Rank The Following In Order Of Increasing Molar Solubility

The molar solubility of a compound is the number of moles of the compound that can dissolve in one liter of solution before the solution becomes saturated. This value is influenced by several factors, most notably the solubility product constant (Ksp) and the presence of common ions. Ranking compounds in order of increasing molar solubility requires a careful consideration of these factors. This article will explain how to rank different compounds in order of increasing molar solubility, covering the underlying principles and providing examples to illustrate the process.

Understanding Molar Solubility and Ksp

Molar solubility is expressed in units of moles per liter (mol/L or M). A compound's solubility is governed by its solubility product constant (Ksp), which is the equilibrium constant for the dissolution of a solid in an aqueous solution. For a generic salt, AB, the dissolution equilibrium can be represented as:

AB(s) <=> A+(aq) + B-(aq)

The Ksp expression for this equilibrium is:

Ksp = [A+][B-]

Where [A+] and [B-] are the equilibrium concentrations of the ions A+ and B- in the saturated solution. A larger Ksp value generally indicates higher solubility, but comparing Ksp values directly is only valid for compounds that dissociate into the same number of ions.

Factors Affecting Molar Solubility

Several factors can affect the molar solubility of a compound:

1. Ksp Value:* As mentioned earlier, a higher Ksp value generally indicates greater solubility, provided the compounds being compared dissociate into the same number of ions.

2. Common Ion Effect: The solubility of a sparingly soluble salt is reduced when a soluble salt containing a common ion is added to the solution. This is known as the common ion effect.

3. pH: The solubility of salts containing basic or acidic anions is affected by pH. For example, the solubility of hydroxides, carbonates, and phosphates increases in acidic solutions.

4. Temperature: The solubility of most ionic compounds increases with increasing temperature, although there are exceptions.

5. Complex Ion Formation: The formation of complex ions can increase the solubility of sparingly soluble salts.

Ranking Compounds by Molar Solubility

Ranking compounds by molar solubility involves several steps:

1. Identify the Compounds and Their Ksp Values: Gather the Ksp values for each compound. This information is typically available in chemical handbooks or online databases.

2. Write the Dissolution Equilibrium: Write the balanced dissolution equilibrium for each compound to determine how many ions each compound dissociates into.

3. Calculate Molar Solubility: Calculate the molar solubility (s) for each compound using its Ksp value and the stoichiometry of the dissolution reaction.

4. Consider Common Ion Effect and pH: Evaluate whether the common ion effect or pH will affect the solubility of the compounds.

5. Rank the Compounds: Rank the compounds in order of increasing molar solubility based on the calculations and considerations above.

Step-by-Step Calculation of Molar Solubility

To calculate the molar solubility (s) of a compound, follow these steps:

1. Write the Dissolution Equilibrium: Write the balanced equation for the dissolution of the compound in water.

2. Set Up an ICE Table: Create an ICE (Initial, Change, Equilibrium) table to determine the equilibrium concentrations of the ions.

3. Write the Ksp Expression: Write the Ksp expression in terms of the equilibrium concentrations.

4. Solve for s: Solve the Ksp expression for s to find the molar solubility.

Example 1: Simple Salts

Consider the following compounds and their Ksp values:

• Silver chloride (AgCl): Ksp = 1.8 x 10-10
• Barium sulfate (BaSO4): Ksp = 1.1 x 10-10

Both AgCl and BaSO4 dissociate into two ions each:

AgCl(s) <=> Ag+(aq) + Cl-(aq)
BaSO4(s) <=> Ba2+(aq) + SO42-(aq)

For AgCl:

Ksp = [Ag+][Cl-] = s * s = s^2
s = √(Ksp) = √(1.8 x 10-10) = 1.34 x 10-5 M

For BaSO4:

Ksp = [Ba2+][SO42-] = s * s = s^2
s = √(Ksp) = √(1.1 x 10-10) = 1.05 x 10-5 M

In this case, BaSO4 (1.05 x 10-5 M) is less soluble than AgCl (1.34 x 10-5 M). Therefore, in order of increasing molar solubility:

BaSO4 < AgCl

Example 2: Salts with Different Stoichiometries

Consider the following compounds and their Ksp values:

• Silver chloride (AgCl): Ksp = 1.8 x 10-10
• Calcium fluoride (CaF2): Ksp = 3.9 x 10-11

AgCl dissociates into two ions, while CaF2 dissociates into three ions:

AgCl(s) <=> Ag+(aq) + Cl-(aq)
CaF2(s) <=> Ca2+(aq) + 2F-(aq)

For AgCl:

Ksp = [Ag+][Cl-] = s * s = s^2
s = √(Ksp) = √(1.8 x 10-10) = 1.34 x 10-5 M

For CaF2:

Ksp = [Ca2+][F-]^2 = s * (2s)^2 = 4s^3
s = ∛(Ksp/4) = ∛(3.9 x 10-11 / 4) = 2.14 x 10-4 M

In this case, AgCl (1.34 x 10-5 M) is less soluble than CaF2 (2.14 x 10-4 M), despite having a slightly higher Ksp value. Therefore, in order of increasing molar solubility:

AgCl < CaF2

Example 3: Common Ion Effect

Consider the molar solubility of AgCl in pure water and in a solution containing 0.1 M NaCl.

