Chapter 10 – Solutions

Introduction

Solutions are homogeneous mixtures, i.e., mixtures whose properties are uniform throughout. Solutions are all around us. We live in a solution of gases called the atmosphere. A carbonated beverage is a solution of a gas in a liquid. Brass and solder are solutions of a solid in a solid. Solutions that are predominately water are called aqueous solutions. Drinks, blood, and the ocean are all aqueous solutions. All of the reactions we discuss at the end of this chapter and in the following two chapters take place in aqueous solutions, and an understanding of solutions is necessary to understanding these reactions. In this chapter, we examine the properties of solutions, predict whether one substance will dissolve in another, and discuss the nature of aqueous solutions of ionic substances.

10.1 Concentration

Introduction

The properties of a solution made from substances A and B depend upon the dominant type of interaction in the solution. The dominant interaction, A-A, B-B, or A-B, depends upon the relative number of each type of molecule, which is given by their concentrations. If the concentration of A is much greater than that of B, then A-A interactions dominate, and the solution properties are similar to those of A. Thus, the concentration of each substance in a solution is an important property of the solution. Although there are many ways to express concentration, we focus on the most common form used in the chemistry laboratory in this section.

Prerequisites

• •
  7.1 Partial Pressures

Objectives

• •
  Define the terms solution, solvent, and solute.
• •
  Distinguish between homogeneous and heterogeneous mixtures.
• •
  Determine the molarity of a solution given the amount of solute a given volume of solution contains.
• •
  Determine the volume required to deliver a given number of moles of solute or the number of moles of solute in a given volume of a solution of known molarity.

10.1-1. Definitions

homogeneous mixture	Homogeneous mixtures are mixtures that have constant composition throughout. A mixture made by mixing water and alcohol or by dissolving sugar in water is homogeneous because the alcohol, sugar, and water molecules are dispersed evenly throughout the mixture. Thus, the ratio of sugar or alcohol molecules to water molecules is the same no matter the location or size of the sample. Consequently, the properties of the mixture are also the same throughout.
heterogeneous mixture	Heterogeneous mixtures do not have uniform composition. Mixing table salt and sugar or water and oil produces a heterogeneous mixture because the properties of a sample of the mixture can vary from those of one substance to those of the other.
solution	A solution is a homogeneous mixture. A mixture of water and alcohol is a solution, as is a mixture made by dissolving sugar in water.
solvent	The component of a solution that dictates the phase of a solution. Water is the most common solvent. If more than one liquid is present, the liquid in greater amount is usually considered to be the solvent, but water is sometimes considered the solvent even if it is not present in the greatest amount.
solute	A solute is a component of a solution that is not the solvent. A solution is made by dissolving one or more solutes in a solvent.
concentration	The concentration of a solute is the ratio that relates the amount of the solute to the amount of either the solvent or the entire solution.

Table 10.1: Some Definitions

10.1-2. Molarity

The concentration of a solute gives the amount of solute present in a given amount of solution or solvent. There are many ways to give concentration, but the most common method in the chemistry laboratory is molarity. The molarity of a solute is defined as the number of moles of solute per liter of solution, which can be stated mathematically as follows. The expression "[A] = 0.1 M" is read as "the concentration of A is 0.1 molar." It means that each liter of solution contains 0.1 mol A. Molarity is useful in determining how much solute is needed to prepare a solution. It is also useful in determining the amount of solute in a given amount of solution.

10.1-3. Molarity Exercise

10.1-4. Solute to Solvent Ratio

Most of the solutions that we encounter are aqueous solutions, and their properties depend upon the ratio of solute to water particles. In this section, we examine the ratio of solute and solvent particles in a typical aqueous solution. We can determine the number of moles of solute present in a given volume of solution of known molarity, but, in order to determine the number of moles of solvent in a liter of solution, we must know the density of the solution, i.e., we must know the mass of a unit volume of the solution. The density of water is 1.0 g/mL, or 1.0 g/cm³. The density of a solution that is predominately water will be close to that of pure water.

10.1-5. Solution Exercise

10.2 Solution Process

Introduction

In this section, we break the solution process into steps and examine the energy requirements of each step.

Prerequisites

• •
  9.2 Enthalpy (definition of enthalpy)
• •
  9.7 Free Energy (relationship between the standard free energy and the extent of a process)
• •
  9.11 Equilibrium and the Equilibrium Constant
• •
  9.5 Entropy (meaning of entropy)

Objectives

• •
  Define the term solubility.
• •
  Explain the three events involved in dissolving one substance in another and predict the sign of the enthalpy change for each.

