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# Solubility and Factors Affecting Solubility

7-Up. Coca-Cola. Sprite. Pepsi. and Lava Lamps. Which of these things is not like the others? Take as much time as you need... Alright, time's up. The answer seems obvious, right? The first four are all refreshing carbonated drinks that you probably drink on occasion and the last one is a novelty item that you (hopefully) will never consume. But despite this difference, all of these do share something important in common. In fact, what they share is what makes each physically possible. This fundamental similarity is their relationship with the concept of solubility. More than that, solubility plays a huge role in our reality, extending far beyond explaining carbonation, lava lamps and instant hand-warmers.

### Introduction

Lava lamps usually consist of two immiscible liquids (both liquids do not mix) of differing density. That is, the solute in this instance is insoluble with the solvent - meaning that its value of solubility is ~0, so essentially none of the solute is dissolved in the solvent. Solubility can range from insoluble (as in the case of lava lamps) to very soluble (salt in water).

### Important Terms

• The solubility of a solute is the concentration of the saturated solution.
• saturated solution a solution in which the maximum amount of solute has dissolved in the solvent at a given temperature.
• An unsaturated solution a solution in which the solute has completely dissolved in the solvent.
• supersaturated solution is a solution in which the amount of solute dissolved under given conditions exceeds it's supposed upper limit.
• Le Châtelier's Principle states that when a system in chemical equilibrium is stressed, the system will shift in a way that alleviates the stress.
• Endothermic reaction: a reaction in which heat is absorbed (ΔH>0)
• Exothermic reaction: a reaction in which heat is released (ΔH < 0)

### Solubility

is defined as the upper limit of solute that can be dissolved in a given amount of solvent at equilibrium. In such equilibrium, Le Chatelier's Principle can be used to explain most of the main factors that affect solubility. Furthermore, solubility is a physical process (meaning that it does not involve changes to chemical identities) that can be quantitatively measured.

### Le Châtelier's Principle

Le Châtelier's Principle  dictates that the effect of a stress upon a system in chemical equilibrium can be predicted in that the system tends to shift in such a way as to alleviate that stress.

### Factors that Affect Solubility

#### Solute-Solvent Relations

The relation between the solute and solvent is very important in determining solubility. Strong solute-solvent attractions equate to greater solubility while weak solute-solvent attractions equate to lesser solubility. In turn, Polar solutes tend to dissolve best in polar solvents while non-polar solutes tend to dissolve best in non-polar solvents. In the case of a polar solute and non-polar solvent (or vice versa), it tends to be insoluble or only soluble to a miniscule degree. The general rule to remember is "Like Dissolves Like".

#### Common-Ion Effect

The common-ion effect is a term that describes the decrease in solubility of an ionic compound when a salt that contains an ion that already exists in the chemical equilibrium is added to the mixture. This effect best be explained by Le Châtelier's Principle. Imagine if we were add the slightly soluble ionic compound Calcium Sulfate $$CaSO_4$$ into water. The net ionic equation for the resulting chemical equilibrium would be:

$CaSO_4(s) \rightleftharpoons Ca^2+ (aq) + SO_4^2- (aq)$

Calcium Sulfate is slightly soluble meaning that at equilibrium, most of the calcium and sulfate exists in the solid form of Calcium Sulfate.

Let's say that we now add the soluble ionic compound Copper Sulfate ( $$CuSO_4$$) into the solution. Copper Sulfate is soluble, therefore its only important effect on the net ionic equation is the addition of more Sulfate $$SO_4^2-$$ ions.

The Sulfate ions dissociated from Copper Sulfate are already present (common to) in the mixture from the slight dissociation of Calcium Sulfate. Thus, this addition of Sulfate ions places stress on the previously established equilibrium. Le Châtelier's Principle dictates that the additional stress on this product side of the equilibrium results in the shift of equilibrium towards the reactants side in order to alleviate this new stress. In shifting towards the reactant side, we can see that from the above equation that the solubility of the slightly soluble Calcium Sulfate $$CaSO_4$$ is reduced even further.

#### Temperature

Temperature changes affect the solubility of Solids, Liquids and Gases differently. However, those effects have only finitely determined for Solids and Gases.

##### Solids

The effects of temperature on the solubility of solids differ depending on whether the reaction is endothermic or exothermic. Using Le Chatelier's Principle, we can determine the effects of temperature in both scenarios.

First, imagine an endothermic reaction (heat is on the reactants side where the solid is). Increasing the temperature would result in stress on the reactants side from the additional heat. Le Châtelier's Principle predicts that the system would shift towards the product's side in order to alleviate this stress. By shifting towards the product's side, more of the solid is dissociated when equilibrium is again established - which equates to increased solubility.

Second, imagine an exothermic reaction (heat is on the products side where the dissociated ions from the solid are). Increasing the temperature would result in stress on the products side from the additional heat. Le Châtelier's Principle predicts that the system would shift towards the reactant's side in order to alleviate this stress. By shifting towards the reactant's side, less of the solid is dissociated when equilibrium is again established - which equates to decreased solubility.

##### Liquids

In the case of liquids, there is no defined trends for the effects of temperature on the solubility of liquids. As such, you will probably never encounter liquid-liquid solute-solvent mixtures in problems.

##### Gases

In understanding the effects of temperature on the solubility of gases, it is first important to remember that temperature is the measure of the average kinetic energy. As temperature increases, kinetic energy increases. The greater kinetic energy results in greater molecular motion of the gas particles. As a result, the gas particles dissolved in the liquid are more likely to escape to the gas phase and the existing gas particles are less likely to be dissolved. The converse is true as well. So, the trend now appears as follows : increased temperatures mean lesser solubility and decreased temperatures mean higher solubility.

