You're told from a young age that brushing your teeth twice a day is of the utmost importance. It helps keep your mouth clean and prevents acidic conditions that erode teeth. To help you understand the potential consequences of poor oral hygiene, teachers often place a baby tooth in a glass of soda. It may not happen overnight, but leave the tooth long enough, and it eventually dissolves into the fizzy beverage.
You see, the enamel on your teeth is made from a type of calcium phosphate. Calcium phosphate barely dissolves under neutral conditions, but if you decrease the pH, suddenly it becomes a lot more soluble. Sadly, tooth decay is all-too-common - over half of US teenagers have a cavity in one of their permanent teeth1. The dissolution of the calcium phosphate in tooth enamel in acidic conditions is a classic example of solubility equilibria.
- This article is about solubility equilibria in chemistry.
- We'll define soluble and solubility before finding out about saturated solutions.
- After that, we'll explore the equilibria of slightly soluble ionic species.
- This will involve learning about the solubility product constant.
- We'll then investigate factors affecting solubility, such as pH, the common-ion effect, and complex ion formation.
- Finally, we'll introduce you to acid-base solubility equilibria.
Solubility and Simultaneous Equilibria
What is Solubility?
Think of a soluble substance - say, table salt. If you add a spoonful to water, the crystals change from solid to aqueous solution. In other words, they dissolve.
A soluble substance is one that is able to dissolve in a liquid, typically water, to form a solution. We call the dissolved substance a solute.
But simply saying that one substance is soluble whilst another is not is a very simplistic approach. In fact, all ionic species are soluble to some extent, from limestone rock (CaCO3) to the silver bromide (AgBr) used in photography equipment. If you add any solid ionic compound to water, at least some of it will dissolve.
However, some compounds are more soluble than others. Some might be extremely soluble in one set of conditions - say, in an ammonium solution at 350K - but much less soluble in others. In order to compare how soluble different ionic species are in a more quantifiable way, scientists use the term solubility.
Solubility is the maximum amount of a solute that dissolves in a saturated solution. It is typically measured in g L-1 or M L-1.
Solubility values many useful applications, from optimizing chemical reactions to improving drug design and efficacy. Solubility values also theoretically allow us to decide on a line between soluble and insoluble:
- Roughly speaking, species with a solubility above 1 g·dL-1 (10 g·L-1) are considered fully soluble, or simply just soluble.
- Likewise, species with a solubility below 0.1g·dL-1 (1 g·L-1) are considered insoluble.
- Species with a solubility that falls somewhere between these two values are considered slightly soluble.
Saturated Solutions
We used the term saturated solution in the definition of solubility. What does this mean?
A saturated solution is one in which no more of the species will dissolve.
Once a solution is saturated, it doesn't matter how much more ionic solid you add to it - nothing will change. It is easy to determine whether a solution is saturated or unsaturated using the solute's solubility.
- An ionic solute will dissolve in solution if its concentration is less than its solubility.
- If a solute's concentration in solution equals its solubility, no further solute will dissolve. Instead, it remains as an undissolved solid.
Equilibria of Slightly Soluble Ionic Compounds
We note that saturated solutions form an equilibrium. Dissolving is also known as dissociation or dissolution. Dissolution is a reversible reaction. We can represent the dissolution of the imaginary ionic species, AB, with the following equation:
$$AB(s)\rightleftharpoons A^+(aq)+B^-(aq)$$
Like all reversible reactions, dissolution can reach a point of equilibrium. For dissolution reactions, equilibrium is achieved when we reach a saturated solution. For example, consider what happens when we gradually add an ionic species to water.
- When you first add the solute to water, it dissolves, and the solid turns into aqueous ions.
- As the ionic solute keeps on dissolving we say you have an unsaturated solution.
- A fully soluble species dissociates almost entirely in solution, and so their equilibrium lies far to the right - so far that we can generally treat the reaction as irreversible. Until we reach a saturated solution, we don't achieve equilibrium, and so the solid keeps on dissolving.
- But if you use a slightly soluble species, the solution rapidly becomes saturated.
- Once you've formed a saturated solution, you've reached equilibrium. We're able to form a saturated solution quickly for a slightly soluble species because they dissociate only partially in solution.
