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Which of these statements is not correct? A) In a reaction where ฮ๐บ is negative, the forward reaction is spontaneous. B) In a reaction where ฮ๐ป is positive and ฮ๐ is negative, the forward reaction is nonspontaneous. C) In a reaction where ฮ๐บ is positive, ฮ๐ may also be positive. D) In an endothermic reaction, ฮ๐ป is positive and the enthalpy increases. Or E) In an exothermic reaction, ฮ๐ป is positive and the enthalpy increases.

There are quite a lot of terms and expressions in this question. So letโs go through them one by one. ฮ๐บ is the change in Gibbs free energy because of a reaction. ฮ๐ป is the change in enthalpy because of a reaction. And ฮ๐ 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 itโs said that a reaction has a negative ฮ๐บ, 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 ฮ๐บ is negative, the reaction will always be spontaneous. So statement A is actually true. But weโre looking for a false statement or a statement thatโs 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 thatโs 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 thatโs 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. Letโs just plug in a positive ฮ๐ into a ฮ๐บ equation. As I mentioned before, temperature is always a positive value. So ฮ๐บ equals ฮ๐ป minus two positive numbers multiplied together. This means that the contribution from the entropy change to ฮ๐บ is going to be negative. We can also substitute in the ฮ๐บ is positive. If we add ๐ฮ๐ to both sides, weโre going to have a positive change in enthalpy. But weโll only get a positive change in Gibbs free energy if the change in enthalpy is greater than ๐ฮ๐. 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 thatโs positive. So while it isnโt true that all reactions where ฮ๐บ is positive have a positive ฮ๐, 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 weโve 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 itโs 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, ฮ๐ป is positive and the enthalpy increases as well. Weโve 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 thatโs negative. And the enthalpy would decrease. Meaning that, of these five statements, the only one thatโs not correct is in an exothermic reaction, ฮ๐ป is positive and the enthalpy increases.