Solubility
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C ONCEPT
Concept 1. Solubility
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Solubility
Lesson Objectives
• Define the term solubility and describe factors affecting the solubility of a particular solution.
• Predict whether a substance will dissolve or dissociate in water. Describe what it means for a solution to be
saturated, supersaturated, or unsaturated.
• Define and give examples of both miscible and immiscible mixtures.
• Explain the statement "like dissolves like" at the molecular level, and give specific examples of this concept.
• Describe how pressure and temperature affect the solubility of a liquid or solid in solution.
• Describe how pressure and temperature affect the solubility of gases in solutions, and use Henry’s Law to
predict the solubility of a gas in a solution given the necessary variables.
Vocabulary
• solubility: The degree to which a solute dissolves in a solvent.
• saturated: The point at which no more solute is able to dissolve.
• unsaturated: A solution in which more solute could be dissolved, solute concentration is less than predicted
by solubility properties.
• supersaturated: When the amount of solute dissolved exceeds the solubility. Occurs when a solution is
saturated and the temperature slowly drops.
• miscible: Molecules mix well with one another, and form a homogeneous mixture.
• immiscible: Molecules don’t mix well together, and form a heterogeneous mixture exhibiting a noticeable
bilayer.
• van’t Hoff factor: Describes the number of moles of particles that dissociate from solid.
• Henry’s law: Mathematically describes the relationship between the vapor pressure of the solution and the
solute concentration.
Check Your Understanding
1. What type of intermolecular forces will exist between molecules of the following substances?
a.
b.
c.
d.
e.
f.
H2 O
CO2
CH4
N2
CO
NH3
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Introduction
Have you ever wondered why it is easier to stir sugar into hot tea rather than into ice tea? Or, why no matter how
much you shake a jar of oil and vinegar, it always seems to separate? These observations can be explained by a
property of solutions known as solubility. In this section, you’ll learn how molecular structure and binding forces
contribute to the solubility properties of various solutions and mixtures.
Solubility
Solubility is the degree to which a given solute dissolves in a particular solvent. It depends on various factors,
including temperature and pressure. A common way to express the solubility of a given solute-solvent pair is to state
the maximum amount of solute that can be dissolved by 100 grams of the solvent. The temperature dependence of
the solubilities for various compounds in water is shown in Figure 1.1.
FIGURE 1.1
Solubility Curve for Ionic Solids
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Concept 1. Solubility
The aqueous solubility of a given substance is determined experimentally by dissolving increasing amounts into
a known mass of water at a specific temperature until no more solid dissolves. A solution that cannot hold any
more of a given solute is said to be saturated. For example, in Figure 1.1 we see that the solubility of sodium
nitrate (NaNO3 ) is approximately 90 g per 100 g of H2 O at 20°C. At this temperature, a 100 gram sample of H2 O
in which 90 grams of sodium nitrate is dissolved would be saturated, and a solution in which less sodium nitrate
is dissolved would be unsaturated. Note that this ratio also holds for samples in which the solvent is present in
different amounts; 50 grams of water would hold 45 grams of sodium nitrate at 20°C, and 300 grams of water would
hold 270 g of NaNO3 . Notice that even relative solubilities of various compounds are temperature dependent. For
example, at 20°C, KCl has a higher solubility than NaCl, but at 50°C, this relationship is reversed.
Solutions can also become supersaturated, where the amount of solute dissolved exceeds its solubility. Supersaturation most commonly occurs when a saturated solution is slowly cooled. They occur frequently in geological
and meteorological processes. Supersaturated systems are unstable, and eventually, the solute will precipitate until
a saturated solution is regenerated. We can quantify supersaturation by looking at solubility curves. If the ratio of
solute to solvent is above the saturation curve at the given temperature, the solution is supersaturated. If it is on the
curve, the solution is saturated, and if it is below the curve, the solution is unsaturated.
Solubility can be described for any solute-solvent pairing, but because water is such a fundamentally important
solvent, we are mainly focusing on aqueous solutions.
Example 16.1
You dissolve 40 g of KCl in 100 g of water at 40°C. You then cool the solution to 20°C, during which you notice
solid KCl precipitating. How many grams of KCl would you expect to precipitate?
