Chapter 7: Problem 143
Let the solubilities of
Short Answer
Expert verified
The correct relationship is: .
Step by step solution
01
- Identify the Solubility Product (Ksp) of AgCl
Identify the solubility product constant, Ksp, of AgCl. AgCl dissociates as . The Ksp is given by .
02
- Solubility of AgCl in Pure Water (S1)
For in pure water, consider that there are no common ion effects. Assuming 'S' is the solubility, we have and .
03
- Solubility of AgCl in 0.01 M CaCl2 (S2)
Add a common ion effect. dissociates into and . The presence of extra decreases the solubility of . So, will be less than .
04
- Solubility of AgCl in 0.01 M NaCl (S3)
Again, a common ion effect is present. dissociates into and , adding more to the solution. Thus, will be less than . The solubility of will be similarly affected as with , hence .
05
- Solubility of AgCl in 0.05 M AgNO3 (S4)
Add a common ion effect of . dissociates into and . The presence of extra decreases the solubility of significantly. Therefore, will be much less than .
06
- Conclusion
From these observations, we can see that will be greater than which will be greater than .
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Solubility Product Constant (Ksp)
The Solubility Product Constant, commonly abbreviated as Ksp, is a key concept in understanding the solubility of sparingly soluble salts. For a salt like , it dissociates in water as:
The Ksp expression for is given by:
Here, and represent the molar concentrations of the respective ions in a saturated solution at equilibrium. The Ksp value is fixed at a given temperature and indicates how much of the salt can dissolve to form a saturated solution.
Common Ion Effect
The Common Ion Effect refers to the decrease in solubility of an ionic compound when a common ion is added to the solution. For example: and are less than , the solubility of in pure water.
- When
or is added to a solution containing , both dissociate to release ions. - This increase in
ion concentration shifts the equilibrium to the left, reducing the solubility of .
Chemical Equilibrium
Chemical Equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products.
In the context of solubility, the equilibrium involving is described by the dissociation reaction:
The equilibrium expression derived from this reaction reflects the product of the ion concentrations raised to the power of their coefficients in the balanced chemical equation.
In the context of solubility, the equilibrium involving
Dissociation Reactions
Dissociation Reactions involve the separation of an ionic compound into its individual ions in solution. For instance:
-
dissociates as - Similarly,
dissociates into and ions as
Molar Solubility
Molar Solubility is defined as the number of moles of a solute that can dissolve per liter of solution to form a saturated solution. It directly relates to the Ksp value for a given compound.
If the molar solubility of in pure water is , then:
When common ions are added, such as ions from or , the molar solubility decreases. This effect is due to the shift in equilibrium, aligning with Le Chatelier’s principle, thereby reducing the amount of that can dissolve in the presence of common ions.
If the molar solubility of