Solubility Product Constant: Ksp: Videos & Practice Problems

The solubility product constant ($K_{\mathrm{sp}}$) is a specialized equilibrium constant that measures the solubility of solid ionic compounds in a solvent. $K_{\mathrm{sp}}$ values indicate the degree of solubility: a higher $K_{\mathrm{sp}}$ means greater solubility, while a lower $K_{\mathrm{sp}}$ indicates less. Comparisons of $K_{\mathrm{sp}}$ are only valid between compounds that dissociate into the same number of ions. Solubility is an equilibrium process, often requiring an ICE chart for calculations. The $K_{\mathrm{sp}}$ expression is unique because it only includes the concentrations of the products (ions in solution), as solids and liquids are not included in equilibrium expressions. Thus, $K_{\mathrm{sp}}$ is calculated by taking the product of the ion concentrations, each raised to the power of its coefficient in the balanced chemical equation. This understanding is crucial for predicting solubility and performing related calculations in chemistry.

Solubility Product Constant

The solubility product constant, denoted as K_sp, is a specific type of equilibrium constant that quantifies the solubility of solid ionic compounds in a solvent at equilibrium. Solubility, in this context, refers to the maximum amount of a solid that can dissolve in a solvent, typically expressed in terms of molar solubility (M).

The magnitude of K_sp is directly related to the solubility of the ionic compound: a higher K_sp value indicates greater solubility, while a lower K_sp value suggests lower solubility. However, this comparison is only valid among compounds that dissociate into the same number of ions. For instance, sodium chloride (NaCl) dissociates into two ions (Na⁺ and Cl^-), while lithium bromide (LiBr) also dissociates into two ions (Li⁺ and Br^-). Therefore, their K_sp values can be directly compared to determine which is more soluble.

In contrast, when comparing compounds that dissociate into different numbers of ions, such as barium chloride (BaCl₂), which breaks into three ions (Ba²⁺ and 2 Cl^-), a simple comparison of K_sp values is insufficient. In such cases, further calculations are necessary to accurately assess and compare their solubility.

Ksp and Solubility Example

To determine which ionic compound produces the highest concentration of hydroxide ions (\( \text{OH}^- \)) in solution, we need to consider the solubility of each compound, which is often represented by its solubility product constant (\( K_{sp} \)). The \( K_{sp} \) value indicates how well a compound dissolves in water; a higher \( K_{sp} \) means greater solubility and, consequently, a higher concentration of ions in solution.When ionic compounds dissolve, they dissociate into their constituent ions. For the compounds in question, each dissociates into a metal ion and two hydroxide ions. Therefore, the concentration of hydroxide ions produced is directly related to the solubility of the compound.By comparing the \( K_{sp} \) values of the compounds, we can identify which one is the most soluble. In this case, magnesium hydroxide has the highest \( K_{sp} \) value among the compounds considered. This indicates that magnesium hydroxide is the most soluble, leading to the production of the greatest number of hydroxide ions in solution.In summary, magnesium hydroxide, due to its higher \( K_{sp} \), will produce the highest concentration of hydroxide ions, resulting in a more alkaline solution. Thus, when evaluating ionic compounds for their hydroxide ion concentration, always consider their solubility as indicated by \( K_{sp} \).

Ksp Calculations

In the context of solubility product constant (K_sp) calculations, it is essential to understand that solubility is an equilibrium process. This means that when approaching K_sp problems, utilizing an ICE (Initial, Change, Equilibrium) chart is crucial for organizing the concentrations of reactants and products at equilibrium.

K_sp specifically pertains to the solubility of ionic solids, which dissociate into their constituent ions in solution. For example, consider a generic ionic solid that dissociates into ions B^m+ and C^n-. The dissociation can be represented as:

A(s) ⇌ mB^m+(aq) + nC^n-(aq)

In this equation, A represents the solid ionic compound, while B and C are the ions produced. The coefficients m and n indicate the number of moles of each ion produced during the dissociation.

K_sp is defined as an equilibrium constant that reflects the concentrations of the ions in solution at equilibrium. The general form of the K_sp expression is:

K_sp = [B^m+]^m × [C^n-]ⁿ

It is important to note that in K_sp calculations, the solid reactant (A) is not included in the expression because the concentration of a pure solid does not change. Therefore, K_sp simplifies to the product of the concentrations of the ions, each raised to the power of their respective coefficients from the balanced equation.

In summary, when calculating K_sp, remember to focus on the concentrations of the ions produced from the dissociation of the solid, while ignoring the solid itself in the equilibrium expression.

Molar Solubility Example

Lead(II) fluoride, a white solid, is utilized in various fields such as pharmaceuticals, metallurgy, and technology. To determine its molar solubility at 25 degrees Celsius, we start with the known solubility product constant (K_sp) of 3.6 × 10^-8 and a concentration of 4.2 M.

