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Chapter 5: Problem 12

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

Expert verified
(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

01

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.
02

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.
03

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 \(\Delta H_{rxn} < 0\).
04

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.

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