### Video Transcript

Which of the following values is equivalent to Ξπ» three? (A) Negative Ξπ» one plus Ξπ» two plus Ξπ» four. (B) Negative Ξπ» one minus Ξπ» two minus Ξπ» four. (C) Ξπ» one minus Ξπ» two minus Ξπ» four. (D) Ξπ» one plus Ξπ» two minus Ξπ» four. (E) Ξπ» one plus Ξπ» two plus Ξπ» four.

In this question, we are provided a reaction pathway diagram consisting of four chemical reactions. The letters provided inside the boxes represent the substances involved in the chemical reactions. Each reaction has an associated enthalpy change. Letβs look closely at reaction number three in the diagram. This reaction directly converts substance πΈ into substance πΆ. But letβs suppose that we cannot directly measure the enthalpy change for reaction three. Reasons for this include safety, control, and speed of the reaction and difficulty in measuring the enthalpy change. When the enthalpy change for a reaction cannot be directly measured, that enthalpy change can be calculated by adding together enthalpy changes from reactions in an alternative pathway to the desired product.

This idea is summarized by Hessβs law, which states that the enthalpy change of a reaction is independent of the path taken. Our job in solving this question is to determine how we can add together the enthalpy values of the three other reactions in the diagram to calculate the enthalpy change of reaction three. Letβs use the diagram to find an alternative pathway of reactions starting with substance πΈ and ending with substance πΆ. We can begin by reversing reaction four. We can write this reverse reaction as πΈ reacts to form πΉ plus πΊ. Whenever we reverse a reaction in an enthalpy cycle or reaction pathway, we need to change the sign of the enthalpy change. We should write the enthalpy change of this reverse reaction as negative Ξπ» four.

Letβs keep track of the rest of the reactions and enthalpy changes for the alternative pathway. To get one step closer to producing substance πΆ, we should reverse reaction number two. We can write this reaction as πΉ plus πΊ react to produce π΄ plus π΅. The enthalpy change for this reverse reaction is negative Ξπ» two. The last step in the alternative reaction pathway is to complete reaction one in the direction that it is written. We can write this reaction as π΄ plus π΅ react to form πΆ. And the enthalpy change is Ξπ» one.

There is a way to check if our alternative pathway is correct. Substances that appear on opposite sides in two different equations can be eliminated as we add the reactions together. For example, substances πΉ and πΊ are products of reaction four, but these substances are then used up as reactants in reaction two. Therefore, we can eliminate πΉ and πΊ from both equations. We also notice that substances π΄ and π΅ are the products of reaction two and the reactants of reaction one. This means we can eliminate substances π΄ and π΅ from both equations. When we add the three equations together, the resulting equation is πΈ reacts to form πΆ.

We have successfully confirmed that our alternative pathway is another way to produce substance πΆ from substance πΈ. According to Hessβs law, the sum of the enthalpy changes of the reactions in the alternative pathway will be equal to the enthalpy change of the direct route. Letβs write an equation to represent this relationship. We can write Ξπ» three is equal to negative Ξπ» four plus negative Ξπ» two plus Ξπ» one. We can rewrite the equation as Ξπ» three equals Ξπ» one minus Ξπ» two minus Ξπ» four. The value which is equivalent to Ξπ» three is answer choice (C).