10.2-1. Solubility

The maximum concentration that a solute can have in a given solvent at a given temperature is called its solubility in that solvent at that temperature. We will use the following terms to describe relative solubilities.

• •
  soluble: A solute is soluble if its solubility is at least 0.1 M.
• •
  slightly soluble: Substances with solubilities between 0.01 M and 0.1 M are slightly soluble.
• •
  insoluble: Substances with solubilities less than 0.01 M are insoluble.
• •
  miscible: Two liquids that are completely soluble in one another are said to be miscible. For example, alcohol and water are miscible, but water and gasoline are not.

Substance	Solubility in Water at 25 °C	Description		Substance	Solubility in Water at 25 °C	Description
NaCl	6 M	soluble		CaSO4	0.02 M	slightly soluble
MgO	0.0003 M	insoluble		CuS	10–18 M	insoluble

Table 10.2: Some Solubilities

A solution in which the solute concentration is equal to its solubility is said to be saturated. When excess solid is added to a saturated solution, an equilibrium is established between the solid and the dissolved solute. For example, the following equilibrium is established when an excess of NaCl solid is added to water. The solubility of NaCl is given by the extent of the above reaction, which is given by the value of ΔG° for the reaction. ΔG° = 0 when [NaCl] = 1 M, which is above the minimum concentration established for a soluble substance (0.1 M). Thus, a substance is considered soluble when ΔG° is negative or only slightly positive. ΔS° is frequently positive for the solution process, so a substance is usually soluble if ΔH° of solution is negative or only slightly positive. We consider the factors that determine ΔH° of solution in the next section.

10.2-2. Solution Process for Dissolving a Polar Solute in H₂O

The following enthalpy changes must take place in order to create a solution. Note that all changes are at standard conditions, but the superscript zero has been omitted.

• •
  ΔH_solute is the energy required to separate the solute particles.
• •
  ΔH_solvent is the energy required to create the cavities in the solvent that will accommodate the solute particles.
• •
  ΔH_mixing is the energy change produced when the solute particles enter the cavities in the solvent.

The processes and the energies involved when a polar solute dissolves in water are shown below. Dipolar and dispersion forces between solute particles keep the solute in the solid state, while dispersion, dipolar, and hydrogen bonding forces keep the solvent in the liquid state. For ionic solutes, it is the ionic bonds that are holding the ions in the solid. ΔH_solute is the energy required to overcome the forces that hold the solute particles together. Dipolar and dispersion forces must be overcome for polar solutes, and ionic bonds must be broken for ionic solutes. ΔH_solute is always positive because separating the solute particles always requires energy. ΔH_solvent is the energy required to separate solvent molecules to create cavities for the solute particles. ΔH_solvent is always positive because intermolecular forces must be overcome when the solvent particles are separated. When water is the solvent, the primary contribution to ΔH_solvent is the energy required to break hydrogen bonds. ΔH_mixing is the energy change that results when the solute enters the solvent cavities. ΔH_mixing is negative because interactions between the solvent and the solute always lower the energy of the system. The negative ends of the water dipoles interact with the positive ends of the solute dipoles (blue), while the positive ends of the water dipoles interact with the negative ends of the solute dipoles (red) to lower the energy. The solute is said to be solvated (hydrated when the solvent is water) as a result of these interactions.

10.2-3. Solvation

The last two steps of the solution process (creating the cavities and placing the solute in the cavities) are combined into one term called solvation. The result is that the solute becomes solvated. When the solvent is water, the process is called hydration and the solute becomes hydrated. The energy change of the solution process can then be expressed as: ΔH_solution = ΔH_solute + ΔH_solvation. Recall that a substance is soluble in a solvent when ΔH_solution is negative or only slightly positive. Thus, a solute is most soluble in solvents in which the energy of solvation (ΔH_solvation) is sufficiently exothermic to overcome the energy required to separate the solute particles (ΔH_solute). Consequently, a solute is most soluble in a solvent when the solute-solvent interactions are strong, but interactions between different particles are strong when the same type of interactions are common to both types of particles. This is summarized by the general statement that like dissolves like, which implies the following.

• •
  Ionic and polar solutes are soluble in polar solvents.
• •
  Nonpolar molecules are soluble in nonpolar solvents.

Thus, water is a good solvent for ionic compounds, such as NaCl and NH₄NO₃, and polar molecules, such as HCl and NH₃, but it is a poor solvent for nonpolar molecules, such as I₂ and CCl₄.

