When aqueous solutions of sodium carbonate [tex]\(\text{Na}_2\text{CO}_3\)[/tex] and calcium chloride [tex]\(\text{CaCl}_2\)[/tex] are mixed, a chemical reaction occurs. Let's analyze this reaction step by step.
The reaction can be written as:
[tex]\[
\text{Na}_2\text{CO}_3(aq) + \text{CaCl}_2(aq) \rightarrow \text{CaCO}_3(s) + 2 \text{NaCl}(aq)
\][/tex]
Here’s the detailed breakdown of what happens:
1. Reactants: We start with sodium carbonate ([tex]\(\text{Na}_2\text{CO}_3\)[/tex]) and calcium chloride ([tex]\(\text{CaCl}_2\)[/tex]), both in aqueous form. This means that they are dissolved in water and exist as ions.
2. Dissociation in Water: In aqueous solution, sodium carbonate and calcium chloride dissociate into their respective ions:
[tex]\[
\text{Na}_2\text{CO}_3(aq) \rightarrow 2 \text{Na}^+(aq) + \text{CO}_3^{2-}(aq)
\][/tex]
[tex]\[
\text{CaCl}_2(aq) \rightarrow \text{Ca}^{2+}(aq) + 2 \text{Cl}^-(aq)
\][/tex]
3. Reaction of Ions: When these solutions are mixed, the [tex]\(\text{Ca}^{2+}\)[/tex] ions from [tex]\(\text{CaCl}_2\)[/tex] react with the [tex]\(\text{CO}_3^{2-}\)[/tex] ions from [tex]\(\text{Na}_2\text{CO}_3\)[/tex] to form calcium carbonate ([tex]\(\text{CaCO}_3\)[/tex]).
4. Formation of Precipitate: Calcium carbonate ([tex]\(\text{CaCO}_3\)[/tex]) is insoluble in water and therefore precipitates out of the solution. This is why [tex]\(\text{CaCO}_3\)[/tex] appears as a solid (s):
[tex]\[
\text{Ca}^{2+}(aq) + \text{CO}_3^{2-}(aq) \rightarrow \text{CaCO}_3(s)
\][/tex]
5. Remaining Ions in Solution: The sodium ions ([tex]\(\text{Na}^+\)[/tex]) and chloride ions ([tex]\(\text{Cl}^-\)[/tex]) remain in the aqueous solution and do not form a precipitate:
[tex]\[
\text{2 Na}^+(aq) + 2 \text{Cl}^-(aq) \rightarrow 2 \text{NaCl}(aq)
\][/tex]
So, the overall balanced chemical equation is:
[tex]\[
\text{Na}_2\text{CO}_3(aq) + \text{CaCl}_2(aq) \rightarrow \text{CaCO}_3(s) + 2 \text{NaCl}(aq)
\][/tex]
Thus, the precipitate that forms when aqueous solutions of sodium carbonate ([tex]\(\text{Na}_2\text{CO}_3\)[/tex]) and calcium chloride ([tex]\(\text{CaCl}_2\)[/tex]) are mixed is calcium carbonate ([tex]\(\text{CaCO}_3\)[/tex]).
Therefore, the correct answer is:
[tex]\[
\boxed{\text{CaCO}_3(s)}
\][/tex]
