Solubility, Ksp and Equilibrium

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Questions and Answers

How does adding HNO3 affect the solubility of Ag3PO4?

  • It decreases the solubility by reacting with Ag+.
  • It increases the solubility by reacting with Ag3PO4 to form a precipitate.
  • It has no effect on the solubility.
  • It increases the solubility by reacting with PO43-. (correct)

Increasing the pH increases the solubility of compounds of the type M(OH)n.

False (B)

In a saturated solution, what characterizes the state of dynamic equilibrium?

  • The precipitation rate is greater than the dissolution rate.
  • The dissolution rate is equal to the precipitation rate. (correct)
  • The dissolution rate is greater than the precipitation rate.
  • Both dissolution and precipitation cease to occur.

Write the net ionic equation for the reaction that occurs when AgCl(s) dissolves in aqueous ammonia, forming the diamminesilver(I) complex.

<p>AgCl(s) + 2NH3(aq) ⇌ Ag(NH3)2+(aq) + Cl-(aq)</p> Signup and view all the answers

In a solution at dynamic equilibrium, the concentrations of the dissolved ions remain constant because the solid stops dissolving.

<p>False (B)</p> Signup and view all the answers

The formation of ______ ions increases the solubility of slightly soluble ionic compounds.

<p>complex</p> Signup and view all the answers

Write the solubility product expression ($K_{sp}$) for silver chloride (AgCl).

<p>$K_{sp} = [Ag^+][Cl^-]$</p> Signup and view all the answers

Match the following species with their roles in the context of AgCl solubility:

<p>Cl- = Common ion that decreases AgCl solubility NH3 = Ligand that forms a complex ion with Ag+, increasing solubility Ag(NH3)2+ = Complex ion formed that enhances AgCl solubility</p> Signup and view all the answers

The solubility product constant, often denoted as $K_{sp}$, is a measure of the extent to which a solid compound dissolves in water. A higher $K_{sp}$ value indicates ______ solubility.

<p>greater</p> Signup and view all the answers

What is the correct $K_{sp}$ expression for Copper(II) Nitrate, $Cu(NO_3)_2$?

<p>$K_{sp} = [Cu^{2+}][NO_3^-]^2$ (A)</p> Signup and view all the answers

What is the overall formation constant ($K_f$) for the reaction $Cu^{2+}(aq) + 4NH_3(aq) ightleftharpoons [Cu(NH_3)_4]^{2+}(aq)$, given the stepwise formation constants $K_1 = 1.9 imes 10^4$, $K_2 = 3.9 imes 10^3$, $K_3 = 1.0 imes 10^3$, and $K_4 = 1.5 imes 10^2$?

<p>$1.1 \times 10^{13}$ (A)</p> Signup and view all the answers

In the stepwise formation of complex ions, the equilibrium constant for each step remains constant, regardless of the number of ligands already attached to the metal ion.

<p>False (B)</p> Signup and view all the answers

Write out the equation for the overall formation constant, (K_f), for the formation of (Ag(NH_3)_2^+) from (Ag^+) and (NH_3).

<p>$K_f = \frac{[Ag(NH_3)_2^+]}{[Ag^+][NH_3]^2}$</p> Signup and view all the answers

The overall formation constant, (K_f), for a complex ion is the product of the equilibrium constants of the individual __________ formation steps.

<p>stepwise</p> Signup and view all the answers

Match the stepwise equilibrium reactions with their corresponding equilibrium constant expressions:

<p>Ag+(aq) + NH3(aq) ⇌ Ag(NH3)+(aq) = $K_{f1} = \frac{[Ag(NH_3)^+]}{[Ag^+][NH_3]}$ Ag(NH3)+(aq) + NH3(aq) ⇌ Ag(NH3)2+(aq) = $K_{f2} = \frac{[Ag(NH_3)_2^+]}{[Ag(NH_3)^+][NH_3]}$ Cu2+(aq) + NH3(aq) ⇌ Cu(NH3)2+(aq) = $K_1 = \frac{[Cu(NH_3)^{2+}]}{[Cu^{2+}][NH_3]}$ Cu(NH3)2+(aq) + NH3(aq) ⇌ Cu(NH3)_22+(aq) = $K_2 = \frac{[Cu(NH_3)_2^{2+}]}{[Cu(NH_3)^{2+}][NH_3]}$</p> Signup and view all the answers

What condition indicates that a solution is saturated and a precipitate will form?

