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

The given reactions are: 1. \(A \longrightarrow B\), with enthalpy change \(\Delta H_1 = +30\, \text{kJ}\) 2. \(B \longrightarrow C\), with enthalpy change \(\Delta H_2 = +60\, \text{kJ}\) Our goal is to find the enthalpy change for the reaction \(A \longrightarrow C\).

According to Hess's law, the enthalpy change of the desired reaction (\((A \longrightarrow C)\)) is equal to the sum of the enthalpy changes of the given reactions. So, \(\Delta H_{Total} = \Delta H_1 + \Delta H_2\) Substitute the given enthalpy changes: \(\Delta H_{Total} = (+30\, \text{kJ}) + (+60\, \text{kJ})\) \(\Delta H_{Total} = +90\, \text{kJ}\) Therefore, the enthalpy change for the reaction \(A \longrightarrow C\) is \(+90\, \text{kJ}\). #b) Construct an enthalpy diagram for substances A, and C#

An enthalpy diagram is a graphical representation of the enthalpy changes in chemical reactions. It allows us to visualize how the enthalpy changes as the reactants transform into products. On the vertical axis, we will represent the enthalpy level (H). We start by showing substances \(A\), \(B\), and \(C\) on the horizontal axis.

Now, we will represent the given reactions and their enthalpy changes on the enthalpy diagram: 1. For the reaction \(A \longrightarrow B\), draw an arrow from \(A\) to \(B\) with a positive slope (since \(\Delta H_1 = +30\, \text{kJ}\) is an endothermic reaction). Label the arrow with \(\Delta H_1=+30\, \text{kJ}\). 2. For the reaction \(B \longrightarrow C\), draw an arrow from \(B\) to \(C\) with a positive slope (since \(\Delta H_2 = +60\, \text{kJ}\) is again an endothermic reaction). Label the arrow with \(\Delta H_2=+60\, \text{kJ}\). 3. To represent the overall reaction \(A \longrightarrow C\), draw an arrow directly from \(A\) to \(C\), skipping \(B\). According to Hess's law, the enthalpy change for this reaction will be equal to the sum of \(\Delta H_1\) and \(\Delta H_2\), calculated in part (a). Label the arrow with \(\Delta H_{Total}=+90\, \text{kJ}\). The enthalpy diagram shows the enthalpy changes for each given reaction and the overall reaction \(A \longrightarrow C\). It visually demonstrates how Hess's law applies: the enthalpy change for the direct reaction \(A \longrightarrow C\) is equal to the sum of the enthalpy changes for the two hypothetical reactions.