Chapter 8: Problem 89
The solubility of \(\mathrm{AgCl}\) in \(0.2 \mathrm{M} \mathrm{NaCl}\) is \([\mathrm{Ksp} \mathrm{AgCl}=\) \(\left.1.8 \times 10^{-10}\right]\) (a) \(1.8 \times 10^{-11} \mathrm{M}\) (b) \(9 \times 10^{-10} \mathrm{M}\) (c) \(6.5 \times 10^{-12} \mathrm{M}\) (d) \(5.6 \times 10^{-11} \mathrm{M}\)
Short Answer
Step by step solution
Understand the problem
Write the solubility product expression
Substitute known values into Ksp equation
Calculate Ag+ concentration
Solve for solubility s
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Common Ion Effect and Its Impact on Solubility
- Cl- is the common ion in this case when both NaCl and AgCl are in the solution.
- The higher the concentration of the common ion, the lower the solubility of the salt in question.
Solubility of Salts in Ionic Solutions
In the presence of a strong electrolyte like NaCl, the solubility process is influenced by the concentration of ions contributed by NaCl. For AgCl in 0.2 M NaCl, the substantial presence of chloride ions shifts the equilibrium, reducing the amount of AgCl that can successfully dissolve. This adjustment in solubility due to ion presence is a profound concept in solution chemistry, especially when dealing with ionic compounds.
Chemistry Problem Solving with Ionic Equilibria
Approaching a typical problem involves:
- Identifying the salts and ions present in the solution.
- Recognizing significant constants such as the Ksp, or solubility product.
- Using known concentrations to approximate unknowns reasonably, such as applying the common ion effect knowledge.
- Substituting values into equilibrium expressions to calculate desired concentrations or solubilities.
Equilibrium Expressions for Solubility Calculations
For the dissolution of AgCl, the equilibrium expression is written based on its solubility product: \[ K_{sp} = [Ag^+][Cl^-] \] Given the known concentration of one ion, one can solve for the other utilizing the Ksp value. In the presence of a common ion, such as Cl- from NaCl in this example, the equation adjusts by incorporating the initial concentration, allowing for the calculation of the remaining ion's equilibrium concentration. Solving these expressions aids in understanding how ionic equilibria operate within different chemical contexts and provides insights into the ways solubility can be modulated by ion presence.