So, if the solution is unsaturated, then the forward dissolution reaction is favored, and the solute keeps dissolving. But if the solution is saturated, then it exists in a state of equilibrium, and no more of the solute dissolves. But note that like all equilibria, solubility equilibria are dynamic - both the forward and backward reactions are constantly ongoing. However, at equilibrium, the rates of the two reactions are equal and there is no net dissolution. This means that the concentration of dissolved aqueous ions remains constant.
Fig. 1: The dissociation of soluble and slightly soluble species in solution. Soluble species dissociate almost entirely in solution, whilst slightly soluble species only partially dissociate.Vaia Original
We can measure the extent of reversible dissolution reactions using a specific equilibrium constant known as the solubility product constant. We can also change the position of a solubility equilibrium by changing some of its conditions. We'll spend the rest of this article introducing you to both of these ideas.
Solubility Equilibria and the Solubility Product Constant
Dynamic equilibria are characterized by fixed relative amounts of products and reactants. We can represent the unchanging ratio of products to reactants using an equilibrium constant.
Solubility equilibria have their own specific equilibrium constant called the solubility product constant, Ksp, that tells you the relative equilibrium concentration of aqueous ions in solution. The solubility product constant gives you information on the proportion of a species that dissolves at equilbrium and so helps you infer its solubility.
The solubility product constant (Ksp) is a type of equilibrium constant that tells you the extent of a compound's dissociation in water. It is a measure of the concentration of aqueous ions in solution.
We write expressions for Ksp like we would for any other equilibrium constant. This means working with concentration, and so ignoring any pure solids or liquids. For example, for the dissolution equation \(A_aB_b(s)\rightleftharpoons aA^{b+}(aq)+bB^{a-}(aq)\) , Ksp has the following expression:
$$K_{sp}={[A^{b+}]_{eqm}}^a\space {[B^{a-}]_{eqm}}^a$$
Here are a few important things that you should know about the solubility product constant:
- Ksp has no units.
- Like with all equilibrium constants, Ksp is unique for a certain species at a specific temperature. If you change the temperature, you change the value of Ksp.
- Ksp isn't affected by variables such as concentration and pH, it is a constant.
- The greater the value of Ksp, the greater the solubility of the ionic species. However, two species with the same solubility may not necessarily have the same Ksp value.
- We typically consider any species with a Ksp value greater than 1.0 to be fully soluble.
Factors Affecting Solubility Equilibria
It is important to not get solubility mixed up with the solubility product constant (Ksp) in order to understand how they are affected by different variables.
- Ksp measures the concentration of aqueous ions at equilibrium and thus the extent of the solute's dissociation.
- An ionic species Ksp value is always the same at a specific temperature but can change when the pH changes or when in the presence of common ions.
- The magnitude of Ksp reflects a species' solubility, but two species with the same solubility don't necessarily have the same value for Ksp.
Changing either the pH or adding common ions to an ionic solution disturbs the equilibrium and causes more of the solute to dissolve or precipitate in order to reach equilibrium again, thus changing its solubility. We can predict these changes using Le Chatelier's Principle. But note that in all cases, the position of the equilibrium shifts in order to offset the change and to keep Ksp constant.
pH
Changing the pH of a solution affects the solubility of any ionic species with a basic anion. This can be explained by a change in concentration.
For example, consider what happens when you acidify a saturated solution containing the slightly soluble compound Ca(OH)2. Ca(OH)2 dissociates into Ca2+ and OH- ions. The solution is initially at equilibrium and so the overall concentration of aqueous solute ions remains constant. However, when we add acid, the dissolved basic OH- ions react with the newly-added acidic H+ ions, decreasing [OH-]. Suddenly, the concentration of aqueous ions in our dissolution equation decreased. Le Chatelier's principle dictates that the position of the equilibrium shifts in order to counteract this disturbance by increasing the overall concentration of dissolved Ca(OH)2. As a result, more of the solute dissolves, and thus its solubility increases. Overall, Ksp remains constant.
