Question

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

Short answer

The enthalpy change for the reaction A → C is calculated using Hess's law as follows: ΔH(A → C) = ΔH(A → B) + ΔH(B → C) Given values: ΔH(A → B) = +30 kJ and ΔH(B → C) = +60 kJ ΔH(A → C) = (+30 kJ) + (+60 kJ) = +90 kJ The enthalpy diagram shows the enthalpy changes for each reaction, with arrows representing the individual reaction pathways. The overall enthalpy change for A → C is the sum of the enthalpy changes for A → B and B → C, in accordance with Hess's law.

Step-by-step solution

(a) Calculating Enthalpy Change (ΔH) for A → C using Hess's Law

Hess's law states that the total enthalpy change is the sum of the individual enthalpy changes for each step in a reaction pathway. Since we are given the enthalpy changes for the A → B and B → C reactions, we can add them to find the ΔH for A → C: ΔH(A → C) = ΔH(A → B) + ΔH(B → C) Given values are: ΔH(A → B) = +30 kJ ΔH(B → C) = +60 kJ Now, substitute the values in the equation: ΔH(A → C) = (+30 kJ) + (+60 kJ) ΔH(A → C) = +90 kJ The enthalpy change for the reaction A → C is +90 kJ.

(b) Construct an Enthalpy Diagram and apply Hess's Law

To create an enthalpy diagram, we will plot the enthalpy changes for each individual reaction on a graph, with the reactants and products on the x-axis and the enthalpy on the y-axis. 1. Start by plotting the enthalpy of A as a point on the y-axis, labeled "A". 2. From point A, draw an arrow upwards representing the enthalpy change (+30 kJ) for the reaction A → B. Label this point "B". 3. From point B, draw another arrow upwards representing the enthalpy change (+60 kJ) for the reaction B → C. Label this point "C". 4. Draw a third arrow from point A (bottom) to point C (top) representing the overall enthalpy change for the reaction A → C. Label the arrow with +90 kJ. 5. With these arrows representing the enthalpy changes, you can see that Hess's Law is applied by demonstrating that the total enthalpy change for the reaction A → C is equal to the sum of the enthalpy changes for the individual reactions A → B and B → C. In conclusion, the enthalpy change for the reaction A → C is +90 kJ, and the enthalpy diagram demonstrates how Hess's law is applied by summing up individual enthalpy changes in a reaction pathway.

Key concepts

Enthalpy Change

Enthalpy change, denoted as \( \Delta H \), is a measure of the total heat content in a chemical reaction. It's an indication of how much energy is absorbed or released when a reaction occurs at constant pressure. It can be positive or negative; a positive \( \Delta H \) implies that the reaction absorbs heat (endothermic), while a negative \( \Delta H \) indicates that heat is released (exothermic). In educational problems, such as our example with reactions A to B and B to C, enthalpy changes are often provided to help students apply Hess's Law.

In applying this law, the enthalpy changes given for each step of the reaction can simply be summed. For instance, if you're calculating the enthalpy change for a compound transforming from state A directly to state C, and you know the enthalpy changes from A to B and from B to C, you sum these values. Our exercise demonstrates this beautifully; by adding \( +30 \text{kJ} \) and \( +60 \text{kJ} \) from each step, you find that \( \Delta H \) for the reaction A to C is \( +90 \text{kJ} \). The enthalpy change is always the same regardless of the path taken, which is the core essence of Hess's Law.

Reaction Pathway

The reaction pathway refers to the sequence of molecular events or steps that occur when reactants transform into products in a chemical reaction. According to Hess's Law, the total enthalpy change of a chemical reaction is independent of the pathway taken; it only depends on the initial and final states of the reaction. This is because enthalpy is a state function, a property that only depends on the current state of the system, not the path it took to get there.

For educational exercises where you are dealing with reaction pathways, like the A to B to C example, you persistently apply Hess's Law by considering the entirety of the steps involved. It's like climbing a mountain: whether you take a direct route or a winding path with multiple stops (intermediate reactions), the change in altitude (enthalpy change) from base to summit is constant. This principle allows chemists to calculate unknown enthalpy changes for complex reactions by using known values from simpler, related reactions.

Enthalpy Diagram

An enthalpy diagram graphically represents the enthalpy changes occurring during a chemical reaction. It is an extremely useful tool in chemistry education, aiding students to visualize the concept of enthalpy changes and how Hess's Law can be applied.

In the example with substances A, B, and C, the enthalpy diagram is constructed by plotting the energy levels of these substances and the corresponding enthalpy changes. From the reference level of A, we see an upward arrow indicating a \( +30 \text{kJ} \) change in enthalpy for the reaction A \rightarrow B, culminating in an energy level for B. Continuing upward, another arrow represents the \( +60 \text{kJ} \) change for B \rightarrow C, reaching the energy level for C.

By drawing a direct arrow from A to C with an enthalpy change of \( +90 \text{kJ} \), we can visually confirm the application of Hess's Law: the total enthalpy change for A to C via B is equivalent to the direct enthalpy change from A to C. The clarity of this visual representation in the diagram aids students in understanding the inherently abstract concept of Hess’s Law, which is foundational in Thermodynamics.