Question

For each pair of compounds, use \(K_{s p}\) values to determine which has the greater molar solubility: (a) CdS or CuS, (b) \(\mathrm{PbCO}_{3}\) or \(\mathrm{BaCrO}_{4}\), (c) \(\mathrm{Ni}(\mathrm{OH})_{2}\) or \(\mathrm{NiCO}_{3}\), (d) \(\mathrm{AgI}\) or \(\mathrm{Ag}_{2} \mathrm{SO}_{4}\)

Short answer

(a) CdS has a greater molar solubility than CuS (\(2.83 \times 10^{-14}\) vs. \(7.75 \times 10^{-19}\)). (b) BaCrO4 has a greater molar solubility than PbCO3 (\(1.08 \times 10^{-5}\) vs. \(1.22 \times 10^{-7}\)). (c) Ni(OH)2 has a greater molar solubility than NiCO3 (\(1.82 \times 10^{-5}\) vs. \(4 \times 10^{-10}\)). (d) Ag2SO4 has a greater molar solubility than AgI (\(2.29 \times 10^{-2}\) vs. \(2.91 \times 10^{-9}\)).

Step-by-step solution

(a) Cadmium sulfide (CdS) vs Copper sulfide (CuS)

First, we will need the Ksp values for CdS and CuS. You can find these values in a chemistry reference book or online: Ksp_CdS = 8 x 10^-27 Ksp_CuS = 6 x 10^-37 Now, calculate the molar solubility for each compound. Molar solubility_CdS = \( \sqrt{8 \times 10^{-27}} \approx 2.83 \times 10^{-14}\) Molar solubility_CuS = \( \sqrt{6 \times 10^{-37}} \approx 7.75 \times 10^{-19}\) Comparing the molar solubilities, CdS has a greater molar solubility than CuS.

(b) Lead(II) carbonate (PbCO3) vs Barium chromate (BaCrO4)

List the Ksp values for PbCO3 and BaCrO4: Ksp_PbCO3 = 1.5 x 10^-13 Ksp_BaCrO4 = 1.17 x 10^-10 Calculate the molar solubility of each compound. Molar solubility_PbCO3 = \( \sqrt{1.5 \times 10^{-13}} \approx 1.22 \times 10^{-7}\) Molar solubility_BaCrO4 = \( \sqrt{1.17 \times 10^{-10}} \approx 1.08 \times 10^{-5}\) Comparing the molar solubilities, BaCrO4 has a greater molar solubility than PbCO3.

(c) Nickel(II) hydroxide (Ni(OH)2) vs Nickel(II) carbonate (NiCO3)

Identify the Ksp values for Ni(OH)2 and NiCO3: Ksp_NiOH2 = 6 x 10^-16 Ksp_NiCO3 = 1.6 x 10^-19 Calculate the molar solubility of each compound. Molar solubility_NiOH2 = \( \sqrt[3]{6 \times 10^{-16}} \approx 1.82 \times 10^{-5}\) Molar solubility_NiCO3 = \( \sqrt{1.6 \times 10^{-19}} \approx 4 \times 10^{-10}\) Comparing the molar solubilities, Ni(OH)2 has a greater molar solubility than NiCO3.

(d) Silver iodide (AgI) vs Silver sulfate (Ag2SO4)

Determine the Ksp values for AgI and Ag2SO4: Ksp_AgI = 8.5 x 10^-17 Ksp_Ag2SO4 = 1.2 x 10^-5 Calculate the molar solubility for each compound. Molar solubility_AgI = \( \sqrt{8.5 \times 10^{-17}} \approx 2.91 \times 10^{-9}\) Molar solubility_Ag2SO4 = \( \sqrt[3]{1.2 \times 10^{-5}} \approx 2.29 \times 10^{-2}\) Comparing the molar solubilities, Ag2SO4 has a greater molar solubility than AgI.

Key concepts

Molar Solubility

Molar solubility is a term used in chemistry to describe the number of moles of a solute that can dissolve in one liter of solution to form a saturated solution. Essentially, it's an expression of the concentration of a solute at equilibrium in a particular solvent. To find molar solubility, you need to first understand the concept of solver equilibrium, where the solvent can dissolve no more solute. In this state, the solvent contains the maximum concentration of ions from the solute.
To calculate molar solubility, you often begin with the solubility product constant, or Ksp. For example, if you're working with a compound like CdS, where each molecule dissociates into one cadmium ion and one sulfide ion, the Ksp expression would be the product of the concentrations of these ions. The square root of the Ksp then gives you the molar solubility, as was calculated for CdS and CuS in the example. This process is similarly followed for other salts that dissociate completely in solution.
Molar solubility can be influenced by factors such as temperature and pH of the solution, which can shift the solubility equilibrium and thereby affect how much solute can dissolve.

Ksp Values

The solubility product constant, or Ksp, is a crucial factor in understanding chemical solubility. Ksp is a numerical representation of a compound's solubility. It indicates the extent to which a compound can dissociate into its ions in a given solvent. The lower the Ksp value, the less soluble the compound is under given conditions.
To use Ksp values effectively, consider how they represent a balance between the dissolved ions of a compound and its undissolved form. In the example of AgI vs Ag2SO4, the significantly higher Ksp value for Ag2SO4 compared to AgI indicates that Ag2SO4 can dissolve more in the solution, thus having a higher molar solubility.
By comparing Ksp values of different compounds, you can predict which compounds would dissolve more and form solutions with higher concentrations of ions, making Ksp values especially useful in determining comparative solubilities across various compounds.

Chemical Solubility

Chemical solubility encompasses the broader concept of how much of a substance can be dissolved in a solvent to achieve a saturated solution. A solute reaches solubility equilibrium when no more solute can be dissolved at the given temperature and pressure. This is a key concept when working with solutions in chemistry.
Solubility varies not only with different solutes but also with different solvents and environmental factors such as temperature and pressure. For instance, increasing the temperature typically increases the solubility of solids in liquids but can decrease the solubility of gases. When analyzing solubility, it is essential to take into account other factors such as common ion effect and the potential formation of complex ions, which can further influence solubility. In competitive scenarios like the query about PbCO3 and BaCrO4, it is important to consider these aspects as they affect the dissolution rate and equilibrium states in different solutions.
Ultimately, understanding chemical solubility helps in anticipating how substances behave in a solution and can guide practical applications, such as forming desired concentrations in pharmaceutical contexts or managing reactions in laboratory experiments.