In pure water:

AgCl(s) <=> Ag+(aq) + Cl-(aq)
Ksp = [Ag+][Cl-] = s * s = s^2
s = √(Ksp) = √(1.8 x 10-10) = 1.34 x 10-5 M

In 0.1 M NaCl solution:

The initial concentration of Cl- is 0.1 M due to the presence of NaCl.

AgCl(s) <=> Ag+(aq) + Cl-(aq)
Ksp = [Ag+][Cl-] = s * (0.1 + s)

Since s is much smaller than 0.1, we can approximate:

Ksp ≈ s * 0.1
s ≈ Ksp / 0.1 = (1.8 x 10-10) / 0.1 = 1.8 x 10-9 M

The molar solubility of AgCl is significantly reduced in the presence of the common ion Cl-.

Example 4: pH Effect

Consider the solubility of magnesium hydroxide (Mg(OH)2) in acidic and basic solutions.

Mg(OH)2(s) <=> Mg2+(aq) + 2OH-(aq)
Ksp = [Mg2+][OH-]^2 = 5.61 x 10-12

In pure water:

Ksp = s * (2s)^2 = 4s^3
s = ∛(Ksp/4) = ∛(5.61 x 10-12 / 4) = 1.12 x 10-4 M

In an acidic solution, the concentration of OH- decreases, which shifts the equilibrium to the right, increasing the solubility of Mg(OH)2. In a basic solution, the concentration of OH- increases, which shifts the equilibrium to the left, decreasing the solubility of Mg(OH)2.

Practice Problems

Here are a few practice problems to test your understanding of ranking compounds by molar solubility:

1. Rank the following compounds in order of increasing molar solubility:

   • Lead(II) iodide (PbI2): Ksp = 7.1 x 10-9
   • Silver bromide (AgBr): Ksp = 5.4 x 10-13
   • Copper(I) chloride (CuCl): Ksp = 1.7 x 10-7

2. Which compound has a higher molar solubility in a 0.1 M solution of Na2CO3: Ag2CO3 (Ksp = 8.1 x 10-12) or BaCO3 (Ksp = 8.1 x 10-9)?

3. How does the pH affect the solubility of zinc hydroxide (Zn(OH)2)? Explain.

Advanced Considerations

1. Ion Pairing: In concentrated solutions, ions can associate to form ion pairs, which can affect the apparent solubility of the salt.

2. Temperature Dependence: The Ksp value is temperature-dependent, so solubility rankings can change with temperature.

3. Complex Formation: The presence of ligands that can form complexes with the metal cation can significantly increase the solubility of the salt.

Real-World Applications

Understanding molar solubility is crucial in various fields, including:

1. Environmental Science: Predicting the fate of pollutants in aquatic environments.

2. Pharmaceutical Chemistry: Designing drug formulations with desired solubility characteristics.

3. Geochemistry: Understanding mineral formation and dissolution in geological processes.

4. Analytical Chemistry: Developing methods for separating and quantifying ions in solution.

FAQ

Q: How do I determine the Ksp value for a compound?

A: Ksp values can be found in chemical handbooks, online databases, or by experimental determination.

Q: Can I directly compare Ksp values to determine solubility?

A: Only if the compounds dissociate into the same number of ions. Otherwise, you must calculate the molar solubility.

Q: What is the common ion effect?

A: The decrease in the solubility of a sparingly soluble salt when a soluble salt containing a common ion is added to the solution.

Q: How does pH affect solubility?

A: The solubility of salts containing basic or acidic anions is affected by pH. Salts with basic anions are more soluble in acidic solutions, and vice versa.

Q: What is molar solubility?

A: Molar solubility is the number of moles of the compound that can dissolve in one liter of solution before the solution becomes saturated.

Conclusion

Ranking compounds in order of increasing molar solubility requires a thorough understanding of Ksp values, stoichiometry, and the factors that affect solubility, such as the common ion effect and pH. By following the steps outlined in this article and considering these factors, you can accurately predict and compare the solubilities of different compounds. Mastering these concepts is essential in various scientific and industrial applications, from environmental science to pharmaceutical chemistry. The ability to calculate and compare molar solubilities provides a valuable tool for understanding and predicting chemical behavior in aqueous solutions.