Question Video: Using Hess’s Law to Find an Equivalent Enthalpy Change Chemistry • First Year of Secondary School

Video Transcript

Which of the following values is equivalent to Δ𝐻 three? (A) Negative Δ𝐻 one plus Δ𝐻 two plus Δ𝐻 four. (B) Negative Δ𝐻 one minus Δ𝐻 two minus Δ𝐻 four. (C) Δ𝐻 one minus Δ𝐻 two minus Δ𝐻 four. (D) Δ𝐻 one plus Δ𝐻 two minus Δ𝐻 four. (E) Δ𝐻 one plus Δ𝐻 two plus Δ𝐻 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. Let’s look closely at reaction number three in the diagram. This reaction directly converts substance 𝐸 into substance 𝐶. But let’s 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 Hess’s 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. Let’s use the diagram to find an alternative pathway of reactions starting with substance 𝐸 and ending with substance 𝐶. We can begin by reversing reaction four. We can write this reverse reaction as 𝐸 reacts to form 𝐹 plus 𝐺. 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 Δ𝐻 four.

Let’s keep track of the rest of the reactions and enthalpy changes for the alternative pathway. To get one step closer to producing substance 𝐶, we should reverse reaction number two. We can write this reaction as 𝐹 plus 𝐺 react to produce 𝐴 plus 𝐵. The enthalpy change for this reverse reaction is negative Δ𝐻 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 𝐴 plus 𝐵 react to form 𝐶. And the enthalpy change is Δ𝐻 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 𝐹 and 𝐺 are products of reaction four, but these substances are then used up as reactants in reaction two. Therefore, we can eliminate 𝐹 and 𝐺 from both equations. We also notice that substances 𝐴 and 𝐵 are the products of reaction two and the reactants of reaction one. This means we can eliminate substances 𝐴 and 𝐵 from both equations. When we add the three equations together, the resulting equation is 𝐸 reacts to form 𝐶.

We have successfully confirmed that our alternative pathway is another way to produce substance 𝐶 from substance 𝐸. According to Hess’s 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. Let’s write an equation to represent this relationship. We can write Δ𝐻 three is equal to negative Δ𝐻 four plus negative Δ𝐻 two plus Δ𝐻 one. We can rewrite the equation as Δ𝐻 three equals Δ𝐻 one minus Δ𝐻 two minus Δ𝐻 four. The value which is equivalent to Δ𝐻 three is answer choice (C).