Have you ever wondered why some salts dissolve completely in water while others leave a sediment at the bottom of your container? This has everything to do with solubility, a property that determines the ability of a substance to dissolve in a particular solvent.
While solubility varies from one substance to the other, it is also affected by factors such as temperature, pressure, and the concentration of other ions present. In this article, we will explore the concept of solubility constant (K sp), how it relates to molar solubility, the direct relationship between these two variables, as well as the inability to compare solubility based on K sp values.
Definition of K sp:
K sp, also known as solubility product constant, is a mathematical constant that describes the equilibrium of a sparingly soluble salt in a solution. A sparingly soluble salt is a substance that has a low solubility in water, and when dissolved, it leaves some undissolved solid.
This equilibrium occurs when the rate of dissolution is equal to the rate of precipitation or when the solution is saturated. K sp is an equilibrium constant and is a measure of the concentration of the ions that are present in a solution when an equilibrium is established.
Calculation of K sp from Molar Solubility:
Molar solubility refers to the concentration of a substance that is dissolved in a solution. It is calculated by dividing the number of moles of the solute by the volume of the solution.
Using the example of the sparingly soluble salt – calcium carbonate, when it dissolves, it becomes unbalanced:
CaCO3 (s) Ca2+ (aq) + CO32 (aq)
In this equation, the K sp is defined as:
K sp = [Ca2+] [CO32]
Where square brackets around a substance denote concentration. The specific ion concentrations can be calculated using the molar solubility, S:
CaCO3(s) Ca2+(aq) + CO32(aq) S 0 0
S S S
The concentration of Ca2+ ions and CO32 ions at equilibrium can be expressed in terms of ‘S’ (since, at equilibrium, the salt is in an equalibrium state which resembles concentration):
[Ca2+] = S (initially ‘0’)
[CO32] = S (initially ‘0’)
So, plugging the values, and solving for K sp, we get:
K sp = [S]^2
Direct Relationship between K sp and Molar Solubility:
The solubility of a substance depends on various factors such as temperature and the concentration of other ions in the solution.
However, for a given substance, there exists a direct relationship between K sp and molar solubility. This means that the higher the K sp value for a substance, the more soluble it is in a given solvent, and thus, the greater the molar solubility.
For example, the molar solubility of calcium carbonate is directly proportional to its K sp value. Inability to Compare Solubility Based on K sp Values:
Although K sp is a useful measure of solubility, it is not enough to compare the solubility of different substances since the K sp is only valid for a specific compound under specific conditions.
For comparing different salts, we need to take into account the different mole ratios of ions that make up the salt. For example, the K sp value of copper (II) oxide is different from that of copper (II) sulfate pentahydrate due to the difference in their mole ratios.
Thus, we cannot directly compare their solubilities based on K sp values. Conclusion:
In conclusion, the solubility constant (K sp) is a measure of a substance’s ability to dissolve in a given solvent.
The higher the K sp value, the more soluble the substance is in the solvent. K sp can be calculated using molar solubility, which refers to the concentration of a substance dissolved in a solution.
However, K sp values cannot be used to compare the solubility of different substances since they are specific to the compound and not comparable between different salts. It is essential to understand the concept of K sp to gain a better understanding of the solubility behavior of different substances.In the previous section, we discussed the concept of K sp and how it relates to molar solubility.
In this section, we will explore some examples of calculating K sp from molar solubility. These examples will help us understand how to use the equilibrium concentrations of ions in a solution to determine the K sp values for various salts, including barium sulfate, calcium fluoride, magnesium phosphate, and silver sulfide.
Example 1: Calculation of K sp for BaSO 4
Barium sulfate, BaSO4, is a sparingly soluble salt that forms a white precipitate when it reacts with sulfate ions in a solution. In this example, we will calculate the K sp value for BaSO4 based on its molar solubility at 25oC, which is 1.0 x 10^5 M.
The balanced dissolution equation for BaSO4 can be written as:
BaSO4 (s) Ba2+ (aq) + SO42 (aq)
At equilibrium, the concentration of Ba2+ ions and SO42 ions is equal to the molar solubility, S. [Ba2+] = S = 1.0 x 10^5 M
[SO42] = S = 1.0 x 10^5 M
