Question

Write reactions for which the enthalpy change will be a. \(\Delta H_{\mathrm{f}}^{\circ}\) for solid aluminum oxide. b. The standard enthalpy of combustion of liquid ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l) .\) c. The standard enthalpy of neutralization of sodium hydroxide solution by hydrochloric acid. d. \(\Delta H_{\mathrm{f}}^{\circ}\) for gaseous vinyl chloride, \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}(g)\). e. The enthalpy of combustion of liquid benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}(l)\). f. The enthalpy of solution of solid ammonium bromide.

Short answer

a. \(2 \mathrm{Al}(s) + \frac{3}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{Al}_{2} \mathrm{O}_{3}(s)\) b. \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l) + 3\mathrm{O}_{2}(g) \rightarrow 2\mathrm{CO}_{2}(g) + 3\mathrm{H}_{2}\mathrm{O}(l)\) c. \(\mathrm{NaOH}_{(aq)} + \mathrm{HCl}_{(aq)} \rightarrow \mathrm{H}_{2}\mathrm{O}(l) + \mathrm{NaCl}_{(aq)}\) d. \(2\mathrm{C}(s) + \frac{3}{2}\mathrm{H}_{2}(g) + \frac{1}{2}\mathrm{Cl}_{2}(g) \rightarrow \mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}(g)\) e. \(\mathrm{C}_{6} \mathrm{H}_{6}(l) + \frac{15}{2} \mathrm{O}_{2}(g) \rightarrow 6\mathrm{CO}_{2}(g) + 3\mathrm{H}_{2}\mathrm{O}(l)\) f. \(\mathrm{NH}_{4} \mathrm{Br}(s) \rightarrow \mathrm{NH}_{4}^{+}_{(aq)} + \mathrm{Br}^{-}_{(aq)}\)

Step-by-step solution

a. Enthalpy of formation for solid aluminum oxide.

To write the reaction for the enthalpy of formation of solid aluminum oxide, we need to combine its constituent elements (aluminum and oxygen) in their standard states. The balanced reaction is: \[2 \mathrm{Al}(s) + \frac{3}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{Al}_{2} \mathrm{O}_{3}(s)\]

b. Standard enthalpy of combustion of liquid ethanol.

In the combustion of liquid ethanol, it reacts with oxygen gas to produce carbon dioxide and water as products. The balanced reaction is: \[\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l) + 3\mathrm{O}_{2}(g) \rightarrow 2\mathrm{CO}_{2}(g) + 3\mathrm{H}_{2}\mathrm{O}(l)\]

c. Standard enthalpy of neutralization of sodium hydroxide solution by hydrochloric acid.

In this reaction, sodium hydroxide, a strong base, reacts with hydrochloric acid, a strong acid, to form water and sodium chloride as products. The balanced reaction is: \[\mathrm{NaOH}_{(aq)} + \mathrm{HCl}_{(aq)} \rightarrow \mathrm{H}_{2}\mathrm{O}(l) + \mathrm{NaCl}_{(aq)}\]

d. Enthalpy of formation for gaseous vinyl chloride.

To write the reaction for the enthalpy of formation of gaseous vinyl chloride, we need to combine its constituent elements (carbon, hydrogen, and chlorine) in their standard states. The balanced reaction is: \[2\mathrm{C}(s) + \frac{3}{2}\mathrm{H}_{2}(g) + \frac{1}{2}\mathrm{Cl}_{2}(g) \rightarrow \mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}(g)\]

e. Enthalpy of combustion of liquid benzene.

In the combustion of liquid benzene, it reacts with oxygen gas to produce carbon dioxide and water as products. The balanced reaction is: \[\mathrm{C}_{6} \mathrm{H}_{6}(l) + \frac{15}{2} \mathrm{O}_{2}(g) \rightarrow 6\mathrm{CO}_{2}(g) + 3\mathrm{H}_{2}\mathrm{O}(l)\]

f. Enthalpy of solution of solid ammonium bromide.

