Introduction to Gibbs free energy

- [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.