Question

Use the following data to calculate the \(K_{\mathrm{sp}}\) value for each solid. a. The solubility of \(\mathrm{CaC}_{2} \mathrm{O}_{4}\) is \(4.8 \times 10^{-5} \mathrm{mol} / \mathrm{L}\) b. The solubility of \(\mathrm{BiI}_{3}\) is \(1.32 \times 10^{-5} \mathrm{mol} / \mathrm{L}\)

Short answer

The Ksp value for CaC2O4 is \(2.304 \times 10^{-9}\) and the Ksp value for BiI3 is \(8.269 \times 10^{-22}\).

Step-by-step solution

Write the solubility equilibrium equation

For the solubility equilibrium of CaC2O4, the equation is: \[\mathrm{CaC_2O_4 (s)} \rightleftharpoons \mathrm{Ca^{2+} (aq)} + \mathrm{C_2O_4^{2-} (aq)}\]

Write the expression for Ksp

The Ksp expression for the solubility equilibrium is: \[K_{\mathrm{sp}} = [\mathrm{Ca^{2+}}] [\mathrm{C_2O_4^{2-}}]\]

Calculate Ksp using the solubility data

The solubility of CaC2O4 is given as \(4.8 \times 10^{-5}\,\text{mol}/\text{L}\). This means both the concentrations of Ca2+ and C2O42- in the saturated solution are equal to this value. \[K_{\mathrm{sp}} = (4.8 \times 10^{-5})(4.8 \times 10^{-5}) = 2.304 \times 10^{-9}\] So, the Ksp value for CaC2O4 is \(2.304 \times 10^{-9}\). #b. Calculate Ksp for BiI3#

Write the solubility equilibrium equation

For the solubility equilibrium of BiI3, the equation is: \[\mathrm{BiI_3 (s)} \rightleftharpoons \mathrm{Bi^{3+} (aq)} + 3\,\mathrm{I^- (aq)}\]

Write the expression for Ksp

The Ksp expression for the solubility equilibrium is: \[K_{\mathrm{sp}} = [\mathrm{Bi^{3+}}] [\mathrm{I^-}]^3\]

Calculate Ksp using the solubility data

The solubility of BiI3 is given as \(1.32 \times 10^{-5} \, \text{mol}/\text{L}\). The concentration of Bi3+ ions is equal to this value, while the concentration of I- ions is three times this value as there are three iodide ions for every bismuth ion. So, the concentration of I- ions is \(3 \times 1.32 \times 10^{-5} = 3.96 \times 10^{-5} \, \text{mol}/\text{L}\). Now we can plug the concentrations into the Ksp expression: \[K_{\mathrm{sp}} = (1.32 \times 10^{-5})(3.96 \times 10^{-5})^3 = 8.269 \times 10^{-22}\] So, the Ksp value for BiI3 is \(8.269 \times 10^{-22}\).

Key concepts

Solubility Equilibrium

Imagine a handful of salt tossing into a glass of water and stirring; the salt disappears. This is a process called dissolution, where the solute (salt) disperses in the solvent (water).

Sometimes, though, not all the salt can dissolve. When this happens, the solution reaches a point where it can't take any more solute; it becomes saturated. Solubility equilibrium is the perfect balance between undissolved solids and dissolved ions in such a saturated solution. It represents a dynamic, but stable system: some solid dissolves while an equal amount of ions join back to form the solid, maintaining a constant concentration of ions in the solution.

Equilibrium Expression

Every chemical equilibrium can be represented by an equilibrium expression. For solubility equilibriums, we use the Solubility Product Constant (Ksp) to quantify the saturation point of a solute in the solvent.

This expression is derived from the balanced chemical equation of the dissolution process. It involves the concentrations of the dissolved ions each raised to the power of their stoichiometric coefficients. The beauty of the Ksp expression lies in its ability to help us predict whether a precipitate will form when two solutions are mixed. A higher Ksp value indicates higher solubility of the ionic compound in the solvent.

Molar Solubility

Molar solubility is the number of moles of a substance that can dissolve in one liter of solvent to form a saturated solution at a given temperature.

It is closely tied to Ksp; knowing one helps calculate the other. Simply put, it's how we measure the solubility of a compound in moles per liter. This is particularly helpful when we deal with reactions in a lab or industrial processes because it provides a quantitative measure of the solute that can be dissolved before reaching saturation.

Chemical Saturation

Think about adding sugar to your tea until no more can dissolve and some sugar grains start to settle at the bottom—that’s chemical saturation.

In our context, a solution is considered saturated when it contains the maximum concentration of ions that can be dissolved in it without forming a precipitate under given conditions. Saturation is a key concept when dealing with solubility: it sets the upper limit of solute concentration in a solution. It’s essential for understanding phenomena like crystallization or the formation of scale in boilers.

Precipitation Chemistry

Precipitation is the opposite of dissolution. When a solution becomes supersaturated, or conditions change such as temperature or pH, solutes can 'drop out' of the solution as a precipitate.

Precipitation chemistry is involved in natural processes like the formation of stalagmites in caves, and in critical industrial processes like waste treatment. Understanding how and when a compound will precipitate is crucial to many fields including medicine, environmental science, and engineering. Ksp helps predict whether a precipitate will form under specific conditions.