Calculate the enthalpy change when infinitely dilute solution of `CaCl_(2)` and `Na_(2)CO_(3)` are mixed. `Delta_(f)H^(Theta)` for `Ca^(2+)(aq), CO_(3)^(2-)(aq)`, and `CaCO_(3)(s)` are `-129.80, -161.65`, and `-288.50 kcal mol^(-1)` respectively.

Explanation

To calculate the enthalpy change when infinitely dilute solutions of \( \text{CaCl}_2 \) and \( \text{Na}_2\text{CO}_3 \) are mixed, we can follow these steps:

### Step 1: Write the balanced chemical equation for the reaction.
When \( \text{CaCl}_2 \) and \( \text{Na}_2\text{CO}_3 \) are mixed, the following reaction occurs:
\[ \text{Ca}^{2+}(aq) + \text{CO}_3^{2-}(aq) \rightarrow \text{CaCO}_3(s) \]
The sodium ions \( \text{Na}^+ \) and chloride ions \( \text{Cl}^- \) remain in solution and do not participate in the formation of the solid.
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