Problem 64 - Chemistry Matter and Change

Question

Write a balanced chemical equation for each of the following. \begin{equation} \begin{array}{l}{\text { a. the dissociation of solid magnesium hydroxide in }} \\ {\text { water }} \\ {\text { b. the reaction of magnesium metal and hydrobromic }} \\ {\text { acid }} \\ {\text { c. the ionization of propanoic acid (CH_ }_{3} \mathrm{CH}_{2} \mathrm{COOH} )} \\ {\text { in water }} \\ {\text { d. the second ionization of sulfuric acid in water }}\end{array} \end{equation}

Step-by-Step Solution

Answer

(a) \( \text{Mg(OH)}_2 \rightarrow \text{Mg}^{2+} + 2 \text{OH}^- \); (b) \( \text{Mg} + 2 \text{HBr} \rightarrow \text{MgBr}_2 + \text{H}_2 \); (c) \( \text{CH}_3\text{CH}_2\text{COOH} \rightleftharpoons \text{CH}_3\text{CH}_2\text{COO}^- + \text{H}^+ \); (d) \( \text{HSO}_4^- \rightleftharpoons \text{SO}_4^{2-} + \text{H}^+ \).

Step 1: Dissociation of Magnesium Hydroxide

Write the chemical formula for magnesium hydroxide: \( \text{Mg(OH)}_2 \). When magnesium hydroxide dissociates in water, it breaks into its ions: magnesium ions (\( \text{Mg}^{2+} \)) and hydroxide ions (\( \text{OH}^- \)). The balanced equation is: \[\text{Mg(OH)}_2 (s) \rightarrow \text{Mg}^{2+} (aq) + 2 \text{OH}^- (aq)\]

Step 2: Reaction of Magnesium Metal with Hydrobromic Acid

Write the chemical formulas for magnesium and hydrobromic acid: \( \text{Mg} \) and \( \text{HBr} \). When magnesium reacts with hydrobromic acid, magnesium bromide (\( \text{MgBr}_2 \)) and hydrogen gas (\( \text{H}_2 \)) are formed. The balanced equation is: \[\text{Mg} (s) + 2 \text{HBr} (aq) \rightarrow \text{MgBr}_2 (aq) + \text{H}_2 (g)\]

Step 3: Ionization of Propanoic Acid

Write the chemical formula for propanoic acid: \( \text{CH}_3\text{CH}_2\text{COOH} \). In water, propanoic acid partially ionizes to form propanoate ions (\( \text{CH}_3\text{CH}_2\text{COO}^- \)) and hydrogen ions (\( \text{H}^+ \)). The balanced equation is: \[\text{CH}_3\text{CH}_2\text{COOH} (aq) \rightleftharpoons \text{CH}_3\text{CH}_2\text{COO}^- (aq) + \text{H}^+ (aq)\]

Step 4: Second Ionization of Sulfuric Acid

Recognize that sulfuric acid (\( \text{H}_2\text{SO}_4 \)) has two ionizable hydrogens. The first ionization results in \( \text{HSO}_4^- \) and \( \text{H}^+ \), and the second ionization of \( \text{HSO}_4^- \) in water leads to \( \text{SO}_4^{2-} \) and \( \text{H}^+ \). The balanced equation for the second ionization is: \[\text{HSO}_4^- (aq) \rightleftharpoons \text{SO}_4^{2-} (aq) + \text{H}^+(aq)\]

Key Concepts

Dissociation of Magnesium Hydroxide

Magnesium hydroxide, known with the chemical formula \( \text{Mg(OH)}_2 \), is a common compound used in antacids and laxatives. When it dissociates in water, it separates into magnesium ions \( (\text{Mg}^{2+}) \) and hydroxide ions \( (\text{OH}^-) \). This dissociation process is crucial because it increases the number of ions in the solution, which affects the solution's properties. Here's what happens:

\( \text{Mg(OH)}_2 (s) \rightarrow \text{Mg}^{2+} (aq) + 2 \text{OH}^- (aq) \)

The solid magnesium hydroxide dissolves, breaking its ionic bonds, and the ions are released into the water. The equation shows that for every one formula unit of magnesium hydroxide that dissociates, two hydroxide ions and one magnesium ion are produced. Knowing this reaction is essential for understanding how magnesium hydroxide neutralizes stomach acid. It's a simple yet fascinating process that demonstrates fundamental chemical principles.

Reaction of Magnesium with Hydrobromic Acid

When magnesium, a shiny gray metal, interacts with hydrobromic acid \( \text{HBr} \), an exciting chemical transformation occurs. This reaction results in the formation of magnesium bromide \( \text{MgBr}_2 \) and hydrogen gas \( \text{H}_2 \). The overall balanced chemical equation for this reaction is:

\( \text{Mg} (s) + 2 \text{HBr} (aq) \rightarrow \text{MgBr}_2 (aq) + \text{H}_2 (g) \)

In this reaction, magnesium acts as a reducing agent. It gives away electrons to the hydrobromic acid, which is reduced to hydrogen gas. This process is an example of a redox reaction, where oxidation and reduction occur simultaneously. It's an excellent demonstration of magnesium's reactivity, as it can easily lose electrons to form magnesium ions \( (\text{Mg}^{2+}) \). Observing these types of reactions helps to grasp the reactivity of metals and how acids can liberate hydrogen gas.

Ionization of Propanoic Acid

Propanoic acid, a carboxylic acid with the formula \( \text{CH}_3\text{CH}_2\text{COOH} \), partially ionizes in water. As an organic acid, it does not ionize completely, meaning it is a weak acid. In this process, propanoic acid forms propanoate ions \( \text{CH}_3\text{CH}_2\text{COO}^- \) and hydrogen ions \( \text{H}^+ \). The reversible reaction in water is reflected in the equation:

\( \text{CH}_3\text{CH}_2\text{COOH} (aq) \rightleftharpoons \text{CH}_3\text{CH}_2\text{COO}^- (aq) + \text{H}^+ (aq) \)

This reaction shows the equilibrium established between the unionized and ionized forms. The partial ionization indicates that not all of the propanoic acid molecules lose a proton to form ions. Understanding such equilibria is important in chemistry because they describe many biological and chemical processes. The concept of weak acids and their ionization is fundamental in subjects like biochemistry, where acids like these play various roles.

Second Ionization of Sulfuric Acid

Sulfuric acid \( \text{H}_2\text{SO}_4 \) is a strong, dibasic acid, meaning it can release two protons. The second ionization, which follows the first, involves the conversion of the bisulfate ion \( \text{HSO}_4^- \) to the sulfate ion \( \text{SO}_4^{2-} \), releasing another hydrogen ion \( \text{H}^+ \). The second ionization can be represented by the equation:

\( \text{HSO}_4^- (aq) \rightleftharpoons \text{SO}_4^{2-} (aq) + \text{H}^+(aq) \)

This step is crucial because it illustrates sulfuric acid's role as a diprotic acid. In water, it first ionizes completely to form hydrogen ions and bisulfate ions, and then it partially ionizes in the second step to form sulfate ions. The concept of multiple ionization steps is critical in acid-base chemistry and environmental chemistry, as it influences the concentration of ions in solutions and determines the acid's strength at different stages. Understanding these ionization steps is essential for predicting the behavior of acids in various contexts.