10.2-4. Like Dissolves Like Exercise

10.3 Organic Compounds

Introduction

We concluded the last section with "like dissolves like." That is, polar solutes tend to be soluble in polar solvents such as water, while nonpolar molecules tend to be soluble in nonpolar solvents and insoluble in polar solvents such as water. However, large molecules can have both polar and nonpolar regions. In this section, we examine the solubility of such molecules in water.

Prerequisites

• •
  7.3 Intermolecular Interactions

Objectives

• •
  Distinguish between hydrophobic and hydrophilic and explain the hydrophobic effect.
• •
  Relate the solubility of a substance in water to the relative sizes of its hydrophilic and hydrophobic regions.

10.3-1. Organic Compounds

Water is such an important solvent that we classify molecules by how well they interact with it. The term hydrophilic comes from the Greek for "water-loving" and is applied to molecules and regions of molecules that interact strongly with water. HCl and NH₃ are both polar molecules, so they are hydrophilic and water soluble molecules. The term hydrophobic comes from the Greek for "water-hating" and is applied to molecules that do not interact well with water and are not water soluble. I₂ and CCl₄ are nonpolar molecules that do not interact well with water, so they are both hydrophobic and water insoluble. Organic compounds are based on carbon and usually contain a number of C–C and C–H bonds, both of which are nonpolar and hydrophobic, but organic molecules can also contain C–O and C–N bonds, both of which are polar and hydrophilic. Thus, organic compounds can contain both hydrophilic and hydrophobic regions. Water molecules interact so much better with one another than with hydrophobic regions that water excludes or avoids hydrophobic regions whenever possible. In fact, water sets up an ice-like structure around hydrophobic regions. Indeed, it is the entropy decrease resulting from the formation of the ice-like structure that is most responsible for the low solubilities of hydrophobic substances. This effect is so strong and important that it is called the hydrophobic effect. This effect is critical in the folding of proteins and formation of biological membranes.

10.3-2. Hydrophobic and Hydrophilic Examples

10.3-3. Acetone

Acetone, (CH₃)₂C=O, is a common laboratory solvent because many organic substances are soluble in it, and it is miscible with water. Acetone contains CH₃ groups that interact with other organic compounds through dispersion forces, so many organic substances dissolve in acetone. However, it also contains a polar C=O group, which makes the molecule hydrophilic. As with alcohols, the water solubility of compounds like this depends upon the lengths of the carbon chains; as the hydrophobic portion of the molecule increases, its solubility in water decreases. For example, (CH₃CH₂CH₂CH₂)₂C=O is only slightly soluble in water.

10.3-4. Alcohols

The water solubility of compounds that contain both hydrophobic and hydrophilic regions depends upon the relative sizes of the two regions. Consider the solubilities of alcohols in water and hexane (C₆H₁₄) shown in Table 10.3. The hydroxyl (O–H) group is hydrophilic, while the CH₂ groups are hydrophobic. Consequently, the solubility of an alcohol in water depends upon the relative number of O–H and CH₂ groups in the alcohol. As the relative number of CH₂ groups increases, the hydrophobic nature of the alcohol increases and its solubility in water decreases, while its solubility in nonpolar solvents, such as C₆H₁₄, increases. Increasing the relative number of hydroxyl groups makes the alcohol more hydrophilic and more soluble in water. Thus, hexanol (CH₃(CH₂)₅OH) is only slightly soluble in water (0.059 M), but hexanediol (HO(CH₂)₆OH), which has one hydroxyl group at each end, is miscible with water.

	Solvent
Alcohol	H2O	C6H14
CH3OH	∞	0.12 M
CH3CH2OH	∞	∞
CH3(CH2)2OH	∞	∞
CH3(CH2)3OH	0.91 M	∞
CH3(CH2)4OH	0.31 M	∞
CH3(CH2)5OH	0.059 M	∞
CH3(CH2)6OH	0.015 M	∞

Table 10.3: Solubilities of Some Alcohols

10.3-5. Ether or Water Exercise

Ether is a common solvent that contains hydrophobic regions and is not very polar, but water is a very polar solvent with no hydrophobic regions. Consequently, polar substances are more soluble in water, and nonpolar substances are more soluble in ether (like dissolves like).

10.4. Detergents and Micelles

Introduction

Grease and stains are hydrophobic, but we remove them by washing our dishes and clothing in water. We can do this because of the special properties of detergents, the topic of this section.

Prerequisites

• •
  7.3 Intermolecular Interactions

Objectives

• •
  Describe a detergent and identify its head and tail.
• •
  Describe monolayers and explain why they form.
• •
  Describe micelles and explain how they function to dissolve hydrophobic materials in water.