Answer:
Consult Figure 1.1 to find the solubility of KCl at 20°C (approximately 32 g KCl/100 g H2 O). Therefore, we would
expect approximately 8 g KCl to precipitate out (40 g – 32 g = 8 g).
Factors Affecting Solubility
There are three main factors that control solubility.
1. Identities of the solute and solvent
2. Temperature
3. Pressure (for gases only)
Solute and Solvent
Ultimately, the ability of a solute to dissolve in a particular solvent will be dictated by the relative favorability of
solute-solvent interactions compared to solute-solute and solvent-solvent interaction. In particular, the polarity of
these two substances has a major effect on whether a significant amount of solute is able to dissolve. Polar solutes
are typically quite soluble in polar solvents (e.g., ethanol in water), and nonpolar solutes generally dissolve well in
nonpolar solvents (e.g., grease in gasoline). Conversely, polar solutes will have low solubilities in nonpolar solvents
(e.g., NaCl in CCl4 ), and solubilities will be low for nonpolar solutes in polar solvents (e.g., oil in vinegar).
Temperature
As you can see in Figure 1.1, solid and liquid solutes generally become more soluble as the temperature increases.
This is true for solvents other than water as well. This effect varies quite a bit by substance. For example, the
solubility of KNO3 has a very strong temperature dependence (its solubility curve has a large slope), whereas the
solubility of NaCl is minimally influenced by temperature (its solubility curve is nearly flat). For gaseous solutes,
solubility decreases at higher temperatures. We will look more at this effect later in the lesson.
Pressure
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Higher pressures increase the solubility of gases. You are probably familiar with this concept as it relates to
carbonated beverages. Before opening the container, the inside is pressurized, so a large amount of CO2 is dissolved
in the liquid. After opening, the pressure decreases (to the ambient pressure), so the solubility of CO2 drops, causing
it to bubble out of solution. Because they are not compressible like gases, solid and liquid solutes do not have
noticeable changes in solubility at different external pressures.
A Review of Intermolecular Forces
Our understanding of the behavior of solutes and solvents can be largely explained at the molecular level using our
model of intermolecular forces. Some substances will mix freely while others barely mix at all. This is due to the
interactions between particles of the solvent and solute. Recall that nonpolar molecular substances are held together
in the solid and liquid phases by relatively weak London dispersion forces, in which induced dipoles line up into a
favorable arrangement. An example of this is the interactions found between molecules of iodine (I2 ). In contrast,
polar molecules are held together by stronger dipole-dipole interactions. Additionally, molecules that contain N-H,
O-H, or F-H bonds exhibit a special dipole-dipole interaction called hydrogen bonding, which is unusually strong
even for a polar interaction. Ammonia (NH3 ) and water are examples of small molecules that exhibit hydrogen
bonding. The cations and anions in an ionic compound are held together by very strong ionic bonds, but ion-dipole
interactions are nearly as strong. Ion-dipole interactions would be found, for example, when an ionic substance like
NaCl is dissolved in water. Each ion is attracted to the appropriate end of the dipole on surrounding molecules of
water.
FIGURE 1.2
Decision tree for types of intermolecular
interactions
Liquid Solutes
When combining two liquids, we can generally predict whether they will mix to form a homogeneous solution or
not by looking at the relative polarity of each substance. We will consider three scenarios: the combination of two
polar liquids, the combination of one polar and one nonpolar liquid, and the mixing of two nonpolar liquids.
Polar-Polar Interactions
Polar-polar interactions occur when two or more polar liquids are mixed. An example of this is when methanol
mixes with water. Both of these are small polar molecules containing O-H bonds, which means that they can
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Concept 1. Solubility
both participate in hydrogen bonding. Figure 1.3 shows molecules of methanol and water connected by hydrogen
bonds. Because of these strong interactions, the two substances mix freely to form a homogeneous mixture; they
are miscible. One way to remember this interaction is the phrase "like dissolves like." In this case, a polar solvent
dissolves polar solutes.
