In some foam-type fire extinguishers, the reactants are `Al_2 (SO_4)_3`
(aq) and `NaHCO_3` (aq). When the extinguisher is activated, these reactants are allowed to mix producing `Al(OH)_(3(s))` and ` CO_(2(g))`.
The ` Al (OH)_3` - `CO_2` form extinguishes the fire . `CO_2` is formed as
a result of :

Options

A. reaction between ` Al^(3+)` and ` HCO_3^Θ`
B. reaction between hydrolysis product of `Al^(3+)` and `HCO_3^Θ`
C. reaction between hydrolysis product of `NaHCO_3` and `Al_2(SO_4)_3`
D. direct reaction between ` Al_2 (SO_4)_3` and ` NaHCO_3`

Answer

To solve the question regarding the formation of CO₂ in foam-type fire extinguishers, we will follow these steps:

### Step 1: Identify the Reactants
The reactants given in the question are:
- Aluminum sulfate, \( \text{Al}_2(\text{SO}_4)_3 \) (aqueous)
- Sodium bicarbonate, \( \text{NaHCO}_3 \) (aqueous)

### Step 2: Write the Reaction
When these reactants mix, they undergo a series of reactions. The first reaction involves the hydrolysis of aluminum sulfate in water, which can be represented as:
\[ \text{Al}_2(\text{SO}_4)_3 + 6 \text{H}_2\text{O} \rightarrow 2 \text{Al(OH)}_3(s) + 3 \text{H}_2\text{SO}_4 \]

### Step 3: Identify the Hydrolysis Product
The hydrolysis product is aluminum hydroxide, \( \text{Al(OH)}_3 \), and sulfuric acid, \( \text{H}_2\text{SO}_4 \).

### Step 4: Reaction of Sulfuric Acid with Sodium Bicarbonate
Next, the sulfuric acid reacts with sodium bicarbonate:
\[ \text{H}_2\text{SO}_4 + 2 \text{NaHCO}_3 \rightarrow \text{Na}_2\text{SO}_4 + 2 \text{H}_2\text{O} + 2 \text{CO}_2(g) \]

### Step 5: Formation of Carbon Dioxide
In this reaction, carbon dioxide (\( \text{CO}_2 \)) is produced as a result of the reaction between sulfuric acid and sodium bicarbonate. The bicarbonate ion decomposes to release carbon dioxide gas.

### Conclusion
Thus, the formation of \( \text{CO}_2 \) is a result of the reaction between the hydrolysis product of \( \text{Al}^{3+} \) (from aluminum sulfate) and \( \text{HCO}_3^- \) (from sodium bicarbonate).

### Final Answer
The correct answer is that \( \text{CO}_2 \) is formed as a result of the reaction between the hydrolysis product of \( \text{Al}^{3+} \) and \( \text{HCO}_3^- \).

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