<p>Qsp &gt; Ksp (D)</p> Signup and view all the answers

For the dissolution of $Mg(OH)2$ in water, which of the following expressions correctly relates the solubility (s) to the solubility product constant ($K{sp}$)?

<p>$K_{sp} = 4s^3$ (C)</p> Signup and view all the answers

Complex ions consist of central metal ions and ligands ionically bonded to the metal ions.

<p>False (B)</p> Signup and view all the answers

Increasing the concentration of a common ion always increases the solubility of a sparingly soluble salt.

<p>False (B)</p> Signup and view all the answers

What is the concentration of free silver ion, Ag+, in a solution of 1.0 M ammonia, given the solubility (S) of AgCl is 0.047 mol/L and assuming each mole of AgCl dissolved produces one mole of $Ag(NH_3)_2^+$?

<p>0.047</p> Signup and view all the answers

If the solubility of $Ca_3(PO_4)_2$ is 's' mol/L, express the concentration of $Ca^{2+}$ in terms of 's'.

<p>3s</p> Signup and view all the answers

In complex ion equilibria, if stronger ligands are present in an aqueous solution, ligand _______ occur, and equilibrium is established.

<p>exchanges</p> Signup and view all the answers

The solubility of ionic compounds containing anions that are conjugate bases of weak acids is affected by the solution's ________.

<p>pH</p> Signup and view all the answers

Match the following scenarios with the appropriate outcome based on the relationship between $Q_{sp}$ and $K_{sp}$:

<p>$Q_{sp} = K_{sp}$ = Saturated solution, no precipitate forms $Q_{sp} &gt; K_{sp}$ = Saturated solution, precipitate forms $Q_{sp} &lt; K_{sp}$ = Unsaturated solution</p> Signup and view all the answers

Which of the listed molecules can function as a ligand in complex ion formation?

<p>H2O (C)</p> Signup and view all the answers

Match the following compounds with the correct expression for their $K_{sp}$ in terms of solubility 's':

<p>AgCl = $s^2$ Ag2CrO4 = $4s^3$ Ag3PO4 = $27s^4$ Ca3(PO4)2 = $108s^5$</p> Signup and view all the answers

A solution contains $[Pb^{2+}] = 0.020 M$ and $[Cl^-] = 0.010 M$. Given that $K_{sp}$ for $PbCl_2 = 1.6 \times 10^{-5}$, will a precipitate form?

<p>No, because $Q_{sp} &lt; K_{sp}$ (B)</p> Signup and view all the answers

Which of the following factors generally increases the solubility of most ionic compounds?

<p>Increasing the temperature (D)</p> Signup and view all the answers

Given the $K_{sp}$ of $AgCl$ is $1.6 \times 10^{-10}$, calculate the solubility (s) of $AgCl$ in mol/L. Express your answer in scientific notation.

<p>1.3e-5</p> Signup and view all the answers

What is the formula for calculating the solubility of a substance in water using its solubility product constant, $K_{sp}$?

<p>√(Ksp)</p> Signup and view all the answers

For the compound $Cr(OH)3$, what is the correct expression for $K{sp}$ in terms of its solubility 's'?

<p>$K_{sp} = 27s^4$ (B)</p> Signup and view all the answers

Flashcards

Solubility Equilibrium

A state where the rate of dissolving equals the rate of precipitation in a saturated solution.

Dynamic Equilibrium

The solid is continuously dissolving into ions, while ions recombine to form the solid at the same rate.

Solubility Product Constant (Ksp)

Equilibrium constant for the dissolution of a solid into an aqueous solution.

General Dissolution Expression

MmXn(s) ⇄ mMn+(aq) + nXm-(aq)

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Ksp for AgCl

Ksp = [Ag+][Cl-]

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Solubility of AgCl with Cl-

The solubility of AgCl decreases in the presence of Cl- ions due to the common ion effect.

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Effect of pH on Ag3PO4 solubility

The solubility of salts like Ag3PO4 (containing anions that are conjugate bases of weak acids) increases as pH decreases (more acidic).

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Effect of pH on M(OH)n solubility

The solubility of compounds like M(OH)n decreases as pH increases (more basic) and increases as pH decreases (more acidic).