10.4-1. Detergents and Soaps

A detergent is a substance that has both a hydrophobic region, which interacts well with grease and stains, and a hydrophilic region, which interacts well with water. As an example, consider sodium dodecyl sulfate (SDS), which is a small detergent molecule. There are four different representations used for detergents.

• 1
  space-filling
• 2
  ball-and-stick
• 3
  condensed structure that does not show C–H bonds explicitly
• 4
  common abbreviation that is a skeletal drawing that indicates carbon atoms in the tail as the junction of two or more lines; the polar head is represented by a circle

Each drawing type is shown in Figures 10.5a, 10.5b, 10.5c, and 10.5d. The hydrophobic region of SDS consists of eleven CH₂ groups and one CH₃ group. The hydrophilic region consists of an anionic sulfate group. These regions are referred to as the hydrophobic tail and the hydrophilic or polar head of the detergent. The tails of most detergents contain 15 to 19 carbon atoms, so the 12-carbon chain of SDS is short for a detergent. Soaps are derived from fatty acids and are similar to detergents except the polar head is a COO^1– (carboxylate) group. Their Ca²⁺ salts are water insoluble, and, since Ca²⁺ is a major source of water hardness, they do not function very well in hard water.

10.4-2. Monolayers

The hydrophobic tails of a detergent interact well with one another, but the hydrophobic effect is so strong that they avoid water. Thus, when a small amount of a detergent is added to water, the polar heads enter the water but the hydrophobic tails do not. Consequently, a layer of detergent molecules that is only one molecule thick forms on the surface.

10.4-3. Micelles

An increase in detergent concentration coupled with agitation forces the tails into the water, but the hydrophobic interaction is so strong that the tails attract one another (dispersion forces). The result is the formation of spheres, called micelles, that are composed of 80–100 molecules. The surface of the micelle is composed of the polar heads, while the interior is an organic solvent (the strongly interacting tails). Thus, grease and stains are removed in water by the addition of a detergent, which forms micelles with agitation. The hydrophobic grease and stain molecules "dissolve" in the center of the micelle. The micelle, which dissolves in water because the surface is formed of the ionic heads, can then be washed away.

10.5 Electrolytes

Introduction

Ionic compounds are not soluble in most solvents, but water is so polar that some ionic compounds do dissolve in it. Blood contains many ions, and the concentrations of those ions are critical to our well-being. Ions in water are responsible for water "hardness." In this section, we examine the nature of aqueous solutions of ionic compounds.

Prerequisites

• •
  1.8 Electromagnetism and Coulomb's Law
• •
  7.3 Intermolecular Interactions

Objectives

• •
  Indicate whether a substance is an electrolyte or a nonelectrolyte.

10.5-1. Definitions

Consider the apparatus shown in Figures 10.8a and 10.8b. Two pieces of metal (electrodes) are immersed in a solution and connected to a power supply. The light bulb glows only if the solution conducts electricity, which completes the circuit. In order for solutions to conduct electricity, they must contain charged particles, i.e., ions. Thus, the light bulb glows only if the electrodes are dipped into a solution that contains ions. Materials that dissolve in water as ions are called strong electrolytes, and those that dissolve as molecules are called nonelectrolytes. However, some compounds dissolve as molecules that react with water to produce ions. If their reaction with water is extensive, they too are classified as strong electrolytes, but if the reaction produces some ions but is not extensive, the compound is classified as a weak electrolyte. Solutions of strong electrolytes cause the light to burn brightly, those of nonelectrolytes do not cause the light to burn at all, and those of weak electrolytes cause the light to burn, but not as brightly because the concentrations of the ions are low. When no electrolytes (ions) are present, electricity is not conducted through the solution and the light bulb does not glow. Compounds whose aqueous solutions do not conduct electricty are called nonelectrolytes.

• •
  Molecular compounds that are not acids or bases are nonelectrolytes. H₂O and most organic compounds are nonelectrolytes.

Electrolytes (ions) conduct charge through the solution and complete the circuit, so the light bulb glows. Two types of compounds are electrolytes.

• •
  Ionic compounds dissolve to produce metal cations and nonmetal anions. The ions can also be derived from polyatomic ions, such as ammonium or sulfate ions.
• •
  Acids are compounds that produce H¹⁺ when they dissolve in water. Production of the H¹⁺ also produces a cation. For example, an aqueous solution of HCl is hydrochloric acid: HCl → H¹⁺ + Cl^1–. Since ions are produced when acids dissolve in water, acids are electrolytes. However, not all hydrogen-containing compounds are acids. Acids are those compounds whose formulas begin with an H. For example, HNO₃, HClO₄, and H₂SO₄ are some other common acids, while CH₄ is not an acid.