Fig. 2: a) A saturated solution is at equilibrium.b) We add hydrogen ions (green), which react with basic solute anions (orange). The concentration of dissolved solute decreases.c) More of the solid ionic species dissolves, restoring the equilibrium.Vaia Originals
Solubility and Simultaneous Equilibria
You see a similar change in solubility with some ionic species if you add in an appropriate ligand. Ligands can react with certain transition metal cations to form complex ions. This decreases the concentration of the original aqueous solute and so takes the system out of equilibrium. Thus, more of the solute dissolves in order to reach equilibrium once again. Overall, adding in a ligand that is able to form a complex ion with the solute means that solubility increases, but once again, Ksp remains the same.
The Common-ion Effect
The solubility of a species decreases if we add in a common ion. Once again, this is all to do with a change in concentration.
A common ion is an ion that is found in two different species.
For example, consider what happens if you add the fully soluble compound CaCl2 to our original saturated solution of Ca(OH)2 that we considered above. CaCl2 dissociates completely in solution, so we have essentially just increased the concentration of Ca2+ ions and Cl- ions. This is problematic because Ca2+ is also found in our ionic solute - it is a common ion. Therefore, the concentration of aqueous ions in our dissolution equation has increased and the system is no longer at equilibrium. Le Chatelier's principle tells us that the position of the equilibrium shifts to counteract this disturbance by decreasing the overall concentration of dissolved Ca(OH)2. As a result, more of the solute precipitates and so its solubility decreases. Overall, Ksp remains constant.
Fig. 3: a) A saturated solution is at equilibrium.b) Addition of common ion (red) increases concentration of dissolved solute.c) Some of the dissolved solute precipitates, restoring equilibrium.Vaia Original
Acid Base Solubility Equilibria
Acids and bases also have the ability to form an equilibrium in aqueous solution. There are a few different definitions of acids and bases, but both species are both characterized by their interaction with hydrogen ions (H+) when dissolved in solution.
- Acids dissociate and donate hydrogen ions.
- Bases dissociate and accept hydrogen ions.
Some acids and bases dissociate completely when aqueous. But some only dissociate partially. We call species that only partially dissociate weak acids and bases, and like slightly soluble ionic compounds, they form an equilibrium.
For a weak acid:
$$HA(aq)\rightleftharpoons H^+(aq)+A^-(aq)$$
For a weak base:
$$B(aq)+H_2O(l)\rightleftharpoons HB^+(aq)+OH^-(aq)$$
As you might now expect, we can represent the extent of weak acid and base dissociation using equilibrium constants, known respectively as Ka and Kb:
$$K_a=\frac{[H^+]_{eqm}[A^-]_{eqm}}{[HA]_{eqm}} \qquad K_b=\frac{[HB^+]_{eqm}[OH^-]_{eqm}}{[B]_{eqm}}$$
Solubility Equilibria - Key takeaways
- A soluble substance is one that is able to dissolve in a liquid, typically water, to form a solution. We call the dissolved substance a solute.
- All ionic compounds are partially soluble. Solubility is the maximum amount of a solute that dissolves in a saturated solution.
- Solubility is typically measured in g L-1 or mol L-1.
- An ionic solute dissolves in solution if its concentration is less than its solubility. If its concentration in solution equals its solubility, no further solute dissolves. A solution in which no further solute will dissolve is known as a saturated solution.
- Dissolution is a reversible reaction. When solutions become saturated, they reach a point of equilibrium.
- Fully soluble species dissociate almost completely in solution.
- Slightly soluble species partially dissociate in solution.
- When a solution is saturated, and so at equilibrium, there is no net dissolution. As a result, the concentration of aqueous solute remains constant.
- We can measure the extent of dissolution of a slightly soluble species using a specific equilibrium constant called the solubility product constant (Ksp).
- For the dissolution reaction \(A_aB_b(s)\rightleftharpoons aA^{b+}(aq)+bB^{a-}(aq)\) , Ksp has the expression\(K_{sp}={[A^{b+}]_{eqm}}^a\space {[B^{a-}]_{eqm}}^a\)
- Ksp has no units and is constant for a certain ionic species at a specific temperature.
- Factors such as pH and the presence of common ions affect solubility but do not change the value of Ksp. In all cases, the position of the equilibrium shifts to keep Ksp the same.
References
- 'Children's Oral Health', CDC (04/06/2022)
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