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Complex Ion effect on Solubility

The formation of complex ions increases the solubility of slightly soluble ionic compounds.

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AgCl Solubility in NH3

AgCl is more soluble in aqueous NH3 than in water due to the formation of the Ag(NH3)2+ complex ion.

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Formation Constant (Kf)

A constant (Kf) representing the overall equilibrium for the formation of a complex ion from its constituent ions.

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Stepwise Formation

The stepwise process where ligand molecules or ions sequentially combine with a metal ion.

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Stepwise Equilibrium Constant

Equilibrium constant for each individual step in the stepwise formation of a complex ion.

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Ag(NH3)+ Formation (Step 1)

Ag+(aq) + NH3(aq) ⇌ Ag(NH3)+(aq). It represents the first step in the complex ion formation between silver ion and ammonia.

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Kf Calculation

The overall formation constant (Kf) is the product of the stepwise equilibrium constants (K1, K2, K3, K4...)

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Solubility Product (Ksp)

Equilibrium constant for the dissolution of a solid into aqueous ions.

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Solubility (s)

The concentration of a solute in a saturated solution.

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AgCl Dissolution

AgCl(s) ⇌ Ag+(aq) + Cl-(aq); Ksp = [Ag+][Cl-].

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Ag2CrO4 Dissolution

Ag2CrO4(s) ⇌ 2Ag+(aq) + CrO42-(aq); Ksp = [Ag+]^2[CrO42-].

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Temperature's effect on solubility

Solubility generally increases as temp increases.

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Common Ion Effect

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

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Salt Effect

The effect on solubility caused by the presence of a salt.

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pH Effect on Solubility

pH can affect the solubility of ionic compounds where the anions are conjugate bases of weak acids,

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Solubility in Water

The solubility of a substance in water is equal to the square root of its solubility product constant (Ksp).

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Qsp (Ion Product)

A measure of the relative amounts of ions in a solution; Used to determines if a precipitate will form. [Ion concentrations].

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Qsp = Ksp

No precipitate will form, and the solution is saturated.

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Qsp > Ksp

A precipitate will form because the solution is supersaturated.

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Qsp < Ksp

The solution is unsaturated, and no precipitate will form.

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Complex Ions

Ions consisting of a central metal ion bonded to surrounding ligands.

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Ligands

Molecules or anions covalently bonded to the central metal ion in a complex ion.

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Complex Ions Formation

Metal ions in aqueous solutions forming complex ions with water molecules acting as ligands.

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Study Notes

  • Dynamic equilibrium exists between undissolved solids and ionic species in saturated solutions.
  • Solids dissolve and ion-pairs form solids continuously
  • Dissolution rate equals precipitation rate.

Solubility Product Constant

  • General Expression: MmXn(s) ⇌ mMn+(aq) + nXm-(aq)
  • Ksp is the solubility product, Ksp = [Mn+]m[Xm-]n
  • AgCl(s) ⇌ Ag+(aq) + Cl-(aq)
  • Ksp = [Ag+][Cl-] = 1.6 x 10-10
  • If s is the solubility of AgCl: [Ag+] = s and [Cl-] = s
  • Ksp = (s)(s) = s² = 1.6 x 10-10
  • s = 1.3 x 10-5 mol/L
  • Ag2CrO4(s) ⇌ 2Ag+(aq) + CrO42-(aq)
  • Ksp = [Ag+]2[CrO42-] = 9.0 x 10-12
  • If s is the solubility of Ag2CrO4: [Ag+] = 2s and [CrO42-] = s
  • Ksp = (2s)²(s) = 4s3 = 9.0 x 10-12
  • s = 1.3 x 10-4 mol/L
  • Ca(IO3)2(s) ⇌ Ca2+(aq) + 2IO3-(aq)
  • Ksp = [Ca2+][IO3-]2 = 7.1 x 10-7
  • If the solubility of Ca(IO3)2(s) is s mol/L: Ksp = 4s3 = 7.1 x 10-7
  • s = 5.6 x 10-3 mol/L
  • Mg(OH)2(s) ⇌ Mg2+(aq) + 2OH-(aq)
  • Ksp = [Mg2+][OH-]² = 8.9 x 10-12
  • If the solubility of Mg(OH)2 is s mol/L: [Mg2+] = s mol/L, and [OH-] = 2s mol/L
  • Ksp = (s)(2s)² = 4s3 = 8.9 x 10-12
  • s = 1.3 x 10-4 mol/L
  • Ag3PO4(s) ⇌ 3Ag+(aq) + PO43-(aq)
  • Ksp = [Ag+]3[PO43-] = 1.8 x 10-18
  • If solubility of Ag3PO4 is s mol/L, then: Ksp = (3s)3(s) = 27s4 = 1.8 x 10-18
  • s = 1.6 x 10-5 mol/L
  • Cr(OH)3(s) ⇌ Cr3+(aq) + 3OH-(aq)
  • Ksp = [Cr3+][OH-]³ = 6.7 x 10-31
  • If the solubility is s mol/L, then: Ksp = [Cr3+][OH-]³ = (s)(3s)³ = 27s4 = 6.7 x 10-31
  • s= 1.3 x 10-8 mol/L
  • Ca3(PO4)2(s) ⇌ 3Ca2+(aq) + 2PO43-(aq)
  • Ksp = [Ca2+]3[PO43-]2 = 1.3 x 10-32
  • If the solubility is s mol/L: [Ca2+] = 3s, and [PO43-] = 2s
  • Ksp = (3s)3(2s)² = 108s5 = 1.3 x 10-32
  • s = 1.6 x 10-7 mol/L

