Problem 29 - General Chemistry: Principles and Modern Applications

Question

In some foam-type fire extinguishers, the reactants are \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}(\mathrm{aq})\) and \(\mathrm{NaHCO}_{3}(\mathrm{aq}) .\) When the extinguisher is activated, these reactants mix, producing \(\mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s})\) and \(\mathrm{CO}_{2}(\mathrm{g}) .\) The \(\mathrm{Al}(\mathrm{OH})_{3}-\mathrm{CO}_{2}\) foam extinguishes the fire. Write a net ionic equation to represent this reaction.

Step-by-Step Solution

Answer

The net ionic equation for this reaction is \(4Al^{3+}(aq) + 12HCO_3^-(aq) → 4Al(OH)_3(s) + 3CO_2(g)\)

Step 1: Write the balanced chemical equation

First, write the complete balanced equation for the given reaction. This can be done by equating the number of each type of atom on both sides of the reaction. \[2Al_2(SO_4)_3(aq) + 12NaHCO_3(aq) → 4Al(OH)_3(s) + 3CO_2(g) + 6Na_2SO_4(aq)\]

Step 2: Write the complete ionic equation

Then, write the complete ionic equation by separating the aqueous compounds into their ions. This provides the total list of all ions present before and after the reaction. \(4Al^{3+}(aq) + 6SO_4^{2-}(aq) + 12Na^+(aq) + 12HCO_3^-(aq) → 4Al(OH)_3(s) + 3CO_2(g) + 12Na^+(aq) + 6SO_4^{2-}(aq)\)

Step 3: Identify and eliminate the spectator ions

Now, identify the spectator ions – ions that have not reacted. In the given reaction, sodium ion (Na+) and the sulfate ion (SO4^{2-}) do not get involved in the reaction, and their states do not change from reactants to products. Therefore, these are the spectator ions and can be removed from both sides.

Step 4: Write the net ionic equation

The net ionic equation includes only those components taking part in the reaction. After eliminating the spectator ions, the net ionic equation is: \(4Al^{3+}(aq) + 12HCO_3^-(aq) → 4Al(OH)_3(s) + 3CO_2(g)\)

Key Concepts

Balanced Chemical Equation

A balanced chemical equation ensures that the law of conservation of mass is respected, meaning the same number of atoms of each element must be present on both sides of the equation. It's like a recipe for a chemical reaction with precise quantities to produce the desired products.

For the foam-type fire extinguisher reaction discussed, the balanced chemical equation represents the substances involved in the reaction and their stoichiometric coefficients, which reflects the proportional amounts that react and form products:

• Reactants: \( \mathrm{Al}_{2}(\mathrm{SO}_{4})_{3}(\mathrm{aq}) \) and \( \mathrm{NaHCO}_{3}(\mathrm{aq}) \)
• Products: \( \mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s}) \) and \( \mathrm{CO}_{2}(\mathrm{g}) \)

Writing a balanced equation involves finding the correct coefficients that balance the atoms on both the reactant and product side, which in this case is:\[2\mathrm{Al}_2(\mathrm{SO}_4)_3(\mathrm{aq}) + 12\mathrm{NaHCO}_3(\mathrm{aq}) \rightarrow 4\mathrm{Al}(\mathrm{OH})_3(\mathrm{s}) + 3\mathrm{CO}_2(\mathrm{g}) + 6\mathrm{Na}_2\mathrm{SO}_4(\mathrm{aq})\].
This equation is pivotal as the foundation from which we can derive the complete ionic and net ionic equations.

Complete Ionic Equation

The complete ionic equation is a step beyond the balanced chemical equation where soluble ionic compounds are expressed as free-floating ions. This type of equation provides a more detailed account of the form each reactant and product takes during the reaction.

Following the balanced equation for our fire extinguisher reaction, the complete ionic equation breaks down the soluble compounds into constituent ions:

• \( \mathrm{Al}^{3+}(\mathrm{aq}) \) - aluminum ion
• \( \mathrm{SO}_4^{2-}(\mathrm{aq}) \) - sulfate ion
• \( \mathrm{Na}^{+}(\mathrm{aq}) \) - sodium ion
• \( \mathrm{HCO}_3^{-}(\mathrm{aq}) \) - bicarbonate ion

By following this representation, the reactants and products are fully illustrated as:\[4\mathrm{Al}^{3+}(\mathrm{aq}) + 6\mathrm{SO}_4^{2-}(\mathrm{aq}) + 12\mathrm{Na}^{+}(\mathrm{aq}) + 12\mathrm{HCO}_3^{-}(\mathrm{aq}) \rightarrow 4\mathrm{Al}(\mathrm{OH})_3(\mathrm{s}) + 3\mathrm{CO}_2(\mathrm{g}) + 12\mathrm{Na}^{+}(\mathrm{aq}) + 6\mathrm{SO}_4^{2-}(\mathrm{aq})\]
Thus, it visualizes all reactants and products, laying the groundwork to identifying spectator ions and moving towards the net ionic equation.

Spectator Ions

Spectator ions are the background actors of a chemical reaction—they're present but do not partake in the actual chemical change. Identifying these ions is essential when progressing from the complete ionic equation to the net ionic equation.

In the reaction within our fire extinguisher, the spectator ions are \( \mathrm{Na}^{+} \) and \( \mathrm{SO}_4^{2-} \), as these ions exist in the same form in both the reactants and products:

• \( \mathrm{Na}^{+}(\mathrm{aq}) \) - appears 12 times on both sides of the complete ionic equation
• \( \mathrm{SO}_4^{2-}(\mathrm{aq}) \) - appears 6 times on both sides of the complete ionic equation

These ions 'watch' the reaction without changing, which means they can be omitted when simplifying to the net ionic equation. Their elimination greatly reduces the equation's complexity and focuses on the actual chemical reaction that is taking place:
\[\text{Net Ionic Equation: } 4\mathrm{Al}^{3+}(\mathrm{aq}) + 12\mathrm{HCO}_3^{-}(\mathrm{aq}) \rightarrow 4\mathrm{Al}(\mathrm{OH})_3(\mathrm{s}) + 3\mathrm{CO}_2(\mathrm{g})\]
Understanding spectator ions is critical for students in distinguishing between the different components of a reaction and in identifying the core changes occurring during chemical processes.