Thus, the solubility product expression for BaSO4 can be written as follows:
K sp = [Ba2+] [SO42] = (1.0 x 10^5) (1.0 x 10^5) = 1.0 x 10^10
Therefore, the value of K sp for BaSO4 at 25oC is 1.0 x 10^10.
Example 2: Calculation of K sp for Calcium Fluoride (CaF 2)
Calcium fluoride, CaF2, is a sparingly soluble salt that forms a colorless solid when it reacts with fluoride ions in a solution. In this example, we will calculate the K sp value for CaF2 based on its molar solubility at 25oC, which is 4.0 x 10^9 M.
The balanced dissolution equation for CaF2 can be written as:
CaF2 (s) Ca2+ (aq) + 2F (aq)
At equilibrium, the concentration of Ca2+ ions is equal to the molar solubility, S, while the concentration of F ions is twice that of the molar solubility. [Ca2+] = S = 4.0 x 10^9 M
[F] = 2S = 8.0 x 10^9 M
Thus, the solubility product expression for CaF2 can be written as follows:
K sp = [Ca2+] [F]^2 = (4.0 x 10^9) (8.0 x 10^9)^2 = 2.56 x 10^24
Therefore, the value of K sp for CaF2 at 25oC is 2.56 x 10^24.
Example 3: Calculation of K sp for Magnesium Phosphate (Mg 3 (PO 4) 2)
Magnesium phosphate, Mg3(PO4)2, is a sparingly soluble salt that forms a white precipitate when it reacts with phosphate ions in a solution. In this example, we will calculate the K sp value for Mg3(PO4)2 based on its molar solubility at 25oC, which is 4.2 x 10^11 M.
The balanced dissolution equation for Mg3(PO4)2 can be written as:
Mg3(PO4)2 (s) 3Mg2+ (aq) + 2PO43 (aq)
At equilibrium, the concentration of Mg2+ ions is three times the molar solubility, while the concentration of PO43 ions is twice the molar solubility. [Mg2+] = 3S = 1.26 x 10^10 M
[PO43] = 2S = 8.4 x 10^11 M
Thus, the solubility product expression for Mg3(PO4)2 can be written as follows:
K sp = [Mg2+]^3 [PO43]^2 = (1.26 x 10^10)^3 (8.4 x 10^11)^2 = 2.0 x 10^27
Therefore, the value of K sp for Mg3(PO4)2 at 25oC is 2.0 x 10^27.
Example 4: Calculation of K sp for Silver Sulfide (Ag 2 S)
Silver sulfide, Ag2S, is a sparingly soluble salt that forms a black precipitate when it reacts with sulfide ions in a solution. In this example, we will calculate the K sp value for Ag2S based on its molar solubility at 25oC, which is 6.0 x 10^20 M.
The balanced dissolution equation for Ag2S can be written as:
Ag2S (s) 2Ag+ (aq) + S2 (aq)
At equilibrium, the concentration of Ag+ ions is twice the molar solubility, while the concentration of S2 ions is equal to the molar solubility. [Ag+] = 2S = 1.2 x 10^19 M
[S2] = S = 6.0 x 10^20 M
Thus, the solubility product expression for Ag2S can be written as follows:
K sp = [Ag+]^2 [S2] = (1.2 x 10^19)^2 (6.0 x 10^20) = 8.64 x 10^60
Therefore, the value of K sp for Ag2S at 25oC is 8.64 x 10^60.
Conclusion:
In conclusion, determining K sp from molar solubility is an important concept when studying the solubility of sparingly soluble salts. The concentration of the ions at equilibrium can be used to calculate the K sp of a salt.
We illustrated this concept by calculating the K sp values for barium sulfate, calcium fluoride, magnesium phosphate, and silver sulfide, using their known molar solubilities. These examples demonstrate how understanding the relationship between K sp and molar solubility can be applied in practical situations.
In this article, we explored the concept of solubility constant (K sp) and its relationship to molar solubility. We also discussed how to calculate K sp values for different salts using molar solubilities.
Understanding K sp is essential in predicting the solubility behavior of sparingly soluble salts, and it can be calculated by utilizing the equilibrium concentrations of ions in a solution. Overall, these examples demonstrate the importance of understanding K sp and molar solubility in predicting the behavior of different salts in solutions.
FAQs:

Q: What is K sp?
A: K sp is a mathematical constant that describes the equilibrium state of a sparingly soluble salt in a solution.

Q: How is K sp calculated?
A: K sp is calculated using the equilibrium concentrations of ions in a solution, which can be determined from the molar solubility.

Q: What is molar solubility?
A: Molar solubility refers to the concentration of a substance that is dissolved in a solution.

Q: What is the relationship between K sp and molar solubility?
A: There is a direct relationship between K sp and molar solubility, where higher K sp values correspond to a higher molar solubility.

Q: Can K sp values be used to compare the solubility of different salts?
A: K sp values are specific to the compound under specific conditions and cannot be used to directly compare the solubility of different salts.

Q: What are some examples of sparingly soluble salts and their K sp values?
A: Examples include barium sulfate (K sp = 1.0 x 10^10), calcium fluoride (K sp = 2.56 x 10^24), magnesium phosphate (K sp = 2.0 x 10^27), and silver sulfide (K sp = 8.64 x 10^60).