Question

Consider the following hypothetical reactions: $$ \begin{array}{ll} \mathrm{A} \rightarrow \mathrm{B} & \Delta H=+30 \mathrm{~kJ} \\ \mathrm{~B} \longrightarrow \mathrm{C} & \Delta H=+60 \mathrm{~kJ} \end{array} $$ (a) Use Hess's law to calculate the enthalpy change for the reaction A - - - - C. (b) Construct an enthalpy diagram for substances \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\), and show how Hess's law applies.

Short answer

The enthalpy change for the reaction A → C is +90 kJ, determined using Hess's law which states the total enthalpy change is the sum of enthalpy changes of individual steps: ΔH(A → C) = ΔH(A → B) + ΔH(B → C) = +30 kJ + +60 kJ = +90 kJ. An enthalpy diagram visually represents these reactions and demonstrates the applicability of Hess's law, showing that the total enthalpy change from A → C is independent of the path taken.

Step-by-step solution

Understand Hess's Law

Hess's law states that the total enthalpy change of a chemical reaction is independent of the path taken and depends only on the initial and final states. In other words, if a reaction can be carried out in several stages, the sum of the enthalpy changes of each stage equals the total enthalpy change of the reaction.

Apply Hess's Law

Since we know the enthalpy changes for the hypothetical reactions A → B and B → C, we can determine the enthalpy change for the reaction A → C. According to Hess's law, the total enthalpy change of the reaction A → C is the sum of the enthalpy changes of A → B and B → C. Thus, for part (a): ΔH(A → C) = ΔH(A → B) + ΔH(B → C) = (+30 kJ) + (+60 kJ) = +90 kJ. The enthalpy change for the reaction A → C is +90 kJ.

Construct an Enthalpy Diagram

An enthalpy diagram shows the change in enthalpy (ΔH) of a chemical reaction. To represent the given data about substances A, B, and C, we can construct the following enthalpy diagram: 1. On the vertical axis, indicate the enthalpy levels with an arbitrary scale. 2. Position substance A at the base of the vertical axis (0 kJ enthalpy). 3. Since the enthalpy change for A → B is +30 kJ, we move upwards 30 kJ for substance B in the diagram. 4. The same way, since the enthalpy change for B → C is +60 kJ, we move upwards 60 kJ for substance C in the diagram. 5. Connect A, B, and C with arrows, indicating the enthalpy changes. In the diagram, we observe that the enthalpy increases from A → B and from B → C. The total enthalpy change from A → C is also visible in the diagram (the difference between the enthalpy levels of C and A).

Show how Hess's Law applies

From the enthalpy diagram, we can visualize how Hess's law applies to this situation. The sum of the enthalpy changes A → B and B → C is equal to the enthalpy change A → C (+90 kJ). Since the enthalpy change is independent of the path taken, it confirms the applicability of Hess's law. In conclusion, the enthalpy change for the reaction A → C is +90 kJ, and the enthalpy diagram visually demonstrates how Hess's law applies to these hypothetical reactions and confirms the calculated enthalpy change.

Key concepts

Enthalpy Change

Enthalpy change represents the heat absorbed or released during a chemical reaction. It is a crucial concept when analyzing reaction processes. When an enthalpy change is positive, it indicates an endothermic reaction, where heat is absorbed from the surroundings. Conversely, a negative enthalpy change denotes an exothermic reaction, where heat is released.
The enthalpy change (\(\Delta H\)) of a reaction is path-independent, meaning that no matter how the reactants transform into products, the total enthalpy change remains constant. This property underlies Hess's Law, which allows us to calculate enthalpy changes by considering alternative reaction pathways. Understanding this concept helps predict the energy profile of reactions and is essential for industrial applications and energy management.

Hypothetical Reactions

Hypothetical reactions are imagined processes used to understand and apply theoretical concepts such as Hess's Law. They provide a straightforward way to examine the thermodynamics of reactions without dealing with real-world complexities. In the context of the exercise, the hypothetical reactions between substances A, B, and C serve an educational purpose.
By assigning arbitrary values of enthalpy change, these reactions make it easier to apply mathematical principles, such as \(\Delta H(A \rightarrow C) = \Delta H(A \rightarrow B) + \Delta H(B \rightarrow C)\). Such exercises develop problem-solving skills and deepen the comprehension of chemical thermodynamics, allowing students to practice calculations and visualize reaction sequences.

Enthalpy Diagram

An enthalpy diagram visually represents the enthalpy changes during a chemical reaction. The vertical axis shows enthalpy levels, while the horizontal connections represent the transition between the reactants and products. This type of diagram is instrumental in understanding energy changes during a reaction.
For the hypothetical reactions A → B → C, constructing an enthalpy diagram involves plotting points for each substance based on their enthalpy levels. Starting at zero for substance A, you increment by the enthalpy change values as you move to substances B and C. The transitions between these points are illustrated with arrows indicating direction and total enthalpy change.
Using an enthalpy diagram, the holistic picture of the reaction is clearer, making the impact and application of Hess's Law more intuitive. It shows how combining stepwise reactions replicates the overall reaction's enthalpy change, reinforcing the concept visually.

Chemical Reaction

Chemical reactions involve the rearrangement of atoms to transform reactants into products. These processes are guided by changes in enthalpy, determining whether a reaction absorbs or releases energy. Reactions are often written with balanced chemical equations, indicating the stoichiometry and energy involved.
For any given reaction, the natural tendency is to proceed towards minimizing energy—either by releasing excess heat in an exothermic reaction or absorbing energy in an endothermic one. Understanding these processes requires analyzing the bonds formed and broken throughout the reaction either through direct experimentation or using theoretical frameworks like Hess’s Law.
Learning about chemical reactions encompasses understanding not only the immediate product formation but also broader applications including energy efficiency and environmental impact. By applying enthalpy principles, we can predict reaction feasibility and energy costs, which is paramount in fields such as chemical engineering and sustainable energy development.