Entropy, Solutions, and Solubility
For a thorough understanding of why ethanol mixes so easily with water but oil does not, we need to begin by asking, Why does any change happen? This question may seem so broad as to be irrelevant, but you will soon discover that it has all sorts of practical ramifications in chemistry. The goals of this section are to explain in general terms why changes happen and then use this knowledge to explain why some substances form solutions and why others do not. When you are finished reading this material, you will have the necessary tools for predicting the solubility of substances in liquids.
The Natural Tendency
to Spread Out
It is common for scientists to develop and explain their ideas by considering
simplified systems first and then applying the ideas that relate to these
simplified systems to more complex systems. Before we try to explain why the
more complicated changes that take place when solutions form, lets take a look
at a much simpler system consisting of four particles that can each be found in
one of nine positions. The figure below shows that
there are 126 ways to arrange these four particles in the nine positions. We
know that the particles in solids are closer together than the particles in a
gas, so in our simple system, lets assume that any arrangement that has the
four particles clustered together is like a solid. The figure
shows that there are four ways to do this. In our system, we will consider any
other, more dispersed (more spread out) arrangement as being like a gas.
The figure shows that there are 122 ways to position
the particles in a gas-like arrangement. Thus over 96% of the possible
arrangements lead to gas-like states. Therefore, if we assume that the particles
can move freely between positions, they are more likely to be found in a
gas-like state than in a solid-like state.
If the four particles had 16 possible positions, there would be 1820 possible combinations. Nine of these would be in solid-like states, and the other 1811 would be in gas-like states. Thus over 99.5% of the possible arrangements would represent gas-like states, as opposed to 96% for the system with 9 possible positions. This shows that an increase in the number of possible positions leads to an increase in the probability that the system will be in a more dispersed, gas-like state. In real systems, which provide a huge number of possible positions for particles, there is an extremely high probability that substances will shift from the less dispersed, solid form, which has fewer ways of arranging the particles, to the more dispersed, gas form, which has more ways of arranging particles.
In general, particles of matter tend to become more dispersed (spread out). The simple system shown in the figure below provides another example. It has two chambers that can be separated by a removable partition. Part a of the figure shows this system with gas on one side only. If the partition is lifted, the motion of the gas particles causes them to move back and forth between the chambers. Because there are more possible arrangements for the gas particles when they are dispersed throughout both chambers than when they are concentrated in one chamber, probability suggests that they will spread out to fill the total volume available to them.
We can apply the conclusions derived from the consideration of simplified systems to real systems. For example, we can use the information about the simple systems described above to explain the behavior of a small amount of dry ice, CO2(s), in a closed container. The movement of particles in the solid CO2 allows some of the CO2 molecules at the surface of the solid to break their attractions to other molecules and escape into the space above the solid. Like all particles in the gas form, the escaped CO2 molecules are constantly moving, colliding with other particles, and changing their direction and velocity. This gives them the possibility of moving anywhere in the container. Because the most spread out or dispersed arrangement of particles is the most probable state, the gaseous CO2 spreads out to fill the total space available to it. Because of the movement of the gaseous molecules, each molecule eventually collides with the surface of the solid. When this happens the particle is attracted to the other particles on the surface of the solid and is likely to return to the solid. Therefore, particles are able to move back and forth between the solid and gaseous form, and we expect to find them in the more probable, more dispersed gas state, which has more equivalent ways to arrange the particles.
Why Do Solutions Form?
Although much of the explanation for why certain substances mix and
form solutions and why others do not is beyond the scope of this text,
we can get a glimpse at why solutions form by taking a look at the
process by which ethanol, C2H5OH, dissolves in
water. Ethanol is actually miscible in water, which means that the two
liquids can be mixed in any proportion without any limit to their
solubility. Much of what we now know about the tendency of particles to
become more dispersed can be used to understand this kind of change as
Because the attractions between the particles are so similar, the freedom of movement of the ethanol molecules in the water solution is about the same as their freedom of movement in the pure ethanol. The same can be said for the water. Because of this freedom of movement, both liquids will spread out to fill the total volume of the combined liquids. In this way, they will shift to the most probable, most dispersed state available, the state of being completely mixed. There are many more possible arrangements for this system when the ethanol and water molecules are dispersed throughout a solution than when they are restricted to separate layers. (Figure below).
We can now explain why automobile radiator coolants dissolve in water. The
coolants typically contain either ethylene glycol or propylene glycol, which,
like ethanol and water, contain hydrogen-bonding O−H bonds.
These substances mix easily with water for the same reason that ethanol mixes easily with water. The attractions broken on mixing are hydrogen bonds, and the attractions formed are also hydrogen bonds. There is no reason why the particles of each liquid cannot move somewhat freely from one liquid to another, and so they shift toward the most probable (most dispersed), mixed state.
Are Hydrocarbons Insoluble in Water?
