Problem 40 - Chemistry and Chemical Reactivity

Question

Gallium hydroxide, like aluminum hydroxide, is amphoteric. (a) Write balanced equations for the reaction of solid \(\mathrm{Ga}(\mathrm{OH})_{3}\) with aqueous \(\mathrm{HCl}\) and \(\mathrm{NaOH}\). (b) What volume of \(0.0112 \mathrm{M} \mathrm{HCl}\) is needed to react completely with \(1.25 \mathrm{g}\) of \(\mathrm{Ga}(\mathrm{OH})_{3} ?\)

Step-by-Step Solution

Answer

2.79 L of HCl is required to react with 1.25 g of Ga(OH)₃.

Step 1: Understand the Concept of Amphoteric Substances

Amphoteric substances can react with both acids and bases. Gallium hydroxide (\(\mathrm{Ga(OH)}_3\)) is amphoteric, so it will react with hydrochloric acid (\(\mathrm{HCl}\)) and sodium hydroxide (\(\mathrm{NaOH}\)).

Step 2: Write Balanced Equation for Reaction with HCl

Gallium hydroxide reacts with hydrochloric acid as an acid-base reaction to form gallium chloride and water. The balanced chemical equation is:\[\mathrm{Ga(OH)}_3 (s) + 3\mathrm{HCl} (aq) \rightarrow \mathrm{GaCl}_3 (aq) + 3\mathrm{H_2O} (l)\]

Step 3: Write Balanced Equation for Reaction with NaOH

Gallium hydroxide reacts with sodium hydroxide by forming a complex ion in solution. The balanced equation is:\[\mathrm{Ga(OH)}_3 (s) + \mathrm{NaOH} (aq) \rightarrow \mathrm{Na[Ga(OH)}_4] (aq)\]

Step 4: Calculate Moles of Ga(OH)3

First, determine the molar mass of \(\mathrm{Ga(OH)}_3\): Ga = 69.72 g/mol, O = 16.00 g/mol, H = 1.01 g/mol. \[\mathrm{Molar\ mass\ of\ Ga(OH)}_3 = 69.72 + 3(16.00 + 1.01) = 120.74\, \mathrm{g/mol}\]Now, calculate the moles of \(1.25\, \mathrm{g}\) of \(\mathrm{Ga(OH)}_3\):\[\text{Moles} = \frac{1.25\, \mathrm{g}}{120.74\, \mathrm{g/mol}} \approx 0.0104\, \mathrm{mol}\]

Step 5: Determine Volume of HCl Required

From the balanced equation with HCl, 1 mole of \(\mathrm{Ga(OH)}_3\) reacts with 3 moles of \(\mathrm{HCl}\). Thus, 0.0104 moles of \(\mathrm{Ga(OH)}_3\) requires:\[3 \times 0.0104 = 0.0312\, \mathrm{mol}\, \mathrm{HCl}\]Calculate the volume of \(0.0112\, \mathrm{M}\, \mathrm{HCl}\) needed:\[\mathrm{Volume} = \frac{0.0312\, \mathrm{mol}}{0.0112\, \mathrm{mol/L}} \approx 2.79\, \mathrm{L}\]

Key Concepts

Chemical Reactions

Chemical reactions involve the transformation of substances through a process that changes their molecular structure. In our example, gallium hydroxide (\(\text{Ga(OH)}_3\)) undergoes reactions with both hydrochloric acid (\(\text{HCl}\)) and sodium hydroxide (\(\text{NaOH}\)). These reactions showcase the ability of certain substances, like \(\text{Ga(OH)}_3\), to participate in different chemical interactions. A chemical reaction can result in the formation of new substances, release of energy or heat, and sometimes even a change of phase. Understanding how substances interact and transform is fundamental in chemistry.

Acid-Base Reactions

Acid-base reactions are a specific type of chemical reaction where an acid reacts with a base. In this context, an acid is a substance that donates protons (H\(^+\)), while a base accepts them. When \(\text{Ga(OH)}_3\) reacts with \(\text{HCl}\), an acid-base reaction occurs, creating water and gallium chloride.

• Formula: \[ \text{Ga(OH)}_3 + 3\text{HCl} \rightarrow \text{GaCl}_3 + 3\text{H}_2\text{O} \]
• Result: Formation of \(\text{GaCl}_3\) and water.

Similarly, when \(\text{Ga(OH)}_3\) reacts with \(\text{NaOH}\), a special type of base reaction occurs forming a complex ion.

• Formula: \[ \text{Ga(OH)}_3 + \text{NaOH} \rightarrow \text{Na[Ga(OH)}_4] \]
• Result: Formation of the complex ion \(\text{Na[Ga(OH)}_4]\).

These reactions highlight the versatility of amphoteric substances.

Balancing Chemical Equations

Balancing chemical equations is essential to represent the conservation of mass in a reaction. A balanced equation ensures that the number of atoms for each element is the same on both sides of the equation. Let's look at how the equation for \(\text{Ga(OH)}_3\) with \(\text{HCl}\) is balanced:

• Reactants: 1 mole of \(\text{Ga(OH)}_3\) and 3 moles of \(\text{HCl}\).
• Products: 1 mole of \(\text{GaCl}_3\) and 3 moles of water.

The key is ensuring the numbers of Ga, O, H, and Cl atoms are equal on both sides. Similarly, the reaction with \(\text{NaOH}\) is balanced by counting the ions and molecules involved. A balanced equation is crucial for the accurate calculation of reactants and products involved in any chemical reaction.

Molar Mass Calculation

Calculating molar mass allows us to relate mass with moles, a fundamental unit in chemistry. The molar mass of gallium hydroxide (\(\text{Ga(OH)}_3\)) is calculated by adding the atomic masses of each element:

• Gallium (Ga): 69.72 g/mol
• Oxygen (O): 16.00 g/mol
• Hydrogen (H): 1.01 g/mol

For \(\text{Ga(OH)}_3\): \[69.72 + 3(16.00 + 1.01) = 120.74 \, \text{g/mol}\]Using this molar mass, you can convert mass to moles. For instance, 1.25 grams of \(\text{Ga(OH)}_3\) is about 0.0104 moles:\[\frac{1.25 \, \text{g}}{120.74 \, \text{g/mol}} \approx 0.0104 \, \text{mol}\]This calculation is vital for determining reactant amounts in stoichiometry.