Questions: Which of the following saturated solutions has the greatest [CO3]2- ? MgCO3 BaCO3 CaCO3 SiCO3

Transcript text: Which of the following saturated solutions has the greatest $\left[\mathrm{CO}_{3}{ }^{2}\right]$ ? $\mathrm{MgCO}_{3}$ $\mathrm{BaCO}_{3}$ $\mathrm{CaCO}_{3}$ $\mathrm{SiCO}_{3}$

Solution

Solution Steps

Step 1: Identify the Solubility Product Constants (Ksp)

To determine which saturated solution has the greatest concentration of $\left[\mathrm{CO}_{3}^{2-}\right]$, we need to compare the solubility product constants ($K_{sp}$) of the given compounds. The solubility product constant is a measure of the solubility of a compound. The higher the $K_{sp}$, the more soluble the compound is, and thus, the higher the concentration of the ions in solution.

Step 2: Write the Dissociation Equations

For each carbonate compound, the dissociation in water can be written as follows:

\[ \mathrm{MgCO}_{3} \leftrightarrow \mathrm{Mg}^{2+} + \mathrm{CO}_{3}^{2-} \]

\[ \mathrm{BaCO}_{3} \leftrightarrow \mathrm{Ba}^{2+} + \mathrm{CO}_{3}^{2-} \]

\[ \mathrm{CaCO}_{3} \leftrightarrow \mathrm{Ca}^{2+} + \mathrm{CO}_{3}^{2-} \]

\[ \mathrm{SiCO}_{3} \leftrightarrow \mathrm{Si}^{2+} + \mathrm{CO}_{3}^{2-} \]

Step 3: Compare the $K_{sp}$ Values

The $K_{sp}$ values for these compounds are typically:

$\mathrm{MgCO}_{3}$: $K_{sp} \approx 6.82 \times 10^{-6}$
$\mathrm{BaCO}_{3}$: $K_{sp} \approx 5.01 \times 10^{-9}$
$\mathrm{CaCO}_{3}$: $K_{sp} \approx 4.96 \times 10^{-9}$
$\mathrm{SiCO}_{3}$: $K_{sp}$ is not commonly listed, but it is generally much lower than the others.

Step 4: Determine the Greatest $\left[\mathrm{CO}_{3}^{2-}\right]$

The concentration of $\left[\mathrm{CO}_{3}^{2-}\right]$ in a saturated solution is directly related to the $K_{sp}$ value. The higher the $K_{sp}$, the higher the concentration of $\left[\mathrm{CO}_{3}^{2-}\right]$.

Given the $K_{sp}$ values, $\mathrm{MgCO}_{3}$ has the highest $K_{sp}$ among the listed compounds.