Solution	Glow	Solution Type	Solution Particles
water	none	nonelectrolyte	H2O molecules
table salt	bright	strong electrolyte	Na1+ + Cl1– ions
HCl	bright	strong electrolyte	HCl → H1+ + Cl1– is extensive.
HF	dim	weak electrolyte	HF → H1+ + F1– is NOT extensive.
table sugar	none	nonelectrolyte	C12H22O11 molecules
NaNO3	bright	strong electrolyte	Na1+ + NO31– ions
NaOH	bright	strong electrolyte	Na1+ + OH1– ions
rubbing alcohol	none	nonelectrolyte	C3H5OH molecules
ammonia	dim	weak electrolyte	NH3 + H2O → NH41+ + OH1– is NOT extensive.

Table 10.4: Conduction Properties of Some Aqueous Solutions

10.5-2. Ionic Compounds as Electrolytes

Ionic compounds are strong electrolytes, so when a solid ionic compound is dissolved in water, it goes into solution completely as ions. We will no longer use (aq) to indicate that an ion is in solution because isolated ions in chemcial equations are always in solution. Consider the following dissociations. A solution of NaCl contains only Na⁺¹ and Cl^1– ions; there are no NaCl molecules. Note that the chemical equation for the dissociation must have the same stoichiometry as the substance. Thus, the formula MgCl₂ indicates that there are two Cl^1– ions for every one Mg²⁺ ion, so the dissociation must express the same stoichiometry. Many ionic compounds contain polyatomic ions, but the bonds that hold the atoms in polyatomic ions are covalent and do not dissociate in water, so polyatomic ions enter solution intact.

10.5-3. Acids and Bases as Electrolytes

Ionic compounds are not the only class of compounds that are electrolytes; acids and bases are electrolytes as well. The first chemical definition of acids and bases was made by Svante Arrhenius. An Arrhenius acid is a substance that produces H¹⁺ ions when dissolved in water, and an Arrhenius base is a substance that produces OH^1– ions when dissolved in water. Acids can be identified because the acidic protons are usually written first in their chemical formulas. For example, H₂S is an acid, so the protons appear first in its formula, but NH₃ is not, so the protons do not appear first in its formula. In Arrhenius theory, acids ionize in water in a manner similar to ionic substances, but only strong acids ionize completely. The common strong acids are HCl, HBr, HI, HNO₃, HClO₄, and H₂SO₄. For example, the following chemical equations represent the Arrhenius view of dissolving three strong acids in water. Most acids dissociate only partially in water, so they are weak acids. Weak acids are weak electrolytes because they produce only small amounts of H¹⁺ and the anion in water. HF, HNO₂, and HClO₂ are examples of weak acids. The light bulb glows only dimly in a 0.1 M solution of a weak electrolyte because there are far fewer ions to conduct the electricity. Hydrofluoric acid is a weak acid as less than 10% of the HF molecules in a typical solution dissociate into their ions. To emphasize the fact that there are many more molecules than ions in a solution of a weak acid, the solution process is written with equilibrium arrows. Metal hydroxides are the most common strong bases. Most weak bases are also ionic and produce OH^1– ions as the result of the reaction of the anion with water. For example, F^1– and NO₂^1– ions are weak bases. Ammonia is the most common example of a molecular substance that is a weak base.

10.5-4. Nonelectrolytes

Sucrose (table sugar) is a nonelectrolyte, so dissolving sucrose in water is represented as

10.5-5. Distinguishing Strong Electrolytes and Nonelectrolytes Exercise

10.5-6. Distinguishing Strong and Weak Electrolytes Exercise

10.5-7. Ion Concentrations in Solutions of Strong Electrolytes

Ionic compounds, such as NaCl, are strong electrolytes because all of the solid NaCl that dissolves dissociates into ions. Thus, a solution labeled 0.10 M NaCl contains Na¹⁺ and Cl^1– ions, but no NaCl molecules. The ions react independently of one another; a chloride ion in a solution of NaCl is the same as one in a solution of KCl or MgCl₂. Thus, it is the concentration of the ion, not the parent compound, that is important in solution chemistry. To convert from the concentration of the parent compound to that of any ion requires the stoichiometry of the chemical equation for the dissociation, which is given by the stoichiometry of the compound.

10.5-8. Ion Concentration Exercise

10.6 Electrolyte Solutions

Introduction

Electrolytes are hydrated in aqueous solution. In this section, you can view an animation showing a crystal of NaCl dissolving in water.

Objectives

• •
  Describe how a crystal of sodium chloride dissolves in water.