FIGURE 1.3
Hydrogen bonding between methanol and
water
Nonpolar-Polar Interactions Toluene (C6 H5 CH3 is an organic compound that is often used as a solvent in paint
thinners. Toluene is a nonpolar compound. When mixed with water, the two substances will separate into two
layers rather than forming a homogeneous solution; these two liquids are immiscible. Toluene is a nonpolar chain
that cannot form hydrogen bonds with water. Dissolving this chain in water would break up the strong hydrogen
bonds between water molecules and replace them with weaker dispersion forces. This is generally not energetically
favorable, so the liquids tend to separate themselves to maximize the number of strong attractive interactions.
Example 16.2
Can you think of two other liquids that are immiscible and form a heterogeneous mixture?
Answer:
Another familiar example is the mixing of vinegar and olive oil. Olive oil is a nonpolar substance, while vinegar
(which is mostly water and acetic acid) is polar. The result is a heterogeneous mixture that exhibits a bilayer.
Nonpolar-Nonpolar Interactions
Nonpolar-nonpolar interactions occur when two nonpolar liquids are mixed. An example of this is the interaction
between toluene and octane (see Figures above and 1.5). The interactions between a molecule of toluene and a
molecule of octane are relatively weak, but so are the toluene-toluene and octane-octane interactions. Because
no strong intermolecular forces (like those between water molecules) need to be broken for mixing to occur, no
strong interactions need to be formed in order for mixing to be a favorable process. Toluene and octane will form
a homogeneous mixture. The phrase "like dissolves like" applies to these mixtures as well. In this case, nonpolar
dissolves nonpolar.
Example 16.3
Can you think of another example of a nonpolar-nonpolar interaction between two different liquids that form a
homogeneous mixture?
Answer:
Another example of a nonpolar-nonpolar interaction between two different liquids would be the mixing of motor oil
and gasoline. Both of these substances are nonpolar, so they are miscible and form a homogeneous mixture when
combined.
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FIGURE 1.4
FIGURE 1.5
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Concept 1. Solubility
Solid Solutes
Solutions can also be comprised of a solid solute and a liquid solvent. These interactions are governed by the
same three interactions we discussed earlier: polar-polar, nonpolar-polar, and nonpolar-nonpolar. The table below
describes these interactions.
TABLE 1.1: 16.2
Solid (solute)
polar
nonpolar
polar
nonpolar
Liquid (solvent)
polar
polar
nonpolar
nonpolar
Example
NaCl + H2 O
I2 + H2 O
NaCl + Toluene
I2 + Toluene
Result
Homogeneous solution
Heterogeneous mixture
Heterogeneous mixture
Homogeneous mixture
Example 16.4
Using the data in the above table, could you replace the solute or the solvent in the heterogeneous mixtures with
another material to make them homogeneous?
Answer:
There are several combinations that could be described. For instance, in the polar-nonpolar mixture between NaCl
and toluene, the NaCl could be replaced with a nonpolar solid, like I2 , or the toluene could be replaced with a polar
substance, like water.
Ionic Solids in Water
When placed in water, ionic solids dissolve to varying degrees. Some ionic solids have a high solubility in water
(e.g., NaCl), while others barely dissolve at all (e.g., AgCl). Still others are moderately soluble (e.g., Ag2 CO3 ).
The solubility rules we studied in the chapter on Chemical Reactions provide guidelines for predicting the relative
solubility of a given ionic compound in water. In this chapter, we will focus primarily on water-soluble ionic solids.
When a soluble ionic solid is added to water, it interacts with water molecules and dissociates into isolated ions that
diffuse out into the solution. These charged particles become solvated by surrounding water molecules (Figure 1.6).
Although the strong ionic bonds in the solid are broken up, they are replaced by numerous favorable interactions
between the charged ions and the partial charges on the appropriate ends of the polar water molecules.
Notice that for each unit of NaCl that dissolves, two particles are freed into solution, the Na+ cation and the Cl−
anion. This means that if one mole of NaCl is dissolved, 2 moles of solute particles are found in the homogeneous
solution (one mole of each ion). This dissociation is quantified by something called the van’t Hoff factor. The
van’t Hoff factor (i) describes the number of moles of solute particles that are found in a solution when one mole of
a substance is completely dissolved. The van’t Hoff factor for NaCl would be expressed as i = 2.