In the process of dissolving solid ammonium bromide in water, the solid dissociates into its constituent ammonium and bromide ions and forms a solution. The balanced reaction is: \[\mathrm{NH}_{4} \mathrm{Br}(s) \rightarrow \mathrm{NH}_{4}^{+}_{(aq)} + \mathrm{Br}^{-}_{(aq)}\]

Key concepts

Enthalpy of Formation

The enthalpy of formation refers to the heat change when one mole of a compound is formed from its elements in their most stable forms at standard conditions (usually 298 K and 1 atm). Consider the formation of solid aluminum oxide (\(\mathrm{Al}_2\mathrm{O}_3\)) from aluminum and oxygen. The reaction is:

• 2 \(\mathrm{Al}(s)\) + \(\frac{3}{2} \mathrm{O}_2(g)\) \(\rightarrow \mathrm{Al}_2 \mathrm{O}_3(s)\)

This reaction shows aluminum in its solid state and oxygen as a diatomic gas, both in their elemental forms, combining to create aluminum oxide. Enthalpy of formation is a key concept as it helps us understand how much energy is required or released when compounds form.

Enthalpy of Combustion

Enthalpy of combustion reveals the amount of heat produced when one mole of a substance burns completely in oxygen. The standard enthalpy of combustion is a particularly useful measure in evaluating fuels. Let's look at ethanol (\(\mathrm{C_2H_5OH}(l)\)), for which the balanced combustion reaction with oxygen is:

• \(\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}(l) + 3\mathrm{O}_2(g) \rightarrow 2\mathrm{CO}_2(g) + 3\mathrm{H}_2\mathrm{O}(l)\)

Here, ethanol reacts with oxygen to produce carbon dioxide and water. This reaction releases energy, which is essential for its use as a biofuel. Like ethanol, benzene (\( \mathrm{C_6H_6}(l)\)) combusts similarly and releases significant energy, expressed in its combustion reaction:

• \( \mathrm{C}_6 \mathrm{H}_6(l) + \frac{15}{2} \mathrm{O}_2(g) \rightarrow 6\mathrm{CO}_2(g) + 3\mathrm{H}_2\mathrm{O}(l)\)

This knowledge aids in selecting fuels with the right energy outputs for different applications.

Enthalpy of Neutralization

The enthalpy of neutralization measures the heat change when an acid reacts with a base during a neutralization reaction, usually forming water and a salt. Consider the reaction between sodium hydroxide (\(\mathrm{NaOH_{(aq)}}\)) and hydrochloric acid (\(\mathrm{HCl_{(aq)}}\)):

• \(\mathrm{NaOH}_{(aq)} + \mathrm{HCl}_{(aq)} \rightarrow \mathrm{H}_2\mathrm{O}(l) + \mathrm{NaCl}_{(aq)}\)

In this process, the hydroxide ions (\(\mathrm{OH}^-\)) from sodium hydroxide and hydrogen ions (\(\mathrm{H}^+\)) from hydrochloric acid combine to form water. The exothermic nature of the reaction is due to the strong bonds formed in the water, releasing heat. This principle is crucial in designing industrial processes and laboratory experiments where temperature control is significant.

Enthalpy of Solution

The enthalpy of solution involves the heat change when a solute dissolves in a solvent, forming a solution. This can either absorb (endothermic) or release (exothermic) heat. For the dissolution of ammonium bromide (\(\mathrm{NH_4Br(s)}\)) in water:

• \(\mathrm{NH}_{4} \mathrm{Br}(s) \rightarrow \mathrm{NH}_{4}^{+}_{(aq)} + \mathrm{Br}^{-}_{(aq)}\)

This dissociation into ions is typically endothermic as it requires energy to break the ionic bonds in the solid. Understanding enthalpy of solution is important for predicting the solubility of compounds and designing cooling systems, where a solute absorbs energy, creating a cooling effect. Analyzing such reactions helps chemists and engineers in pharmaceuticals, manufacturing, and energy management.