Using Le Chatelier's Principle, we can better conceptualize these trends. First, note that the process of dissolving gas in liquid is usually exothermic. As such, increasing temperatures would result in stress on the product's side (since heat is on the product's side). In turn, Le Chatelier's Principle predicts that the system will shift towards the reactant's side in order to alleviate this new stress. Consequently, the equilibrium concentration of the gas particles in gaseous phase would increase - which equates to lowered solubility.

Conversely, decreasing temperatures would result in stress on the reactant's side (since heat is on the product's side). In turn, Le Châtelier's Principle predicts that the system will shift towards the product's side in order to compensate for this new stress. Consequently, the equilibrium concentration of the gas particles in gaseous phase would decrease - which equates to greater solubility.

#### Pressure

The effects of pressure are only significant in affecting the solubility of gases in liquids.

##### Solids & Liquids

The effects of pressure changes on the solubility of solids and liquids are negligible.

##### Gases

The effects of pressure on the solubility of gases in liquids can best be described through a combination of Henry's Law and Le Châtelier Principle. Henry's Law dictates that when temperature is constant, the solubility of the gas corresponds to it's partial pressure. Consider the following formula of Henry's Law:

$p = k_h \; c$

where p is the partial pressure of the gas above the liquid, $$k_h$$ is Henry's Law constant, and c is the concentrate of the gas in the liquid.

From this formula, you can see that (at a constant temperature) when the partial pressure decreases, the concentration of gas in the liquid will decrease as well - which means that solubility also decreases. Conversely, when the partial pressure increases in such a situation, the concentration of gas in the liquid will increase as well - which means that solubility also increases. Extending the implications from Henry's Law, we can now enhance our understanding of Le Châtelier's Principle in predicting the effects of pressure on the solubility of gases. Le Chatelier's Principle dictates that a system will shift in such a way as to alleviate stress.

Consider a system consisting of a gas that is partially dissolved in liquid. An increase in pressure would result in greater partial pressure (since the gas is being further compressed). This increased partial pressure means that more gas particles will enter the liquid (which means less gas above the liquid, so partial pressure decreases) in order to alleviate the stress created by the increase in pressure - which equates to greater solubility.

The converse case in such a system is also true, as a decrease in pressure equates to more gas particles escaping the liquid to compensate.

 Example

Consider the following system that is in equilibrium:

$CO_2 (g) + H_2O (l) \rightleftharpoons H_2CO_3 (aq)$

What will happen to the solubility of the carbon dioxide if -

1. Temperature is increased?
2. Pressure AND Temperature are increased?
3. Pressure is increased BUT Temperature is decreased?
4. Pressure is increased?

Solution:

1. The reaction is exothermic, so an increase in temperature means that solubility would decrease.
2. An increase in pressure and an increase in temperature in this reaction both equate to greater solubility. Thus, the solubility would increase.
3. The change in solubility cannot be determined from the given information.
4. An increase in pressure results in more gas particles entering the liquid in order to decrease the partial pressure. Therefore, the solubility would increase.

 Example

Bob is in the business of purifying silver compounds to extract the actual silver. He is extremely frugal and hoards every penny. One day, he is finds a barrel containing a saturated solution of silver chloride. Bob has a bottle of water, a jar of table salt $$NaCl_(s)$$, and a bottle of vinegar $$CH_3COOH$$. Which of the 3 should Bob add to the solution to maximize the amount of solid silver chloride (so he wants to minimize the solubility of the silver chloride)?

Solution:

Bob should add table salt to the solution. According to the common-ion effect, the additional $$Cl^-$$ ions added would reduce the solubility of the silver chloride, which maximizes the amount of solid silver chloride.

 Example

Allison has always wanted to start her own carbonated drink company. Recently, she opened a factory to produce her drinks. She wants her drink to "out-fizz" all the competitors. That is, she wants to maximize the solubility of the gas in her drink. Under what conditions (high/low temperature, high/low pressure), would it best allow her to achieve this goal?

Solution: She would be able to maximize the solubility of the gas in her drink (maximize fizz) when the pressure is high and temperature is low.

 Example

Butters is trying to increase the solubility of a solid in some water. He begins to frantically stir the mixture. Should he continue stirring? Why or Why not?

Solution: He stop stop stirring. Stirring only affects how fast the system will reach equilibrium and does not affect the solubility of the solid at all.

 Example

With respect to Henry's Law, why is it ideal to open a can of soda in a low pressure environment?

Solution: The lower pressure equates to greater solubility - therefore, the soda will stay carbonated for longer.

### References

1. Petrucci, Harwood, Herring. General Chemistry: Principles & Modern Applications. 8th ed. Upper Saddle River, New Jersey: Pearson/Prentice Hall, 2002.
2. Zumdahl, Steven S. Chemical Principles. 4th ed. Boston: Houghton Mifflin Company, 2002.
3. Yalkowsky, Samuel H. Solubility and Solubilzation in Aqueous Media, 1st Edition. Washington D.C.: An American Chemical Society Publication, 1999.
4. Letcher, Trevor. Thermodynamics, Solubility and Environmental Issues, 1st Edition. Amsterdam: Elsevier Science, 2007.
5. Yalkowsky, Samuel H. Handbook of Aqueous Solubility Data, 1st Edition. Florida: CRC Press, 2003.
6. Butler, James N. Ionic Equilibrium: Solubility and pH Calculations, 1st Edition. New Jersey: Wiley-Interscience, 1998.

### Contributors

• Erica Tran (UCD), Dennis Liu (UCD)