Problem 42 - Chemistry The Central Science In Si Units

Question

Without referring to tables, predict which of the following has the higher enthalpy in each case: (a) \(1 \mathrm{~mol} \mathrm{I}_{2}(s)\) or \(1 \mathrm{~mol} \mathrm{l}_{2}(g)\) at the same temperature, (b) \(2 \mathrm{~mol}\) of iodine atoms or \(1 \mathrm{~mol}\) of \(\mathrm{I}_{2},(\mathbf{c}) 1 \mathrm{~mol} \mathrm{I}_{2}(g)\) and \(1 \mathrm{~mol} \mathrm{H}_{2}(g)\) at \(25^{\circ} \mathrm{C}\) or \(2 \mathrm{~mol} \mathrm{HI}(g)\) at \(25^{\circ} \mathrm{C},\left(\right.\) d) \(1 \mathrm{~mol} \mathrm{H}_{2}(g)\) at \(100^{\circ} \mathrm{C}\) or \(1 \mathrm{~mol} \mathrm{H}_{2}(\mathrm{~g})\) at \(300{ }^{\circ} \mathrm{C} .\)

Step-by-Step Solution

Answer

(a) \(I_{2}(g)\), (b) iodine atoms, (c) \(I_{2}(g) + H_{2}(g)\), (d) \(H_{2}(g)\) at \(300^{\circ} C\).

Step 1: Understanding Enthalpies of Phase Changes

Enthalpy, or heat content, often varies with the state of a substance because energetic contributions differ in solids, liquids, and gases. In its gaseous form, a substance typically has a higher enthalpy compared to its solid form at the same temperature due to the energy required for a phase change (fusion or sublimation). So, \(1 \text{ mol } I_{2}(g)\) has a higher enthalpy than \(1 \text{ mol } I_{2}(s)\).

Step 2: Considering Bond Dissociation vs. Formation

To analyze the enthalpies of iodine molecules vs. dissociated iodine atoms, consider bond energies: breaking \(I_{2}\) into two iodine atoms requires energy input, meaning higher energy (enthalpy) is in the form of separate atoms. Thus, \(2 \text{ mol iodine atoms}\) has a higher enthalpy than \(1 \text{ mol } I_{2}\).

Step 3: Comparing Reaction Enthalpy Changes

For the reaction \(I_{2}(g) + H_{2}(g) \rightarrow 2HI(g)\), if there are bonds being formed in the products (HI) that are stronger than those broken in the reactants (I—-I and H—H), the reaction is exothermic—a common trend for formation of stable diatomic molecules. Therefore, \(1 \text{ mol } I_{2}(g) + 1 \text{ mol } H_{2}(g)\) has higher enthalpy than \(2 \text{ mol } HI(g)\).

Step 4: Examining Temperature Effects on Gas Enthalpy

In gases, increasing temperature usually increases enthalpy due to higher kinetic energy at higher temperatures. Therefore, \(1 \text{ mol } H_{2}(g)\) at \(300^{\circ} C\) has a higher enthalpy than \(1 \text{ mol } H_{2}(g)\) at \(100^{\circ} C\).

Key Concepts

Phase Changes

Phase changes in substances often involve significant changes in enthalpy. When a substance transitions from solid to liquid, or from liquid to gas, it undergoes a process that requires or releases energy, known as enthalpy change. For instance, iodine (\(I_2\)) in its gaseous form has higher enthalpy compared to its solid form. This is because energy is supplied to overcome intermolecular forces during the phase change, whether it be fusion (solid to liquid) or sublimation (solid to gas).

• In solids, the molecules are closely packed, minimizing their energy state.
• In gases, molecules are more dispersed with higher kinetic energy, which translates into higher enthalpy.

Understanding phase changes helps dissect why one mole of gaseous iodine would inherently have a higher enthalpy than its solid counterpart.

Bond Dissociation

Bond dissociation refers to the process of breaking chemical bonds within molecules, which requires energy input. When you consider iodine molecules (\(I_2\)), breaking the bond between the two iodine atoms to form individual atoms consumes energy, leading to increased enthalpy.

• Breaking a bond absorbs energy, a process termed endothermic.
• The energy needed to dissociate bonds directly affects the enthalpy.

Therefore, two moles of iodine atoms, in separate states, possess higher enthalpy compared to one mole of iodine molecule, as energy was required to break them apart.

Reaction Enthalpy

Chemical reactions often involve forming and breaking bonds. The overall enthalpy change in a reaction depends on the energy required to break the initial bonds and the energy released upon forming new ones. In the reaction \(I_2(g) + H_2(g) \rightarrow 2HI(g)\), considering bond strengths is crucial.

• If stronger bonds form in the products than those that were in the reactants, the process is usually exothermic.
• Higher energy is found in reactants when they lead toward the formation of more stable, lower-energy product molecules.

This means the initial gaseous reactants, \(I_2(g)\) and \(H_2(g)\), inherently possess higher enthalpy than the resulting \(2HI(g)\) due to the strong bonds formed in the hydrogen iodide molecules.

Temperature Effects on Gases

Temperature plays a pivotal role in determining the enthalpy of gases. As temperature increases, the kinetic energy of gas particles also increases, thereby elevating their enthalpy. Consider hydrogen gas (\(H_2\)): At higher temperatures, its molecules have more internal energy, leading to higher enthalpy.

• Kinetic energy correlates with temperature increase.
• Higher temperature implies increased molecular motion and, consequently, increased enthalpy.

Therefore, one mole of \(H_2(g)\) at 300°C will have a higher enthalpy compared to the same amount at 100°C, as the heat energy at higher temperatures significantly impacts the internal energy of gas particles.