Problem 110 - Chemistry and Chemical Reactivity

Question

The chemistry of gallium: (a) Gallium hydroxide, like aluminum hydroxide, is amphoteric. Write a balanced equation to show how this hydroxide can dissolve in both HCl(aq) and NaOH(aq). (b) Gallium ion in water, \(\mathrm{Ga}^{3+}(\mathrm{aq}),\) has a \(K_{\mathrm{a}}\) value of \(1.2 \times 10^{-3} .\) Is this ion a stronger or a weaker acid than \(\mathrm{Al}^{3+}(\mathrm{aq}) ?\)

Step-by-Step Solution

Answer

Ga(OH)₃ reacts with both HCl and NaOH, showing amphoteric behavior. Ga³⁺ is a stronger acid than Al³⁺.

Step 1: Understanding Amphoteric Behavior

An amphoteric substance can react as both an acid and a base. Gallium hydroxide (Ga(OH)₃) can react with acids like HCl to form gallium ions and water, and with bases like NaOH to form gallate ions. This means it can dissolve in both acidic and basic solutions.

Step 2: Reaction with HCl

When Ga(OH)₃ reacts with hydrochloric acid, the reaction favors the formation of Ga³⁺ ions and water. The balanced equation for this reaction is:\[ \text{Ga(OH)}_3 (s) + 3 \text{HCl} (aq) \rightarrow \text{GaCl}_3 (aq) + 3 \text{H}_2\text{O} (l) \]

Step 3: Reaction with NaOH

Ga(OH)₃ can also dissolve in a solution of sodium hydroxide to form soluble sodium gallate. The balanced equation for this reaction is:\[ \text{Ga(OH)}_3 (s) + \text{NaOH} (aq) \rightarrow \text{NaGa(OH)}_4 (aq) \]

Step 4: Comparing Acid Strengths

To determine the relative acid strength of \( \text{Ga}^{3+} \) compared to \( \text{Al}^{3+} \), we compare their \( K_a \) values. \( K_a \) represents acid dissociation constant, with a larger \( K_a \) indicating a stronger acid. \( \text{Ga}^{3+} \) has a \( K_a \) of \( 1.2 \times 10^{-3} \), whereas \( \text{Al}^{3+} \) has a \( K_a \) of \( 1.0 \times 10^{-5} \). Therefore, \( \text{Ga}^{3+} \) is a stronger acid than \( \text{Al}^{3+} \).

Key Concepts

Gallium Hydroxide

Gallium hydroxide, denoted as \( \text{Ga(OH)}_3 \), is a fascinating compound that behaves in a unique way due to its amphoteric nature. This means that it can act as both an acid and a base.
For instance:

• When interacting with an acid like hydrochloric acid (HCl), gallium hydroxide dissolves to produce gallium ions and water. The balanced chemical equation is:\[\text{Ga(OH)}_3 (s) + 3 \text{HCl} (aq) \rightarrow \text{GaCl}_3 (aq) + 3 \text{H}_2\text{O} (l)\]
• When it comes into contact with a base such as sodium hydroxide (NaOH), gallium hydroxide forms soluble sodium gallate:\[\text{Ga(OH)}_3 (s) + \text{NaOH} (aq) \rightarrow \text{NaGa(OH)}_4 (aq)\]

This capability makes gallium hydroxide useful in various chemical processes and a subject of interest in the study of acid-base reactions.

Acid-Base Reactions

Acid-base reactions involve the transfer of protons (\(\text{H}^+\)) between reactant species, and these reactions can be observed in many common chemical interactions. Gallium hydroxide exemplifies this with its ability to dissolve in both acidic and basic solutions.

• In acidic environments, substances like \(\text{Ga(OH)}_3\) neutralize acids by forming water and a salt, as seen in its reaction with HCl.
• In basic environments, it reacts to form complex ions, as with sodium hydroxide, creating compounds like sodium gallate.

The dual nature of such reactions highlights the flexibility of amphoteric substances and provides a foundation for many industrial and laboratory chemical processes. Understanding these dynamics is crucial in fields ranging from biochemistry to materials science.

Acid Strength Comparison

When discussing acid strength, the acid dissociation constant, \( K_a \), is key. It measures how easily an acid donates protons in water. A larger \( K_a \) indicates a stronger acid.
With the example of gallium and aluminum ions:

• Gallium ion \( \text{Ga}^{3+} \) has a \( K_a \) of \( 1.2 \times 10^{-3} \).
• Aluminum ion \( \text{Al}^{3+} \) has a \( K_a \) of \( 1.0 \times 10^{-5} \).

Since the \( K_a \) value for \( \text{Ga}^{3+} \) is greater than that of \( \text{Al}^{3+} \), gallium ions are stronger acids. This difference in acid strength has significant implications in both practical applications and theoretical chemistry, influencing how these ions behave in various solutions.