Questions: The solubility of ZnCO3 in water at 25°C is measured to be 0.0013 g/L. Use this information to calculate Ksp for ZnCO3. Round your answer to 2 significant digits.

The solubility of ZnCO3 in water at 25°C is measured to be 0.0013 g/L. Use this information to calculate Ksp for ZnCO3. Round your answer to 2 significant digits.
Transcript text: The solubility of $\mathrm{ZnCO}_{3}$ in water at $25^{\circ} \mathrm{C}$ is measured to be $0.0013 \frac{\mathrm{~g}}{\mathrm{~L}}$. Use this information to calculate $K_{s p}$ for $\mathrm{ZnCO}_{3}$. Round your answer to 2 significant digits.
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Solution

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Solution Steps

Step 1: Convert the solubility to molarity

The solubility of ZnCO3 in water is given as 0.0013 g/L. Using its molar mass of 125.39 g/mol, we convert this to molarity (M) by dividing the solubility by the molar mass. Thus, the molarity of ZnCO3 is $1.04 \times 10^{-5}$ M.

Step 2: Determine the dissociation equation

The balanced chemical equation for the dissolution of ZnCO3 in water is: ZnCO3 -> 1 Zn^2 + 1 CO3^2.

Step 3: Calculate the concentration of each ion in solution

The concentration of Zn in solution, based on the stoichiometry of the dissolution reaction, is $1.04 \times 10^{-5}$ M. The concentration of CO3 in solution, based on the stoichiometry of the dissolution reaction, is $1.04 \times 10^{-5}$ M.

Step 4: Calculate Ksp using the ion concentrations

Using the formula $K_{sp} = [A]^m[B]^n...$, where $[A]$, $[B]$, etc., are the molar concentrations of the ions and $m$, $n$, etc., are their respective stoichiometric coefficients in the dissolution equation, we find that $K_{sp} = 1.07 \times 10^{-10}$.

Final Answer:

The solubility product constant ($K_{sp}$) of ZnCO3 at the given temperature is $1.07 \times 10^{-10}$.

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