10.6-1. The Water Dipole

Ionic bonds must be broken when an ionic substance dissolves, but ionic bonds are strong interactions, so ΔH_solute is large and positive. Thus, ΔH_solvation, the enthalpy of solvation (hydration in this case because the solvent is water), must be large and negative for an ionic substance to dissolve in water. In other words, the interaction between the water molecules and the ions must be very strong. This strong interaction arises because water has a strong dipole, which points from the center of the hydrogen atoms toward the electronegative oxygen atom. The large dipole of water also increases its dielectric constant (ε in Coulomb's Law), so water effectively shields each ion from the charge of surrounding ions.

10.6-2. The Solution Process

• •
  The sodium and chloride ions in a crystal adopt the sodium chloride structure with each sodium ion (represented by the blue spheres) surrounded by six chloride ions (represented by the green spheres) and each chloride ion surrounded by six sodium ions. Water is a very polar molecule with the center of positive charge residing between the two hydrogen atoms, and the negative charge centered on the oxygen atom. Only a small fraction of the water molecules are shown. There would be hundreds of water molecules for each ion in a typical solution, and the water molecules would be in contact with each other.
• •
  The positive ends of the water dipoles interact with the chloride anions (green) on the surface of the crystal, while the negative ends interact with the sodium cations (blue) at the surface. The interactions are sufficiently strong to pull the ions on the surface of the crystal out into the solution.
• •
  Six strongly interacting water molecules solvate (or hydrate in this case) each chloride ion in solution. There are many layers of water molecules around each ion. Note that the positive end of the dipole of each water molecule faces the chloride ion.
• •
  The sodium ion is hydrated in the same manner as the chloride ion, except that it is the negative end of the water dipole that faces the cation. As in the case of the anion, the cation is surrounded by several layers of water molecules. The two oppositely charged ions do not recombine because the dipoles of the intervening water molecules arrange themselves in such a way as to insulate the two charges.

10.7 Dissolution of Ionic Substances

Introduction

Not all ionic substances are soluble in water. Indeed, most are not. In this section, we examine the factors that dictate the solubility of ionic substances in water and develop some simple rules to help us predict solubilities.

Prerequisites

• •
  1.8 Electromagnetism and Coulomb's Law (Describe the factors that dictate the force of attraction of two opposite charges suspended in some medium.)
• •
  4.5 Polyatomic Ions (Identify polyatomic ions.)

Objectives

• •
  Relate solubility to the charge on the ions.

10.7-1. Dissolution and Coulomb's Law

The process whereby an ionic substance dissolves in water is called dissolution. The chemical equation for the dissolution of calcium carbonate is CaCO₃(s) → Ca²⁺ + CO₃^2–. As an approximation, we assume that an ionic substance is soluble when the force of attraction between its ions in solution is small enough that the ions can exist separately in solution, i.e., the force is not great enough that the separated ions attract one another to reverse the dissolution process. The force of attraction is described by Coulomb's Law. Although the solubility of ionic compounds is more complicated than a simple Coulombic attraction of the ions, we can still use Coulomb's Law to understand the process qualitatively by examining the factors that dictate the strength of the force of attraction. Thus, an ionic compound is likely soluble in water if the following are true.

• •
  r is very large. r is a property of the solution because it is the distance between the ions in the solution. r depends only upon concentration; ions in concentrated solutions are closer than ions in dilute solutions. If a substance is soluble, then the force of attraction cannot be great even at moderate concentration, so r cannot be very large.
• •
  ε is large. ε is the dielectric constant of the solvent and measures how well the solvent screens the charges in solution. The dielectric constant of water is about 40 times greater than that of a nonpolar solvent such as hexane (C₆H₁₄). This means that the force of attraction of two oppositely charged ions separated by the same distance is 40 times greater in C₆H₁₄ than in water, so the ions are much less likely to recombine in water. The dielectric constants of several common solvents are given in Table 10.5.
• •
  q₁q₂ is small. The product of the charges on the ions is the only factor that is a property of the ionic solute. Recall that the charges on ions typically fall in the range of –3 to +3; thus, q₁q₂ lies between 1 and 9. If the magnitude of the charge on either ion is 1, the magnitude of q₁q₂ cannot exceed 3, but if neither charge is 1, then the magnitude of q₁q₂ cannot be less than 4. Consequently, we expect that ionic compounds containing highly charged ions will not be as soluble in water as those containing +1 and –1 ions because the force of attraction between highly charged ions is too strong.

