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Chapter 18: Problem 38

For each of the following insoluble salts, (1) write a balanced equation showing the equilibrium occurring when the salt is added to water, and (2) write the \(K_{\mathrm{sp}}\) expression. (a) \(\mathrm{PbSO}_{4}\) (b) \(\mathrm{BaF}_{2}\) (c) \(\mathrm{Ag}_{3} \mathrm{PO}_{4}\)

Short Answer

Expert verified
For each salt: (a) \( K_{\mathrm{sp}} = [\mathrm{Pb}^{2+}][\mathrm{SO}_{4}^{2-}] \); (b) \( K_{\mathrm{sp}} = [\mathrm{Ba}^{2+}][\mathrm{F}^{-}]^2 \); (c) \( K_{\mathrm{sp}} = [\mathrm{Ag}^{+}]^3[\mathrm{PO}_{4}^{3-}] \).

Step by step solution

01

Write the Dissolution Equation for \( \mathrm{PbSO}_{4} \)

The dissolution of \( \mathrm{PbSO}_{4} \) in water can be represented by the following equilibrium equation: \[ \mathrm{PbSO}_{4} (s) \rightleftharpoons \mathrm{Pb}^{2+} (aq) + \mathrm{SO}_{4}^{2-} (aq) \]
02

Write the \( K_{\mathrm{sp}} \) Expression for \( \mathrm{PbSO}_{4} \)

The \( K_{\mathrm{sp}} \) expression is the product of the concentrations of the ions at equilibrium: \[ K_{\mathrm{sp}} = [\mathrm{Pb}^{2+}][\mathrm{SO}_{4}^{2-}] \]
03

Write the Dissolution Equation for \( \mathrm{BaF}_{2} \)

The dissolution of \( \mathrm{BaF}_{2} \) in water can be represented by the equilibrium equation: \[ \mathrm{BaF}_{2} (s) \rightleftharpoons \mathrm{Ba}^{2+} (aq) + 2 \mathrm{F}^{-} (aq) \]
04

Write the \( K_{\mathrm{sp}} \) Expression for \( \mathrm{BaF}_{2} \)

The \( K_{\mathrm{sp}} \) expression is given as: \[ K_{\mathrm{sp}} = [\mathrm{Ba}^{2+}][\mathrm{F}^{-}]^2 \]
05

Write the Dissolution Equation for \( \mathrm{Ag}_{3} \mathrm{PO}_{4} \)

The dissolution of \( \mathrm{Ag}_{3} \mathrm{PO}_{4} \) in water can be represented by: \[ \mathrm{Ag}_{3} \mathrm{PO}_{4} (s) \rightleftharpoons 3 \mathrm{Ag}^{+} (aq) + \mathrm{PO}_{4}^{3-} (aq) \]
06

Write the \( K_{\mathrm{sp}} \) Expression for \( \mathrm{Ag}_{3} \mathrm{PO}_{4} \)

The \( K_{\mathrm{sp}} \) expression is given by: \[ K_{\mathrm{sp}} = [\mathrm{Ag}^{+}]^3[\mathrm{PO}_{4}^{3-}] \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Insoluble Salts
Insoluble salts are compounds that do not dissolve easily in water. This doesn't mean they are completely insolvable, but their solubility is very low compared to other salts. When placed in water, only a small quantity dissolves, establishing a dynamic equilibrium.

The limited solubility occurs because only a few molecules dissociate into ions. The remaining part stays in solid form. Some common examples include lead sulfate (\( \text{PbSO}_4 \)), barium fluoride (\( \text{BaF}_2 \)), and silver phosphate (\( \text{Ag}_3\text{PO}_4 \)). These salts form saturated solutions with ions equilibrating between the dissolved and undissolved states.
  • This equilibrium is essential in predicting the extent of dissolution.
  • Knowing the nature of insoluble salts helps in various chemical processes, including precipitate formation and analysis.
Ksp Expression
The solubility product constant, \( K_{\text{sp}} \), is a measure of the solubility of a compound, which is an essential aspect of understanding the extent to which insoluble salts dissolve. It is specific to each salt and is represented as the product of the concentrations of the ions each raised to the power of their coefficients from the dissolution equation.

For example:
  • For \( \text{PbSO}_4 \), the \( K_{\text{sp}} \) expression is \( K_{\text{sp}} = [\text{Pb}^{2+}][\text{SO}_4^{2-}] \).
  • For \( \text{BaF}_2 \), it is \( K_{\text{sp}} = [\text{Ba}^{2+}][\text{F}^-]^2 \) since two fluoride ions form.
  • Similarly, for \( \text{Ag}_3\text{PO}_4 \), the equation is \( K_{\text{sp}} = [\text{Ag}^+]^3[\text{PO}_4^{3-}] \) due to three silver ions.

