a process increases the change in the universe’s entropy, then that process is spontaneous. So for a process to be spontaneous the ΔSuniv value should be positive which would correspond to a negative ΔG value. So we can tell is a process is spontaneous quickly depending on the sign of the ΔG.

The more negative a ΔG value is the more spontaneous the process is, or the further it will go toward the products to reach equilibrium.

Hope that helps.(2 votes)

- Can Khan Academy make a video about

- ∆Go vs ∆G

- ∆Ho vs ∆H

- ∆So vs ∆S

I don't understand the difference between the two especially when talking about reversible reactions.

It would be great if they also covered the actual meaning of the value of ∆G? What does the actual numerical value indicate? Thermodynamics confuses me so much!(0 votes)- I explained this in a separate question of yours, but the ° symbol stands for standard state. Currently standard state refers to gases at a pressure of 1 bar, concentrations of solutes in solution to be 1 M, and for liquids and solids in their pure and most stable form at a pressure of 1 bar and a temperature of interest (usually 25°C or 298K).

To understand reversible reactions in this context, it’s important to understand the ‘free’ part of free energy. The change in free energy of a chemical reaction represents the maximum amount of energy available, or free, to do work. The change in free energy represents a theoretical limit as to how much work can be done by the reaction. In a real reaction, the amount of energy available to do work is even less than ΔG° because additional energy is lost to the surroundings as heat. A reaction that achieves that theoretical limit with respect to free energy is called a reversible reaction. All real reactions are irreversible reactions and do not achieve this theoretical limit because of heat loss.

So in this sense a negative value of ΔG° still means a spontaneous reaction, but the numerical value represents the theoretical maximum amount of energy free to do work. A positive value of ΔG° means the reaction is nonspontaneous and the numerical value represents the minimum amount of energy required to make the reaction occur.

Hope that helps.(2 votes)

## Video transcript

- [Instructor] Gibbs Free
Energy is symbolized by G and change in Gibbs Free Energy
is symbolized by delta G. And the change in free energy, delta G, is equal to the change
in enthalpy, delta H, minus the temperature in Kelvin, times the change in entropy, delta S. When delta G is less than zero, a chemical or physical process is favored in the forward direction. Therefore, we say that the forward process is thermodynamically favored. As an example, if we look at a reaction where reactants turn into products, if delta G is less than zero, the forward reaction as
thermodynamically favored, meaning the reaction will go to the right to make more products. Textbooks will often use
the word spontaneous. So, when delta G is less than zero, the reaction would be spontaneous
in the forward direction. When delta G is greater than zero, the chemical or physical process is favored in the reverse direction. Therefore, the forward process is not thermodynamically favored. Going back to our reaction, as an example, if delta G is greater than zero, that means the reverse
reaction is favored, which favors the formation
of the reactants. For this example, textbooks will often say that the reaction is non-spontaneous in
the forward direction, which means the reaction is spontaneous in the reverse direction. And when delta G is equal to zero, the chemical or physical
process is at equilibrium. So, for our chemical reaction,
if delta G is equal to zero, the reaction is at equilibrium
and the concentration of reactants and products
will remain constant. When we see delta G with
a superscript naught, we're talking about the
change in Gibbs Free Energy when substances are in
their standard states. By convention, the standard
state of a solid or liquid is referring to the pure
solid or the pure liquid under a pressure of one atmosphere. The standard state of a gas
is referring to the pure gas at a pressure of one atmosphere. And the standard state of a solution is talking about a one
Mueller concentration. If our substances are
in the standard state, we can add a superscript to the
equation that we saw before. So, we could calculate delta G naught, the standard change in free energy by getting the standard change
in enthalpy and from that, subtracting the absolute
temperature in Kelvin, times the standard change in entropy. When the substances are
in their standard states, delta G naught is equal to delta G. Therefore, we can say
that if delta G naught is less than zero, if we're talking about a reaction, the reaction is thermodynamically favored in the forward direction. And if delta G naught
is greater than zero, we could say the reaction is
not thermodynamically favored in the forward direction. Next, let's calculate delta G naught for a chemical reaction. And for our reaction, let's look at the synthesis
of hydrogen fluoride gas from hydrogen gas and fluorine gas. Our goal is to calculate delta G naught for this reaction at 25 degrees Celsius. Delta H naught for this
reaction at 25 degrees Celsius is equal to negative 537.2
kilojoules per mole of reaction. And delta S naught for this
reaction at 25 degrees Celsius is equal to 13.7 joules per
Kelvin mole of reaction. The next step is to plug
everything into our equation. So, to calculate delta
G naught of reaction, we need to plug in delta
H naught of reaction, delta S naught of reaction, and also the temperature in Kelvin. So, we can plug in delta
H naught of reaction into our equations. That's negative 537.2
kilojoules per mole of reaction. Next, we think about the temperature. The temperature is 25 degrees Celsius and we need to convert that into Kelvin. So, 25 plus 273 is equal to 298 Kelvin. Next we think about delta S naught, and here we have to be careful with units because delta H naught was in kilojoules and delta S naught was
given to us in joules. So, one approach is to convert delta S naught into kilojoules per Kelvin mole of reaction. So, we could divide this number by 1,000, or we could move the decimal
place three to the left. So, 13.7 joules per
Kelvin mole of reaction is equal to 0.0137 kilojoules
per Kelvin mole of reaction. Looking at our units,
Kelvin will cancel out and that gives us kilojoules
per mole of reaction. So, when we do the math, delta
G naught for this reaction is equal to negative 541.3
kilojoules per mole of reaction. Since delta G naught for
this reaction is negative, that means the forward reaction is thermodynamically favored. So, we can think about the
reactants coming together to make the products. And since we calculated delta G naught, the reactants and products
are in their standard states. So, what our calculation
means is if we had a mixture of hydrogen gas, fluorine gas,
and hydrogen fluoride gas, and we're at a temperature
of 25 degrees Celsius, and each gas had a partial
pressure of one atmosphere, the forward reaction is
thermodynamically favored, which means the hydrogen
gas and fluorine gas would come together to make
more hydrogen fluoride.