# Video: Applying Knowledge of the Relationship between the Sign of Δ𝐻, the Enthalpy and the Exothermicity/Endothermicity

Which of these statements is not correct? [A] In a reaction where Δ𝐺 is negative, the forward reaction is spontaneous. [B] In a reaction where Δ𝐻 is positive and Δ𝑆 is negative, the forward reaction is nonspontaneous. [C] In a reaction where Δ𝐺 is positive, Δ𝑆 may also be positive. [D] In an endothermic reaction, Δ𝐻 is positive and the enthalpy increases. [E] In an exothermic reaction, Δ𝐻 is positive and the enthalpy increases.

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### Video Transcript

Which of these statements is not correct? A) In a reaction where Δ𝐺 is negative, the forward reaction is spontaneous. B) In a reaction where Δ𝐻 is positive and Δ𝑆 is negative, the forward reaction is nonspontaneous. C) In a reaction where Δ𝐺 is positive, Δ𝑆 may also be positive. D) In an endothermic reaction, Δ𝐻 is positive and the enthalpy increases. Or E) In an exothermic reaction, Δ𝐻 is positive and the enthalpy increases.

There are quite a lot of terms and expressions in this question. So let’s go through them one by one. Δ𝐺 is the change in Gibbs free energy because of a reaction. Δ𝐻 is the change in enthalpy because of a reaction. And Δ𝑆 is the change in entropy because of a reaction. All these changes refer to changes in properties of the system, which we consider to be the reactants and products. Anything else we call the surroundings. Energy can be exchanged between the system and the surroundings as the reaction occurs and indeed after it.

Statement A asserts that, in a reaction where the change in Gibbs free energy is negative, the forward reaction is spontaneous. What this means is that the forward reaction happens on its own. A reaction that lowers the energy of the system will always be spontaneous. When it’s said that a reaction has a negative Δ𝐺, it means that the Gibbs free energy of the products is lower than the Gibbs free energy of the reactants. Gibbs free energy is the metric we use to predict whether a reaction is spontaneous or not. So when Δ𝐺 is negative, the reaction will always be spontaneous. So statement A is actually true. But we’re looking for a false statement or a statement that’s not correct. So statement A is not a correct answer.

Statement B asserts that, in a reaction where the change in enthalpy is positive and the change in entropy is negative, the forward reaction is nonspontaneous. Since statement B discusses spontaneous or nonspontaneous, we need an argument that involves the change in Gibbs free energy. Thankfully, we can calculate a change in Gibbs free energy from the equivalent changes in enthalpy and entropy for a given reaction. For any given reaction, the change in Gibbs free energy is equivalent to the change in enthalpy minus the temperature multiplied by the change in entropy. In this particular example, the change in enthalpy is positive. Temperature will be in Kelvin. So that’s always positive. And the change in entropy is negative. Subtracting a negative gives us a positive number. So for a reaction where the change in enthalpy is positive and the change in entropy is negative, the change in Gibbs free energy is positive. A reaction with a change in Gibbs free energy that’s positive is always nonspontaneous. So statement B is another true statement and therefore an incorrect answer.

Statement C says that, in a reaction where the change in Gibbs free energy is positive, the change in entropy may also be positive. Let’s just plug in a positive Δ𝑆 into a Δ𝐺 equation. As I mentioned before, temperature is always a positive value. So Δ𝐺 equals Δ𝐻 minus two positive numbers multiplied together. This means that the contribution from the entropy change to Δ𝐺 is going to be negative. We can also substitute in the Δ𝐺 is positive. If we add 𝑇Δ𝑆 to both sides, we’re going to have a positive change in enthalpy. But we’ll only get a positive change in Gibbs free energy if the change in enthalpy is greater than 𝑇Δ𝑆. This can and indeed does happen. There are reactions where the change in enthalpy is so positive that it cancels out the negative contribution from the change in entropy. This would leave us with a change in Gibbs free energy that’s positive. So while it isn’t true that all reactions where Δ𝐺 is positive have a positive Δ𝑆, it is true in some cases, which is all the statement asserts. So we could move on to statement D.

Statement D asserts that, in an endothermic reaction, the change in enthalpy is positive and the enthalpy increases. Here, enthalpy refers to the enthalpy of the system. So if we have a reaction where the enthalpy of our reactants is lower than the enthalpy of our products, the change in enthalpy has to be positive because we’ve increased the total enthalpy of the system. This only occurs when the energy received by the system exceeds the energy given out by the system because of the reaction. This is what we call an endothermic reaction. So it’s absolutely true that, in an endothermic reaction, the change in enthalpy is positive and the enthalpy increases. So we can move on to statement E.

Statement E asserts that, in an exothermic reaction, Δ𝐻 is positive and the enthalpy increases as well. We’ve already shown that when the change in enthalpy is positive, the enthalpy of the system increases. So that bit is definitely true. But an exothermic reaction is a reaction where the energy given out exceeds the energy pulled in. If the energy out of a reaction exceeds the energy coming in, then the enthalpy of the products must be lower than the enthalpy of the reactants. So the change in enthalpy for such a process would actually be negative. So while parts of statement E are correct, the whole statement is false, because an exothermic reaction would have a change in enthalpy that’s negative. And the enthalpy would decrease. Meaning that, of these five statements, the only one that’s not correct is in an exothermic reaction, Δ𝐻 is positive and the enthalpy increases.