Factors Affecting Solubility

  • Temperature affects solubility
  • Solubility generally increases with temperature.
  • Common ion effect: common ions reduce solubility
  • Salt effect: the salt effect slightly increases solubility
  • pH of solution affects the solubility of ionic compounds.
  • Anions are conjugate bases of weak acids.
  • Formation of complex ions: the formation of complex ions increases solubility

Common Ion Effect

  • AgCl(s) ⇌ Ag+(aq) + Cl-(aq); Ksp = 1.6 x 10-10
  • The solubility of AgCl is 1.3 x 10-5 mol/L at 25°C.
  • With the addition of NaCl, the equilibrium shifts left.
  • Increased [Cl-] causes AgCl to precipitates out.
  • For example, if [Cl-] = 1.0 x 10-2 M, solubility of AgCl = (1.6 x 10-10)/(1.0 x 10-2)=1.6 x 10-8 mol/L

Effect of pH on Solubility

  • Ag3PO4(s) ⇌ 3Ag+(aq) + PO43-(aq)
  • With the addition of HNO3, the following reaction occurs: H3O+(aq) + PO43-(aq) ⇌ HPO42-(aq) + H2O
  • Reaction reduces PO43- in solution, causing more solid Ag3PO4 to dissolve.
  • The solubility of compounds increases as pH is lowered by adding nitric acid.
  • Mg(OH)2(s) ⇌ Mg2+(aq) + 2OH-(aq)
  • Increasing the pH increases [OH-] and equilibrium shifts to the left.
  • Some of Mg(OH)2 precipitates out.
  • If pH is lowered, [OH-] decreases and equilibrium shifts to the right.
  • Solid Mg(OH)2 dissolves.
  • Solubility of compounds type M(OH)n decreases as pH increases, and increases as pH decreases.

Formation of Complex Ions on Solubility

  • Transition metal ions have a strong affinity for ligands to form complex ions.
  • Ligands are molecules, such as H2O, NH3 and CO, or anions, such as F−, CN− and S2O32−.
  • Complex ions are soluble.
  • Complex ion formation raises solubility of slightly soluble ionic compounds.

Effect of Complex Ion Formation on Solubility

  • AgCl(s) ⇌ Ag+(aq) + Cl-(aq); Ksp = 1.6 x 10-10
  • Ag+(aq) + 2NH3(aq) ⇌ Ag (NH3)2+(aq); Kf = 1.7 x 107
  • Combining two equations: AgCl(s) + 2NH3(aq) ⇌ Ag(NH3)2+(aq) + Cl-(aq)
  • Knet = Ksp x Kf = (1.6 x 10-10) x (1.7 x 107) = 2.7 x 10-3
  • Knet > Ksp implies that AgCl is more soluble in aqueous NH3 than in water.