Thus, \( K_{\text{sp}} \) expressions help predict solubility and are crucial in experiments to calculate ion concentrations at equilibrium.
Dissolution Equations
Dissolution equations illustrate how salts dissociate into their respective ions in water, reaching an equilibrium state. They are vital for understanding how different ions populate a solution when a salt is added. Each equation is balanced to show the correct stoichiometry of reactants and products.

For example:
  • The dissolution of \( \text{PbSO}_4 \) is shown by \( \text{PbSO}_4 (s) \rightleftharpoons \text{Pb}^{2+} (aq) + \text{SO}_4^{2-} (aq) \).
  • \( \text{BaF}_2 \) dissolution results in \( \text{BaF}_2 (s) \rightleftharpoons \text{Ba}^{2+} (aq) + 2\text{F}^- (aq) \), producing two fluoride ions for balance.
  • For \( \text{Ag}_3\text{PO}_4 \), the equation is \( \text{Ag}_3\text{PO}_4 (s) \rightleftharpoons 3\text{Ag}^+ (aq) + \text{PO}_4^{3-} (aq) \).

These dissolution equations are crucial as they provide the basis for writing \( K_{\text{sp}} \) expressions and for understanding the solubility and behavior of ions in a solution.

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Most popular questions from this chapter

Aluminum hydroxide reacts with phosphoric acid to give AIPO \(_{4} .\) The substance is used industrially in adhesives, binders, and cements. (a) Write the balanced equation for the preparation of AlPO \(_{4}\) from aluminum hydroxide and phosphoric acid. (b) If you begin with \(152 \mathrm{g}\) of aluminum hydroxide and \(3.00 \mathrm{L}\) of \(0.750 \mathrm{M}\) phosphoric acid, what is the theoretical yield of AlPO_? (c) If you place \(25.0 \mathrm{g}\) of \(\mathrm{AlPO}_{4}\) in \(1.00 \mathrm{L}\) of water, what are the concentrations of \(\mathrm{Al}^{3+}\) and \(\mathrm{PO}_{4}^{3-}\) at equilibrium? (Neglect hydrolysis of aqueous Al \(^{3+}\) and \(\mathrm{PO}_{4}^{3-}\) ions.) \(K_{\mathrm{sp}}\) for \(\mathrm{AlPO}_{4}\) is \(1.3 \times 10^{-20}\) (d) Does the solubility of AIPO increase ur decrease on adding HCl? Explain. (IMAGE CAN'T COPY)

Which of the following combinations would be the best to buffer the pH of a solution at approximately \(9 ?\) (a) HCl and NaCl (b) \(\mathrm{NH}_{3}\) and \(\mathrm{NH}_{4} \mathrm{Cl}\) (c) \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\) and \(\mathrm{NaCH}_{3} \mathrm{CO}_{2}\)

You titrate \(25.0 \mathrm{mL}\) of \(0.10 \mathrm{M} \mathrm{NH}_{3}\) with \(0.10 \mathrm{M} \mathrm{HCl}\). (a) What is the pH of the NH \(_{3}\) solution before the titration begins? (b) What is the \(\mathrm{pH}\) at the equivalence point? (c) What is the pH at the halfway point of the titration? (d) What indicator in Figure 18.10 could be used to detect the equivalence point? (e) Calculate the pH of the solution after adding 5.00 \(15.0,20.0,22.0,\) and \(30.0 \mathrm{mL}\) of the acid. Combine this information with that in parts (a)-(c) and plot the titration curve.

Calcium hydroxide, \(\mathrm{Ca}(\mathrm{OH})_{2},\) dissolves in water to the extent of 1.78 g per liter. What is the value of \(K_{\mathrm{sp}}\) for \(\mathrm{Ca}(\mathrm{OH})_{2} ?\) $$\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{s}) \rightleftharpoons \mathrm{Ca}^{2+}(\mathrm{aq})+2 \mathrm{OH}^{-}(\mathrm{aq})$$

For each of the following cases, decide whether the pH is less than 7 , equal to 7 , or greater than 7 . (a) Equal volumes of \(0.10 \mathrm{M}\) acetic acid, \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H},\) and \(0.10 \mathrm{M} \mathrm{KOH}\) are mixed. (b) \(25 \mathrm{mL}\) of \(0.015 \mathrm{M} \mathrm{NH}_{3}\) is mixed with \(12 \mathrm{mL}\) of \(0.015 \mathrm{M} \mathrm{HCl}\) (c) \(150 \mathrm{mL}\) of \(0.20 \mathrm{M} \mathrm{HNO}_{3}\) is mixed with \(75 \mathrm{mL}\) of \(0.40 \mathrm{M} \mathrm{NaOH}\) (d) \(25 \mathrm{mL}\) of \(0.45 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) is mixed with \(25 \mathrm{mL}\) of \(0.90 \mathrm{M} \mathrm{NaOH}\)
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