When calculating molar solubility, we denote it as x. The process begins with setting up an ICE (Initial, Change, Equilibrium) chart, focusing on the dissociation of lead(II) fluoride into its ions:

PbF₂ (s) ⇌ Pb²⁺ (aq) + 2F^- (aq)

In the ICE chart, the initial concentration of the products is zero. As the solid dissolves, we denote the change in concentration of Pb²⁺ as x and for F^- as 2x due to the stoichiometry of the reaction. The equilibrium concentrations are then:

• [Pb²⁺] = x
• [F^-] = 2x

Next, we express the K_sp in terms of these equilibrium concentrations:

K_sp = [Pb²⁺][F^-]² = (x)(2x)² = 4x³

Substituting the known K_sp value gives:

3.6 × 10^-8 = 4x³

To isolate x, we first divide both sides by 4:

x³ = 9.0 × 10^-9

Taking the cube root of both sides yields:

x = 2.08 × 10^-3 M

This value represents the molar solubility of lead(II) fluoride. If the question were to ask for the concentration of fluoride ions, we would calculate it as 2x, resulting in:

[F^-] = 2(2.08 × 10^-3) = 4.16 × 10^-3 M

In summary, the molar solubility of lead(II) fluoride is 2.08 × 10^-3 M, while the concentration of fluoride ions in solution is 4.16 × 10^-3 M.

Solubility of Sn(OH)₂ was found to be 1.11 x 10^-9 M; calculate K_sp of this compound.

• A. 5.47 × 10⁻²⁷
• B. 4.44 × 10⁻⁹
• C. 1.23 × 10⁻¹⁸
• D. 1.37 × 10⁻²⁷

Answer: (A)

If a saturated solution of Ag₂CO₃ contains 2.56 × 10⁻⁴ M of Ag⁺ ions, determine its solubility product constant.

• A. 4.30 × 10⁻¹⁵
• B. 8.39 × 10⁻¹²
• C. 1.68 × 10⁻¹¹
• D. 6.55 × 10⁻⁸

Answer: (B)

What is the solubility of CN⁻ ions in a solution of 5.5 M Hg₂(CN)₂, with a K_sp of 5.0 × 10⁻⁴⁰?

• A. 4.5× 10⁻²⁰ M
• B. 5.0 × 10⁻¹⁴ M
• C. 1.1 × 10⁻²⁰ M
• D. 1.0 × 10⁻¹³ M

Answer: (D)

Here’s what students ask on this topic:

What is the solubility product constant?

The solubility product constant, often denoted as K_sp, is a numerical value that represents the equilibrium between a solid and its respective ions in a saturated solution. When a sparingly soluble ionic compound dissolves in water, it dissociates into its constituent ions up to a certain extent. The equilibrium established between the undissolved solid and the dissolved ions can be represented by a chemical equation.

For example, if we have a generic salt AB that dissociates into A⁺ and B^- ions, the equilibrium equation would be:

AB(s) → A⁺(aq) + B^-(aq)

The solubility product constant for this reaction would be expressed as:

K_sp = [A⁺][B^-]

Here, [A⁺] and [B^-] are the molar concentrations of the ions at equilibrium. The K_sp is unique for each compound at a given temperature and is used to predict whether a precipitate will form under certain conditions. A higher K_sp value indicates a more soluble compound. It's important to note that the solubility product does not give the actual solubility in moles per liter, but rather the extent to which a compound can produce ions in solution.

How can the solubility product constant be found?

The solubility product constant, or K_sp, is a measure of the solubility of a compound under specific conditions in a saturated solution. To find the K_sp of a sparingly soluble ionic compound, follow these steps:

1. Prepare a saturated solution of the compound by adding it to a solvent, usually water, until no more dissolves and some solid remains.
2. Allow the solution to reach equilibrium, where the rate of dissolving equals the rate of precipitation.
3. Filter or decant the solution to remove any undissolved solids.
4. Measure the concentration of the ions in the saturated solution using analytical techniques such as titration, spectrophotometry, or conductivity measurements.
5. Use the balanced chemical equation for the dissolution of the compound to determine the molar ratio of the ions.
6. Calculate the K_sp by multiplying the molar concentrations of the ions, each raised to the power of their stoichiometric coefficients in the balanced equation.

For example, if the compound AB dissolves to form A⁺ and B^- ions, and the concentrations are [A⁺] = a and [B^-] = b, then

K_sp = [A⁺]^m * [B^-]ⁿ

where m and n are the stoichiometric coefficients of A⁺ and B^- respectively in the dissolution equation.

Which of the following best defines the solubility product constant Ksp of a salt?

The solubility product constant, denoted as K_sp, is a numerical value that represents the equilibrium between a solid salt and its ions in a saturated solution. It specifically applies to sparingly soluble salts. The K_sp is the product of the concentrations of the ions, each raised to the power of its coefficient in the balanced equation for the dissolution of the salt. For example, if we have a salt AB that dissociates into A⁺ and B^- ions, the K_sp expression would be:

K_sp = [A⁺][B^-]

Here, [A⁺] and [B^-] are the molar concentrations of the ions at equilibrium in the solution. A higher K_sp value indicates a more soluble salt, meaning it dissociates more in solution to produce a greater concentration of ions. Conversely, a lower K_sp value suggests the salt is less soluble. The K_sp is a constant at a given temperature and is unique for each salt. It's important to note that the K_sp does not give the solubility directly but rather the extent to which a salt can dissolve to reach equilibrium.