Problem 84 - 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 \(\mathrm{NaOH}(\mathrm{aq})\) (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

(a) \( \text{Ga(OH)}_3 + 3\text{HCl} \rightarrow \text{GaCl}_3 + 3\text{H}_2\text{O} \) and \( \text{Ga(OH)}_3 + 3\text{NaOH} \rightarrow \text{Na}_3\text{GaO}_3 + 3\text{H}_2\text{O} \); (b) Ga\(^{3+}\) is a stronger acid than Al\(^{3+}\).

Step 1: Writing the Balanced Equation for Reaction with HCl

Gallium hydroxide \( \text{Ga(OH)}_3 \) reacts with hydrochloric acid \( \text{HCl (aq)} \) to form gallium chloride \( \text{GaCl}_3 \) and water. The balanced equation for this reaction is: \[ \text{Ga(OH)}_3 + 3\text{HCl} \rightarrow \text{GaCl}_3 + 3\text{H}_2\text{O} \] This shows the amphoteric nature of gallium hydroxide reacting as a base.

Step 2: Writing the Balanced Equation for Reaction with NaOH

Gallium hydroxide \( \text{Ga(OH)}_3 \) can also react with sodium hydroxide \( \text{NaOH (aq)} \) to form sodium gallate \(\text{Na}_3\text{GaO}_3\) and water. The balanced equation is: \[ \text{Ga(OH)}_3 + 3\text{NaOH} \rightarrow \text{Na}_3\text{GaO}_3 + 3\text{H}_2\text{O} \] This reaction illustrates gallium hydroxide acting as an acid.

Step 3: Comparing Acid Strengths

The strength of an acid is measured by its ionization constant \( K_a \). For \( \text{Ga}^{3+}(aq) \), the \( K_a \) is \( 1.2 \times 10^{-3} \). For \( \text{Al}^{3+}(aq) \), \( K_a \) is typically around \( 10^{-5} \). A larger \( K_a \) value indicates a stronger acid, thus \( \text{Ga}^{3+} \) is a stronger acid than \( \text{Al}^{3+} \).

Key Concepts

Amphoteric Compounds

Amphoteric compounds are fascinating in the chemistry world because they can react with both acids and bases. This ability comes from the presence of both acidic and basic properties within the same substance. A great example of an amphoteric compound is gallium hydroxide, \(\text{Ga(OH)}_3\), which behaves like aluminum hydroxide in this regard.

• When reacting with an acid, such as hydrochloric acid \( \text{HCl} \(\mathrm{aq}\)\), gallium hydroxide acts as a base.
• The reaction with HCl forms gallium chloride \( \text{GaCl}_3 \) and water. The balanced equation is: \\[ \text{Ga(OH)}_3 + 3\text{HCl} \rightarrow \text{GaCl}_3 + 3\text{H}_2\text{O} \]
• Conversely, when it's treated with a strong base like sodium hydroxide \( \text{NaOH (aq)} \), it acts as an acid.
• This forms sodium gallate \( \text{Na}_3\text{GaO}_3 \) and water, shown in this balanced equation: \\[ \text{Ga(OH)}_3 + 3\text{NaOH} \rightarrow \text{Na}_3\text{GaO}_3 + 3\text{H}_2\text{O} \]

This dual nature of being able to react with both acids and bases makes amphoterism an essential concept, revealing the versatile chemistry of these compounds.

Acid Strength Comparison

Understanding acid strength requires examining the ionization constant, or \( K_a\), which tells us how well an acid can give off hydrogen ions. The larger the \( K_a\), the stronger the acid.Gallium ions \( \text{Ga}^{3+}(\mathrm{aq})\) in solution have a \( K_a\) of \( 1.2 \times 10^{-3}\), which is significantly larger than that of aluminum ions, \( \text{Al}^{3+}(\mathrm{aq})\), with a \( K_a\) around \( 10^{-5}\). This means:

• Gallium ions are stronger acids compared to aluminum ions.
• This difference is due to the more significant tendency of gallium ions to release hydrogen ions in solution.

In simple terms, a stronger acid like \( \text{Ga}^{3+}\) will dissociate more in water, making it more reactive and suggesting a more substantial ability to interact with other substances through proton donation. This knowledge helps understand reactions in solutions, industrial processes, or biological systems where different acid strengths play a role.

Chemical Reaction Equations

Chemical reactions can be thoroughly understood through balanced equations, which show the reactants and products involved. For instance, as seen in amphoteric compounds, formulations of gallium hydroxide reactions highlight these crucial details:

• Reaction with hydrochloric acid: This equation \ \[ \text{Ga(OH)}_3 + 3\text{HCl} \rightarrow \text{GaCl}_3 + 3\text{H}_2\text{O} \] is balanced, showing each atom's count is the same on both sides, maintaining the law of conservation of mass.
• Reaction with sodium hydroxide: Similarly, the reaction \ \[ \text{Ga(OH)}_3 + 3\text{NaOH} \rightarrow \text{Na}_3\text{GaO}_3 + 3\text{H}_2\text{O} \] gives a full picture of the transformation occurring on a molecular level.

Balancing equations is essential, ensuring that chemical reactions reflect the reality of conservation laws. This skill is crucial for anyone studying chemistry, providing insights into not only qualitative but quantitative aspects of chemical reactions. Understanding this helps predict outcomes in labs, anticipate product formations, and maintain safety in chemical handling.