Question

Consider the conversion of compound \(A\) into compound \(B\) : \(\mathrm{A} \longrightarrow \mathrm{B}\). For both compounds \(\mathrm{A}\) and \(\mathrm{B}, \Delta H_{f}^{\mathrm{o}}>0 .\) (a) Sketch an enthalpy diagram for the reaction that is analogous to Figure \(5.23 .\) (b) Suppose the overall reaction is exothermic. What can you conclude? [Section 5.7]

Short answer

(a) To sketch the enthalpy diagram, draw the y-axis representing enthalpy and place compound A at some height above the base. Similarly, place compound B higher than compound A since both have positive formation enthalpies. Draw an arrow from A to B representing the reaction. (b) If the overall reaction is exothermic, it implies that energy is released during the conversion of A into B, and the enthalpy of B should be lower than A. However, as drawn, B has higher enthalpy than A. This means there might be an error in the given information or an additional step or intermediate compound is needed to release energy and make the reaction exothermic.

Step-by-step solution

Understand Enthalpy Diagrams

An enthalpy diagram shows the change in enthalpy as reactants are converted into products. In this case, we are given compound A is converted into compound B. Both have \(\Delta H_{f}^{\circ} > 0\) which means they are endothermic. The diagram must show the enthalpy levels of A and B and the change in enthalpy associated with the conversion from A to B.

Sketch the Enthalpy Diagram

Based on the given information, we'll sketch an enthalpy diagram for the reaction. Draw the y-axis of the diagram, representing the enthalpy. Now, place compound A at some height from the base of the y-axis, as its formation enthalpy is positive. Similarly, place compound B higher than compound A, since its formation enthalpy is also positive. Draw an arrow from compound A to compound B representing the reaction.

Determine the Change in Enthalpy for the Reaction

To determine the change in enthalpy for the reaction, \(\Delta H_{rxn}\), we can use the following equation: \[ \Delta H_{rxn}=\Delta H_{f}^{\circ}(B)-\Delta H_{f}^{\circ}(A) \]As mentioned earlier, the overall reaction is exothermic, so \(\Delta H_{rxn} < 0\).

Analyze and Conclude

Since the overall reaction is exothermic, it means that energy is being released during the conversion of compound A into compound B. This implies that the enthalpy of compound B is lower than the enthalpy of compound A. From the enthalpy diagram, we can see that this is not the case, as we have drawn compound B with higher enthalpy than compound A. In conclusion, there is either an error in the information provided in the problem or an additional step or intermediate compound is needed to release the energy, making the overall reaction exothermic.

Key concepts

Endothermic Reactions

In chemistry, understanding endothermic reactions can be crucial when studying energy changes in reactions. An endothermic reaction occurs when energy is absorbed from the surroundings into the system. This is indicated by a positive change in enthalpy ( abla H a) for each component involved in the process.

Features of Endothermic Reactions:

• Absorption of energy: The system takes in heat, usually making the reaction mixture feel cool.
• Increase in enthalpy: The enthalpy of products is higher than that of reactants.
• Example: Melting ice requires energy to transition from solid to liquid water.

In the context of the exercise, both compounds A and B have a positive abla H_f^ abla o, indicating they absorb energy during their formation. However, whether the overall process is endothermic also depends on the relative enthalpies of A and B.

Exothermic Reactions

Exothermic reactions stand as the opposite of endothermic reactions. In these reactions, energy is released into the surroundings, often felt as heat. The key characteristic is a negative enthalpy change ( abla H_{rxn} < 0 a).

Key Characteristics of Exothermic Reactions:

• Release of energy: They release heat, making the surroundings warmer.
• Decrease in enthalpy: The enthalpy of products is less than the enthalpy of reactants.
• Example: Combustion of wood releases heat and light.

In the exercise given, the conversion of A to B is described as exothermic, meaning despite both A and B having positive formation enthalpies, the process releases energy. However, our step-by-step analyses suggest a contradiction in the graphical representation of relative enthalpies, indicating a potential error or missing intermediate.

Enthalpy Change

The concept of enthalpy change (abla Ha) is fundamental in thermochemistry as it helps quantify the energy absorbed or released during a chemical reaction. The enthalpy change for a reaction can tell us if a reaction is endothermic or exothermic.

Mathematically, the enthalpy change for a reaction (abla H_{rxn}) is calculated as:\[abla H_{rxn} = abla H_f^o ( ext{products}) - abla H_f^o ( ext{reactants})\]
Understanding Enthalpy Change

• A positive abla Ha indicates an endothermic process.
• A negative abla Ha indicates an exothermic process.
• Crucially, the magnitude of abla Ha reflects the energy difference, whether absorbed or released.

In any reaction, if errors appear in expected abla Ha values versus practical measurements, it could imply missing reaction steps or intermediates that might alter the perceived overall energy exchange.