We have a different situation when we try to mix hexane, C6H14, and water. If we add hexane to water, the hexane will float on the top of the water with no apparent mixing. The reasons why hexane and water do not mix are complex, but the following gives you a glimpse at why hexane is insoluble in water.
There actually is a very slight mixing of hexane and water molecules. The natural tendency toward dispersal does lead some hexane molecules to move into the water and some water molecules to move into the hexane. When a hexane molecule moves into the water, London forces between hexane molecules and hydrogen bonds between water molecules are broken. New attractions between hexane and water molecules do form, but because the new attractions are very different from the attractions that are broken, they introduce significant changes in the structure of the water. It is believed that the water molecules adjust to compensate for the loss of some hydrogen bonds and the formation of the weaker hexane-water attractions by forming new hydrogen bonds and acquiring a new arrangement.
Overall, the attractions in the system after hexane and other hydrocarbon molecules move into the water are approximately equivalent in strength to the attractions in the separate substances. For this reason, little energy is absorbed or evolved when a small amount of a hydrocarbon is dissolved in water. To explain why only very small amounts of hydrocarbons such as hexane dissolve in water, therefore, we must look at the change in the entropy of the system. It is not obvious, but when hexane molecules move into the water layer, the particles in the new arrangement created are actually less dispersed (lower entropy) than the separate liquids. The natural tendency toward greater dispersal favors the separate hexane and water and keeps them from mixing.
This helps explain why gasoline and water do not mix. Gasoline is a mixture of hydrocarbons, including hexane. Gasoline and water do not mix because the nonpolar hydrocarbon molecules would disrupt the water in such a way as to produce a structure that was actually lower entropy; therefore, the mixture is less likely to exist than the separate liquids.
We can apply what we know about the mixing of ethanol and water to the mixing of two hydrocarbons, such as hexane, C6H14, and pentane, C5H12. When the nonpolar pentane molecules move into the nonpolar hexane, London forces are disrupted between the hexane molecules, but new London forces are formed between hexane and pentane molecules. Because the molecules are so similar, the structure of the solution and the strengths of the attractions between the particles are very similar to the structure and attractions found in the separate liquids. When these properties are not significantly different in the solution than in the separate liquids, we can assume that the solution has higher entropy than the separate liquids. Therefore, when very similar liquids, like pentane and hexane, are mixed, the natural tendency toward increasing entropy drives them into solution.
Exothermic changes lead to an increase in the energy of the surroundings, which leads to an increase in the number of ways that that energy can be arranged in the surroundings, and therefore, leads to an increase in the entropy of the surroundings. Endothermic changes lead to a decrease in the energy of the surroundings, which leads to a decrease in the number of ways that that energy can be arranged in the surroundings, and therefore, leads to a decrease in the entropy of the surroundings. Therefore, exothermic changes are more likely to occur than endothermic changes. We can use this generalization to help us explain why ionic compounds are insoluble in hexane. For an ionic compound to dissolve in hexane, ionic bonds and attractions between hexane molecules would need to be broken, and ion-hexane attractions would form. The new attractions formed between the ions and hexane would be considerably weaker than the attractions broken, making the solution process significantly endothermic. The tendency to shift to the higher entropy solution cannot overcome the decrease in the entropy of the surroundings that accompanies the endothermic change, so ionic compounds are insoluble in hexane.
Ionic compounds are often soluble in water, because the attractions formed between ions and water are frequently strong enough to make their solution either exothermic or only slightly endothermic. For example, the solution of sodium hydroxide is exothermic, and the solution of sodium chloride is somewhat endothermic. Even if the solution is slightly endothermic, the tendency to shift to the higher entropy solution often makes ionic compounds soluble in water.
The dividing line between what we call soluble and what we call insoluble is arbitrary, but the following are common criteria for describing substances as insoluble, soluble, or moderately soluble.
Although it is difficult to determine specific solubilities without either finding them by experiment or referring to a table of solubilities, we do have guidelines that allow us to predict relative solubilities. Principal among these is
For example, this guideline could be used to predict that ethanol,
which is composed of polar molecules, would be soluble in water, which
is also composed of polar molecules. Likewise, pentane (C5H12), which
has nonpolar molecules, is miscible with hexane, which also has nonpolar
molecules. We will use the Like Dissolve Like guideline to predict
whether a substance is likely to be more soluble in water or in hexane.
It can also be used to predict which of two substances is likely to be
more soluble in water and which of two substances is likely to be more
soluble in a nonpolar solvent, such as hexane:
Two additional guidelines are derived from these:
It is more difficult to predict the solubility of polar molecular substances than to predict the solubility of ionic compounds and nonpolar molecular substances. Many polar molecular substances are soluble in both water and hexane. For example, ethanol is miscible with both water and hexane. The following generalization is helpful:
Substances composed of small polar molecules, such as acetone and ethanol, are usually soluble in water. (They are also often soluble in hexane.)
Summary of Solubility Guidelines