Question

A 1.00 -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 $\left({\mathrm{CaC}}_2{\mathrm{O}}_4\right)$ at ${25}^{\circ }\mathrm{C}$ is approximately $2.27\times {10}^{-9}$.

Step-by-step solution

Convert mass to moles

First, we need to determine the number of moles of calcium oxalate in the solution. This can be done by dividing the mass by the molar mass of the compound. The molar mass of calcium oxalate is: CaC2O4: 40.08 (Ca) + 24.02 (2 x C) + 64.00 (4 x O) = 128.1 g/mol Now, divide the mass (0.0061 g) by the molar mass to find the moles of calcium oxalate: moles = mass / molar mass = 0.0061 g / 128.1 g/mol ≈ 4.76 x 10^(-5) mol

Calculate molar concentrations

Now that we have the moles of calcium oxalate, we can determine the molar concentration of each ion in the solution. Since the solution has a volume of 1.00 L, the molar concentrations of Ca^(2+) and C2O4^(2-) ions will be the same as the number of moles of calcium oxalate: [Ca^(2+)] = [C2O4^(2-)] = 4.76 x 10^(-5) mol/L

Write the Ksp expression and calculate Ksp

The solubility-product constant, Ksp, is the product of the equilibrium concentrations of ions in a saturated solution of a slightly soluble ionic compound. The balanced chemical equation for the dissociation of calcium oxalate in water and the corresponding Ksp expression are: CaC2O4(s) ↔ Ca^(2+)(aq) + C2O4^(2-)(aq) Ksp = [Ca^(2+)] [C2O4^(2-)] Now, substitute the calculated concentrations of the ions in the Ksp expression: Ksp = (4.76 x 10^(-5))(4.76 x 10^(-5)) ≈ 2.27 x 10^(-9) So, the solubility-product constant for calcium oxalate at 25°C is approximately 2.27 x 10^(-9).

Key concepts

Solubility in Chemistry

Solubility in chemistry describes how well a substance (solute) can dissolve in a solvent to form a homogeneous mixture, known as a solution. The substance's solubility is often expressed in terms of concentration, which measures the amount of solute dissolved in a given volume of solvent. Factors like temperature, pressure, and the nature of the solute and solvent can greatly influence solubility. For sparingly soluble ionic compounds, such as calcium oxalate in the exercise, solubility can be quantitatively expressed using the solubility-product constant (Ksp).
Ksp is a special type of equilibrium constant that applies to the dissolution of slightly soluble salts. It represents the maximum product of the concentrations of the ions that can exist in the solution at equilibrium. When the product of the ionic concentrations exceeds the Ksp value, precipitation occurs, and the solution becomes saturated.
Understanding solubility is crucial because it influences various applications, including pharmaceuticals, where the solubility of drugs affects their effectiveness, and environmental chemistry, where solubility dictates the mobility of contaminants in water.

Molar Mass Calculation

Molar mass calculation is an essential part of chemistry as it allows chemists to relate the mass of a substance to the number of particles present. It is defined as the mass of one mole of a substance, usually expressed in grams per mole (g/mol). One mole of any substance contains Avogadro's number of particles, which is approximately 6.022 x 10^23 particles.
In the given exercise, the molar mass of calcium oxalate (CaC2O4) is calculated by summing the molar masses of each component atom: calcium (Ca), carbon (C), and oxygen (O). The calculation shows how every mass of a substance can be converted into moles, which is a crucial step in determining the substance's role in a chemical reaction or in a solution, as shown in the subsequent Ksp calculation.
Tip for Improvement: For greater clarity and understanding, specifically highlight the concept of avogadro's number and its significance in the context of molar mass and converting between grams and moles, as it is a cornerstone in stoichiometric calculations.

Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions in a chemical process are equal, leading to a constant concentration of reactants and products. It is dynamic, which means the reactions are still occurring, but there's no net change in the concentrations of each species involved.
In the context of solubility, when a slightly soluble ionic compound is in equilibrium with its saturated solution, the equilibrium represents the solubility of the compound. The solubility-product constant (Ksp) for the compound at a particular temperature is a direct measure of its solubility under those conditions.
Tip for Improvement: When exploring chemical equilibrium, it's helpful to discuss the response of an equilibrium system to changes in conditions, known as Le Chatelier's principle. This principle helps students understand how altering variables such as concentration, temperature, and pressure can affect the position of equilibrium and therefore the solubility of a substance.