Question

A 1.00- \(\mathrm{L}\) solution saturated at \(25^{\circ} \mathrm{C}\) with calcium oxalate \(\left(\mathrm{CaC}_{2} \mathrm{O}_{4}\right)\) contains \(0.0061 \mathrm{~g}\) of \(\mathrm{CaC}_{2} \mathrm{O}_{4}\). Calculate the solubility-product constant for this salt at \(25^{\circ} \mathrm{C}\).

Short answer

The solubility-product constant (Ksp) for calcium oxalate at 25°C is 2.27 × 10⁻⁹.

Step-by-step solution

Write the balanced chemical equation for the dissolution of calcium oxalate

The dissociation of calcium oxalate in water can be represented as: \[ \mathrm{CaC_2O_4 (s) \rightleftharpoons Ca^{2+} (aq) + C_2O_4^{2-} (aq)} \]

Calculate the concentration of dissolved CaC₂O₄ in the solution

Given that 0.0061 g of CaC₂O₄ are dissolved in 1.00 L of solution, we can find the concentration (in mol/L) as follows: 1. Find the molar mass of CaC₂O₄: Molar mass of CaC₂O₄ = 1 × (40.08 g/mol Ca) + 2 × (12.01 g/mol C) + 4 × (16.00 g/mol O) = 128.1 g/mol 2. Convert grams to moles: Moles of CaC₂O₄ = (0.0061 g) / (128.1 g/mol) = 4.76 × 10⁻⁵ mol 3. Calculate the concentration: \[ [\mathrm{CaC_2O_4}] = \frac{4.76 \times 10^{-5} \mathrm{mol}}{1.00\mathrm{L}} = 4.76 \times 10^{-5} \mathrm{M} \]

Calculate the concentrations of Ca²⁺ and C₂O₄²⁻ ions in the solution

Since one mole of CaC₂O₄ yields one mole of Ca²⁺ and one mole of C₂O₄²⁻ ions: \[ [\mathrm{Ca^{2+}}]=[\mathrm{C_2O_4^{2-}}]=4.76 \times 10^{-5} \mathrm{M} \]

Determine the solubility product constant Ksp

Now that we have the concentrations of Ca²⁺ and C₂O₄²⁻ ions, we can calculate the Ksp as the product of their concentrations: \[ K_{sp}=[\mathrm{Ca^{2+}}][\mathrm{C_2O_4^{2-}}] \] Plug in the values: \[ K_{sp}= (4.76 \times 10^{-5})^2 = 2.27 \times 10^{-9} \] The solubility-product constant (Ksp) for calcium oxalate at 25°C is 2.27 × 10⁻⁹.

Key concepts

Chemical Equilibrium

Chemical equilibrium is a state in a chemical reaction where the rates of the forward and reverse reactions are equal, leading to no overall change in the concentrations of the reactants and products over time. It's important to understand that equilibrium does not mean the reactants and products are equal in concentration, but rather that their concentrations have stabilized at a constant ratio.

In the context of solubility, when a substance dissolves in a solvent, it dissociates into ions to form a solution. If the dissolved substance is slightly soluble, such as calcium oxalate, the dissolved particles and the undissolved solid exist in a dynamic equilibrium - constantly dissolving and precipitating at equivalent rates. The solubility-product constant (\(K_{sp}\)) is a numerical value that describes this equilibrium, indicative of how much of the substance can dissolve in a given amount of solvent at a specific temperature.

Dissolution of Calcium Oxalate

The dissolution of calcium oxalate can be considered when a sparingly soluble compound such as calcium oxalate (\r\(CaC_2O_4\)) enters into solution. It doesn't fully dissolve, instead reaching a point where the solid and the dissolved ions are in equilibrium. This process can be represented by the reversible chemical equation:

\r\[ \rCaC_2O_4 (s) \rightleftharpoons Ca^{2+} (aq) + C_2O_4^{2-} (aq) \r\]
\rUpon dissolving, calcium oxalate splits into calcium ions (\r\(Ca^{2+}\)) and oxalate ions (\r\(C_2O_4^{2-}\)). The solubility-product constant is crucial for predicting the extent of dissolution and assessing whether precipitation will occur under certain conditions.

Molar Mass Calculation

Molar mass is defined as the mass of one mole of a substance and is expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all the atoms in a molecule. For calcium oxalate (\r\(CaC_2O_4\)), the molar mass is found as follows:

\r

\r
• 1 calcium (Ca) atom: 40.08 g/mol
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• 2 carbon (C) atoms: 2 x 12.01 g/mol
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• 4 oxygen (O) atoms: 4 x 16.00 g/mol
\r

\r
\rAdding these values together, the molar mass of calcium oxalate is calculated to be 128.1 g/mol. Knowing the molar mass of calcium oxalate allows us to convert between mass (grams) and amount (moles), an essential step in determining the solubility-product constant.

Concentration Calculation

Concentration refers to the amount of a substance within a defined space or volume, typically expressed in moles per liter (\r\(M\), molarity). The process of calculating concentration involves two steps:

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• Convert the mass of the solute (the dissolved substance) from grams to moles using its molar mass.
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• Divide the number of moles by the volume of the solution to get molarity.
\r

\r
\rIn the context of the exercise, once the mass of the dissolved calcium oxalate is given, you first convert that mass to moles using the calculated molar mass, then divide by the volume of the solution to find the concentration. This concentration is crucial to calculate the \r\(K_{sp}\), as it is combined with the stoichiometry of the dissolution reaction to give the concentrations of individual ions in the solution.