Solubility Exercise #1

  • Calculate the solubility of AgCl : H2O at 25°C.
  • Solubility in Water: √ (Ksp) = √ (1.6 x 10-10) = 1.3 x 10-5 mol/L
  • Solubility of AgCl in 1.0 NH3: AgCl(s) + 2NH3(aq) ⇌ Ag(NH3)2+(aq) + Cl-(aq)
    • Initial (M): AgCl(s) + 2NH3(aq) ⇌ Ag(NH3)2+(aq) + Cl-(aq)
    • Change: -2S +S +S
    • Equilibrium (M): (1-2S) S S
  • Knet = [Ag(NH3)2+][Cl-]/[NH3]² = (S²)/(1-2S)² = 2.7 x 10-3
  • Solubility of AgCl in 1.0 NH3 (continued): S/(1-2S) = √ (2.7 x 10^(-3)) = 0.052
  • S = 0.052-0.104S
  • S = 0.052/1.104 = 0.047 mol/L
  • AgCl is much more soluble in NH3 solution than in water.

Predicting Formation of a precipitate

  • Qsp = Ksp → saturated solution, no precipitate
  • Qsp > Ksp → saturated solution, includes precipitate
  • Qsp < Ksp → unsaturated solution
  • Qsp is ion product expressed in the same way as Ksp for a particular system.

Predicting Precipitation

  • 20.0 mL of 0.025 M Pb(NO3)2 is combined with 30.0 mL of 0.10 M NaCl. Predict if precipitate of PbCl2 will form.
  • Ksp for PbCl2 = 1.6 x 10-5
  • Calculation: [Pb2+] = (20.0 mL x 0.025 M)/(50.0 mL) = 0.010 M
  • [Cl-] = (30.0 mL x 0.10 M)/(50.0 mL) = 0.060 M
  • Qsp = [Pb2+][Cl-]² = (0.010 M)(0.060 M)2
  • Qsp = 3.6 x 10-5→ precipitate of PbCl2 will form.

Complex Ion Equilibria

  • Complex ions consist of central metal ions.
  • Ligands are covalently bonded to the metal ions.
  • Ligands are either neutral molecules such as H2O, CO, and NH3, or anions such as Cl-, F-, OH-, and CN¯.
  • A complex ion: [Cu(NH3)4]2+ contains four NH3molecules covalently bonded to Cu2+.

Formation of Complex Ions

  • In aqueous solutions, metal ions form complex ions with water molecules as ligands.
  • With stronger ligands present, ligand exchanges occur, and equilibrium is established.
  • Cu2+(aq) + 4NH3(aq) ⇌ [Cu(NH3)4]2+(aq)
  • Kf = [Cu(NH3)42+]/[Cu2+][NH3]4 = 1.1 x 1013

Stepwise Formation of Complex Ions

  • At the molecular level ligand molecules or combine with metal ions in stepwise manner.
  • Each step carries its equilibrium constant.
  • Ex: Ag+(aq) + NH3(aq) ⇌ Ag(NH3)+(aq)
  • Kf1 = [Ag(NH3)+]/[Ag+][NH3]= 2.1 x 103
  • Ex: Ag(NH3)+(aq) + NH3(aq) ⇌ Ag(NH3)2+(aq)
  • Kf2 = [Ag(NH3)2+]/[Ag(NH3)+][NH3]= 8.2 x 103
  • Combining (1)+(2) yields: Ag+(aq) + 2NH3(aq) ⇌Ag(NH3)2+(aq)
  • Kf = [Ag(NH3)2+]/[Ag+][NH3]² = Kf1 xKf2 = 1.7 x 107

Stepwise Complex Ion Formation for Cu(NH3)42+

  • Individual Equilibrium steps:
  1. Cu2+(aq) + NH3(aq) ⇌ Cu(NH3)2+(aq); K₁ = 1.9 x 104
  2. Cu(NH3)2+(aq) + NH3(aq) ⇌ Cu(NH3)22+(aq); K2 = 3.9 x 103
  3. Cu(NH3)22+(aq) + NH3(aq) ⇌ Cu(NH3)32+(aq); K3 = 1.0 x 103
  4. Cu(NH3)32+(aq) + NH3(aq) ⇌ Cu(NH3)42+(aq); K4 = 1.5 x 102
  • Combining equilibrium:
  • Cu2+(aq) + 4NH3(aq) ⇌ Cu(NH3)42+(aq)
  • Kf = [Cu(NH3)4 2+]/[Cu2+][NH3]4
  • Kf = K₁ X K2 X K3 x K4 = 1.1 x 1013

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