Example 16.5
If one mole of magnesium fluoride (MgF2 ) is added to water and fully dissociates, how many moles of particles will
be formed?
Answer:
We can describe the dissociation of magnesium fluoride as follows:
MgF2 → Mg2+ + 2 F−
Each unit of magnesium fluoride contains three ions (one Mg2+ ion and two F− ions). Using the van’t Hoff factor to
describe this dissociation, we would say that i = 3, because three moles of ions are produced from the dissociation
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FIGURE 1.6
of one mole of the ionic solid.
Gas Solutes
Gases are also capable of dissolving in liquids. There are many examples of this in our everyday lives. For example,
carbonated beverages contain dissolved carbon dioxide. We notice this when bubbles come out of solution when the
beverage is opened. Another example is when oxygen from the air we breathe dissolves in our blood, where it is
transported throughout the body. Fish and other aquatic organisms use gills to capture dissolved oxygen from their
environments.
Because determining the mass of a gaseous sample is generally less convenient than determining how many moles
are present, solubilities for gases are often expressed as concentrations instead of as the mass that can be dissolved
in a specified amount of solvent. A solution in which one mole of a gas is dissolved in one liter of solution has a
concentration of 1 molar (1 M). Because the solubility of most gases is much less than that, the molar solubility is
often given in millimolar (mM). A one millimolar solution contains 1/1000 mol of solute per liter of solution. Other
methods of expressing concentration, such as parts per million (ppm) or parts per billion (ppb), will be discussed in
the following lesson.
Example 16.6
What does it mean if the molar solubility of a gas is 2.0 mM?
Answer:
Each liter of solution can hold a maximum of 2.0 millimoles of that particular gas at the indicated temperature and
pressure.
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Concept 1. Solubility
Temperature Effects
As with all substances, the solubility of gases is temperature dependent. However, in contrast to the situation for
most solids and liquids, higher temperatures will decrease the solubility of a gaseous solute. Figure 1.7 shows this
relationship with several common gases.
FIGURE 1.7
Solubility-Temperature Curves for Various
Common Gases
This inverse relationship between solubility and temperature can be understood by looking at a molecular model.
Recall that higher temperatures are associated with faster particles. Gas particles are held in solution by attractive
interactions with the solvent molecules. If the particles are moving slowly, these attractive forces will pull back any
particles that try to escape the surface of the solution and re-enter the gas phase. However, if the gas particles are
moving fast enough, these interactions will not be sufficiently strong to prevent this process from occurring. As
a result, more particles are able to escape, and the amount of dissolved solute is less than it would be at a lower
temperature.
Pressure Effects
At a constant temperature, the amount a given gas that dissolves in a given type and volume of liquid is directly
proportional to the partial pressure of that gas in the area immediately adjacent to the solution. This principle is
called Henry’s Law and is illustrated in Figure 1.8.
Mathematically, Henry’s Law is expressed as follows:
ρ = kH c
where ρ is the partial pressure of the gas, c is its molar solubility at the given temperature and pressure, and kH is
a constant that depends on the temperature and the identities of both the solute and solvent. Some kH values for
various gases dissolved in water at 298 K are presented below.
TABLE 1.2: 16.3
Gas
He
O2
N2
H2
CO2
NH3
Constant (Pa*mol−1 *L)
282.7 x 106
74.68 x 106
155. x 106
121.2 x 106
2.937 x 106
5.69 x 106
Constant (atm*mol−1 *L)
2865
756.7
1600.
1228
29.76
56.9
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FIGURE 1.8
Illustration of Pressure effects on gas solubility
If we solve the Henry’s Law equation for the molar solubility, we get the following useful relationship:
c=
ρ
kH
Example 16.7
What are the molar solubilities of oxygen gas and nitrogen gas in pure water at 298 K and 1 atm of pressure? Which
gas is more soluble under these conditions?
c
O2
=
1 atm
756.7 (atm∗mol−1 ∗L)
=0.00132 mol/L
=1.32 mM
c
N2
=
1 atm
1600. (atm∗mol−1 ∗L)
=0.000625 mol/L
=0.625 mM
Oxygen gas is more soluble under these conditions. A saturated solution of O2 would have a concentration of 1.32
mM, whereas a saturated solution of N2 would have a concentration of 0.625 mM.
