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# Solubility Equilibria

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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.

• 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.StudySmarter 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.StudySmarter 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.StudySmarter 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

1. 'Children's Oral Health', CDC (04/06/2022)

All ionic species are soluble in solution to some extent. However, some are not as soluble as others and quickly reach a saturated solution, in which no further solute will dissolve. Ionic species in a saturated solution exist in a state of equilibrium. Aqueous ions constantly precipitate back into a solid, whilst the ionic solid constantly dissolves into aqueous ions. However, overall, the concentration of dissolved solute remains the same. This is an example of solubility equilibria.

An ionic species' solubility directly relates to the position of its dissolution equilibrium. For fully soluble species, the equilibrium lies far to the right, and so a large amount of the species dissolves in water before the solution reaches a state of equilibrium. For slightly soluble species, the equilibrium lies to the middle or left, and so you only need to add a small amount of the species to water before the solution reaches equilibrium. Once the concentration of dissolved solute equals its solubility, the solution is said to be saturated and is at equilibrium - there is no further net dissolution.

You calculate Ksp using the equilibrium concentrations of the aqueous ions in an ionic solution. We go through the required method more closely in Examples of Solubility Equilibria.

Adding a common ion to a saturated solution decreases the solubility of the ionic solute.

We carry out solubility equilibria calculations using solubility, the solubility product constant, and the ionic species' dissolution equation. Check out Examples of Solubility Equilibria for further detail.

## Solubility Equilibria Quiz - Teste dein Wissen

Question

How does the common ion effect relate to Le Chatelier's principle?

Adding a common ion leads to a disturbance in terms of concentration. This means that according to Le Chatelier's principle the reaction will shift left, towards the reactants, when excess product or common ions are introduced to the solution.

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Question

What exactly is the common ion effect?

The common ion effect occurs when you introduce an already present ion into the solution. For example, if AgCl is already present in the solution, and you introduce NaCl then the common ion in this case is [Cl-].

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Question

What really happens when we add a common ion?

When we add a common ion, the reaction shifts towards the reactants (left) to balance out the excess product, resulting in more precipitation. This means that the common ion effect DECREASES the solubility of ions.

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Question

Having a higher Ksp means the less soluble a compound is.

true

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Question

Bromide (Br) is more soluble when combined with Sodium (Na) than when combined with Copper (Cu)?

true

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Disturbances involve changes in _____, _____,_____.

temperature, concentration, and structure.

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__________ is the solubility product constant or the max amount in which a solute dissolves in a solution.

Common ion effect

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________ we refer to is the overall net reaction. When a reaction is in equilibrium, the rate of the reactants and products are equivalent.

Chemical equilibrium

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Which of the following is the correct definition of pH?

pH is a measure of the concentration of H+ ions in a solution.

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What is the pH scale range?

From pH 0 to 14

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_____ solutions have a pH of less than 7

Acidic

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_____ solutions have a pH greater than 7.

Basic

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A ______ is a solution that has equal concentrations of H+ and OH- ions

neutral solution

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Which of the following is the correct definition for solubility?

The solubility of a substance is the amount of substance that can be dissolved in a given quantity of solvent at a given temperature.

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Substances with similar intermolecular forces tend to be _____ in one another.

miscible

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True or false: when salts are dissolved in water, they completely dissociate into ions.

True

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The _______ is referred to as the equilibrium constant for an ionic solid dissociating into ions in water.

solubility product constant (Ksp

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Acidic salts are more soluble in ______.

basic solutions

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Basic salts are more soluble in ______.

acidic solutions

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_______ is the molar concentration of the solid that dissociates in water.

Molar solubility

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The ______ at which a protein contains a zero net charge is called the isoelectric point.

pH

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Most hemicelluloses are considered more soluble in ______ solutions

basic

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Define solubility.

The maximum concentration of a solute that can be found dissolved in a saturated solution.

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Give the typical units of solubility.

• g L-1
• mol L-1

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Question

What is the solubility product constant?

A type of equilibrium constant that measures the extent of a compound's dissociation in water.

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What is the symbol for the solubility product constant?

Ksp

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What are the units of the solubility product constant?

No units

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Which factor(s) affect the solubility product constant?

Just temperature.

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Question

At 25 °C, CuCl and AgCl have solubility product constants of 1.7 x 10-7 and 1.8 x 10-10 respectively. Which species is more soluble?

CuCl -  its Ksp value is larger.

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The solubility product constant for fully soluble salts is ____.

Very large.

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If a species has a solubility product constant greater than ____, we consider it to be ____.

1, fully soluble.

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The solubility product constant is based on ____.

Concentration.

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Which of the following feature in the solubility product constant expression?

Aqueous ions.

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What is Ksp?

A type of equilibrium constant that measures the extent of a compound's dissociation in water.

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Question

Which of these species has a greater number of moles of ions in their dissolution equation?

1. BaF2
2. Ba(NO3)2

Ba(NO3)2

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Which of the following species is more soluble?

1. BaF2                 Ksp = 1.84 × 10-7
2. Ba(NO3)2          Ksp = 4.64 × 10-3

BaF2

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Question

The solubility of CuBr is x mol L-1. What is the concentration of Cu+ ions at equilibrium, in units M?

x

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The solubility of Ca3(PO4)2 is x mol L-1. What is the concentration of Ca2+ ions at equilibrium, in units M?

3x

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Suppose that CuBr has a solubility of x mol L-1 and Cu2O has a solubility of y mol L-1. Which species' Ksp expression features an exponential with a higher power?

Cu2O

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CuBr has a solubility of 7.92 × 10-5 mol L-1. Find Ksp.

6.27 × 10-9

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To convert from solubility in g L-1 to solubility in mol L-1, you ____.

Divide by molar mass.

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To convert from solubility in g dL-1 to solubility in g L-1, you ____.

Multiply by 10.

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To convert from solubility in kg L-1 to solubility in g L-1, you ____.

Multiply by 1000.

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Which of the following is/are always needed in Ksp calculations?

Solubility in mol L-1.

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What is a soluble species?

One that is able to dissolve in a liquid, typically water, to form a solution.

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True or false? All ionic species are fully soluble.

False - they are all at least partially soluble.

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Give another term for dissolving.

Dissolution

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Define solubility.

The maximum amount of a solute that dissolves in a saturated solution.

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What are the typical units of solubility?

mol L-1

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What is a saturated solution?

A solution in which no more of the solute will dissolve.

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