Solvent Name	Formula	ε		Solvent Name	Formula	ε
acetic acid	CH3COOH	6.20		acetone	(CH3)2C=O	21.0
benzene	C6H6	2.28		carbon disulfide	CS2	2.63
carbon tetrachloride	CCl4	2.24		dimethyl sulfoxide	(CH3)2S=O	47.2
ether	(C2H5)2O	4.27		ethanol	C2H5OH	25.3
hexane	C6H14	1.89		methanol	CH3OH	33.0
water	H2O	80.10

Table 10.5: Dielectric Constants of Selected Solvents at 20 °C

10.7-2. Dissolution and Coulomb's Law Exercise

10.7-3. Solubility Rules

We have seen that the solubility of simple ionic compounds in water can be related in a simple way to the charge on the ions. The magnitude of q₁q₂ ranges from 1 (1 × 1) to 9 (3 × 3) if ions with charges greater than 3 are neglected. In addition, if the magnitude of either charge is 1, then the product ranges from 1 to 3. However, the magnitude of the charge product ranges from 4 to 9 if neither charge is 1. Thus, the attraction between charges is much smaller if the magnitude of one of the charges is only 1, and as a rough first approximation, ionic substances that contain a +1 or a –1 ion are soluble, while those that contain no +1 or –1 ions are not. This generalization is given by the solubility rules shown in Table 10.6.

Rule 1	Compounds of NH41+ and Group 1A ions are soluble.	Compounds containing a +1 and/or –1 ion are probably soluble. Hydroxides (OH1–) are insoluble except by Rule 1, so they are a common exception.
Rule 2	Compounds of NO31–, ClO41–, ClO31–, and C2H3O21– are soluble.
Rule 3	Compounds of Cl1–, Br1–, and I1– are soluble except those of Ag1+, Cu1+, Tl1+, Hg22+, and Pb2+.	The insoluble halides appear to violate the +1/–1 rule for solubility, but these metals are late metals that are fairly electronegative, so their halides are not very ionic. For example, the Ag–Cl bond is only 30% ionic, and the Pb–Cl bond is only 15% ionic (see Chapter 5.2-5 Exceptions). Consequently, Coulomb's Law doesn't really apply here.
Rule 4	Compounds of SO42– are soluble except those of Ca2+, Sr2+, Ba2+, and Pb2+.	Sulfates are the only soluble compounds that do not have to contain an +1 or –1 ion.
Rule 5	Most others are NOT soluble in water.	If an ionic substance is not soluble by Rules 1 through 4, then it is probably not soluble in water.

Table 10.6: Solubility Rules for Ionic Substances in Water

10.7-4. Solubility is a Matter of Degree

Solubilities vary from very soluble to very insoluble, but no ionic solid is completely soluble in water and none is completely insoluble. As is usually the case in chemistry, it is a matter of degree. Consider the following solubilities of some sulfates.

Compound	Molar Solubility
BaSO4	0.000013
PbSO4	0.00014
SrSO4	0.00073
Hg2SO4	0.00010
CaSO4	0.015
Ag2SO4	0.027
Al2(SO4)4	1.1
FeSO4	1.9
MgSO4	3.0
MnSO4	4.2

Table 10.7

In general, the solubilities in Table 10.7 are consistent with the solubility rules. However, our definition of soluble was that the solubility of the substance had to be at least 0.1 M, and a slightly soluble substance had to have a solubility between 0.01 and 0.1 M, so the following are inconsistencies in the solubility rules.

• •
  CaSO₄ is slightly soluble, not insoluble.
• •
  Ag₂SO₄ is slightly soluble, not soluble.
• •
  Hg₂SO₄ is insoluble, not soluble.

Thus, Ag¹⁺ and Hg₂²⁺ should be added to the list of ions that form insoluble sulfates if Ca²⁺ is included. We conclude that care must be taken when using the solubility rules too literally. They are only very rough guidelines.

10.7-5. Predicting Solubility Exercise

10.8 Precipitation of Ionic Substances

Introduction

Most reactions between ionic compounds take place in aqueous solutions, but not all of the species present in the solutions necessarily take part in the reactions. A net ionic equation, or simply net equation, is one that shows only those ions that are involved in the reaction. In this section, we learn how to predict which ions are involved in precipitation reactions and how to write net ionic equations for their reaction.

Prerequisites

• •
  1.8 Electromagnetism and Coulomb's Law

Objectives

• •
  Write the net ionic equation for a simple precipitation reaction.
• •
  Use the solubility rules to predict whether an ionic compound is expected to be soluble in water.
• •
  Write a net ionic equation for the precipitation of an ionic compound from solution.
• •
  Use the solubility rules to predict whether mixing two solutions will produce a precipitate.