Lesson Summary
• Solubility describes the degree to which a solute will dissolve in a particular solvent.
• Water is a common solvent for dissolving various solids, liquids, and gases.
• The solubilities of solids and liquids are commonly expressed as grams of solute that can be dissolved by 100
g of water at a specified temperature.
• Solutions can be unsaturated, saturated, or supersaturated, depending on the relationship between the solubility
of a substance and the amount that is actually dissolved.
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Concept 1. Solubility
• The solubility of gases, liquids, and solids are affected by changes in temperature.
• Solutes and solvents that have similar polarities (i.e., both are polar, or both are nonpolar) tend to mix well,
creating homogeneous solutions. Solutes and solvents with very different polarities (i.e., one is polar, and the
other is nonpolar) often do not mix well, resulting in the formation of heterogeneous mixtures.
• The solubilities of gases are often described as concentrations (i.e., mM or M) rather than the mass that can
be dissolved by a given mass of solvent.
• The solubility of a gaseous solute is inversely related to the temperature of the solvent and directly proportional
to the partial pressure of the gas in the surrounding atmosphere.
• Henry’s law describes the mathematical relationship between the concentration of a gaseous solute and its
partial pressure in the gas above the solution.
Review Questions
1. Draw the mixture that would be formed when oil and water are combined.
2. Give an example of molecular solid that dissolves in water due to polar-polar interactions.
3. Ammonia (NH3 ) dissolves well in water. Explain how this interaction might occur and the type(s) of intermolecular forces that would be involved.
4. Using the solubility-temperature curve in Figure 1.1, describe conditions under which a solution of potassium
chloride would be unsaturated, saturated, and supersaturated at 20°C.
5. A solution is formed by dissolving 10. grams of potassium chlorate in 100. g of water at 30°C. If the solution
were heated to 40°C, how many more grams of solute could be dissolved?
6. A solution that is saturated with both methane and oxygen gas at 1 atm and 20°C is then heated to 40°C. What
will happen to the dissolved gases as the temperature increases? Referring back to Figure 1.7, how much of
each gas would leave the solution? How much would remain?
7. Which of the gases in Table 1.2 would have the highest solubility in water at 298K? Which would have the
lowest solubility?
8. Urea (CH4 N2 O) is a molecular solid that has a relatively high solubility in water. How would you account for
this fact? The molecular structure for urea is shown below.
FIGURE 1.9
9. Which of the following substances would dissolve better in water: iodine crystals (I2 ) or liquid methanol
(CH3 OH)? How would you categorize the resulting solute-solvent interactions?
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Further Reading / Supplemental Links
• Solubility-pressure curves for a variety of gases: http://www.engineeringtoolbox.com/gases-solubility-water
-d_1148.html
• Supersaturated solution demonstration: http://www.youtube.com/watch?v=D1PDE5OawuI
Points to Consider
• When you open a can of soda or sparkling water, you can usually see some gas escape or bubble out of the
can. Based on the relationship between pressure and gas solubility, why might this occur?
• Why do you suppose it is better to wash your dishes with warm water than with cold water? Explain these
effects in terms of solubility.
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
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CK-12 Foundation - Christopher Auyeung. . CC-BY-NC-SA 3.0
CK-12 Foundation - Jodi So. . CC-BY-NC-SA 3.0
Jü. http://commons.wikimedia.org/wiki/File:Methanol_Hydrogen_Bridge_V.2.svg. CC 0 public domain
NEUROtiker. http://commons.wikimedia.org/wiki/File:Toluol.svg. Public Domain
Bangin. https://commons.wikimedia.org/wiki/File:Octane.svg. Public Domain
Taxman. http://commons.wikimedia.org/wiki/File:Na%2BH2O.svg. Public Domain
CK-12 Foundation - Jodi So and Steven Lai. . CC-BY-NC-SA 3.0
CK-12 Foundation - Jodi So. . CC-BY-NC-SA 3.0
NEUROtiker. http://commons.wikimedia.org/wiki/File:Harnstoff.svg. Public Domain