10.8-1. Formation of AgCl

It is often the case that when two clear solutions are mixed, a solid called a precipitate forms, or a precipitation reaction occurs. The ions that are present in solution but are not involved in the reaction are called spectator ions. Spectator ions are present because they were paired with a reacting ion initially. For example, consider the net ionic equation to explain the fact that when solutions of NaCl and AgNO₃ are mixed, a white precipitate forms. First, we determine if the compound formed from each anion-cation combination is soluble (anion-anion and cation-cation interactions are repulsive and can be ignored). The following are possible combinations.

• •
  Na¹⁺ + NO₃^1–
• •
  Ag¹⁺ + Cl^1–

NaNO₃ is soluble from both Rules 1 and 2, so Na¹⁺ + NO₃^1– are spectator ions. AgCl is NOT soluble from Rule 3. Therefore, the white precipitate is AgCl. The net ionic equation is Ag¹⁺ + Cl^1– → AgCl.

Ag1+ + Cl1–	→	AgCl
	→
The aqueous solution on the right contains Ag1+ and NO31– ions. The aqueous solution on the left contains Na1+ and Cl1– ions.	→	NaNO3 is soluble by Rules 1 and 2, and AgCl is insoluble by Rule 3. Thus, mixing the two solutions produces a solution of Na1+ and NO31– ions as well as a white precipitate of AgCl.

10.8-2. Video on the AgCl Precipitation Process

The animation shows the addition of AgNO₃, which comes in from the top, to a solution of NaCl. Note the hydration of each of the ions. The ions are mobile in solution and do encounter each other. Only a very small fraction of the water molecules are shown for clarity. Recall that there are hundreds of water molecules for each ion.

• •
  When the two cations or the two anions encounter one another, the force is repulsive.
• •
  When Ag¹⁺ and NO₃^1– encounter one another, the force of attraction is weak enough that the shielding of the intervening water molecules (dielectric) prevents reaction.
• •
  When Ag¹⁺ encounters Cl^1–, the driving force to form a bond (mostly covalent in nature) is sufficient to overcome the shielding from water, and AgCl precipitates from solution.

Note that the Na¹⁺ and NO₃^1– ions are surrounded only by water molecules at the beginning and end of the reaction, so they are unaffected by the reaction, i.e., they are spectator ions.

10.8-3. Predicting a Precipitate

10.8-4. Practice

10.9 Solubility Equilibria

Introduction

A precipitate is in equilibrium with its ions in solution, and, in this section, we show how to treat that equilibrium quantitatively.

Prerequisites

• •
  9.11 Equilibrium and the Equilibrium Constant (Write the equilibrium constant expression for a reaction involving solids and solutes.)

Objectives

• •
  Write the chemical equation to which the solubility product constant applies and write the solubility product constant expression for a compound.
• •
  Determine the concentration of an ion in equilibrium with another ion of known concentration in a saturated solution of a compound composed of the ions.

10.9-1. Solubility Equilibria

When the amount of solid that is added to water exceeds the amount that is soluble in water at that temperature, the solid reaches equilibrium with the ions. For example, when solid AgCl is added to water, only a small amount of the solid dissolves as it reaches equilibrium with its ions.

AgCl(s) Ag¹⁺ + Cl¹⁻

Recall that pure solids and liquids enter the equilibrium expression as 1 (unity), so the equilibrium constant for the above process would be written as K = [Ag¹⁺][Cl^1–]/1. Note that the equilibrium concentrations of the ions are determined by the solubility of AgCl and that the equilibrium constant is simply the product of the ion concentrations because the denominator is one. Consequently, the equilibrium constant is called the solubility product constant and given the symbol K_sp. The solubility product constant of AgCl is

K_sp = [Ag¹⁺][Cl¹⁻] = 1.8 × 10⁻¹⁰

The fact that the value of K_sp is so small indicates how insoluble AgCl is. The expressions and values of several silver compounds are given in Table 10.8.

Compound	Ksp expression	Ksp value
AgCl	[Ag1+][Cl1–]	1.8 × 10–10
Ag2CrO4	[Ag1+]2[CrO42–]	1.1 × 10–12
AgI	[Ag1+][I1–]	8.3 × 10–17
Ag2S	[Ag1+]2[S2–]	6.3 × 10–50
Ag3PO4	[Ag1+]3[PO43–]	2.6 × 10–18

Table 10.8: Solubility Product Constant Values and Expressions for Some Compounds of Silver

10.9-2. Exercise

10.9-3. Determining Equilibrium Concentrations

10.10 Exercises and Solutions

Select the links to view either the end-of-chapter exercises or the solutions to the odd exercises.

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