Dependence of Solubility on pH: Videos & Practice Problems

The activity coefficient (γ) and ionic strength (μ) of a solution are related through the extended Debye-Hückel equation. When the size parameter (α) is unknown, the Davies equation is used, particularly for monovalent ions. Cations can create acidic or neutral solutions, with solubility increasing as pH rises. Conversely, anions can be basic or neutral, with solubility increasing in acidic conditions. Understanding these relationships is crucial for predicting solubility and behavior in various chemical reactions.

${\log (\gamma /1+\alpha )}^2=-0.51z^2\sqrt{\mu }/(1+\sqrt{\mu }-0.3\mu )$

Davies Equation

In the study of solutions, the relationship between the activity coefficient (γ) and ionic strength (μ) is crucial for understanding ionic interactions. The extended Debye-Hückel equation provides a way to calculate the activity coefficient, expressed as:

$$\log(\gamma) = -0.51 \frac{z^2 \sqrt{\mu}}{1 + \alpha \frac{\sqrt{\mu}}{3.05}}$$

In this equation, z represents the charge of the ion, and α is the size parameter of the ion, typically measured in nanometers. However, when the size parameter is unknown, particularly for monovalent ions (ions with a charge of ±1, such as sodium or chloride), the Davies equation is more applicable. The Davies equation is given by:

$$\log(\gamma) = -0.51 z^2 \frac{\sqrt{\mu}}{1 + \sqrt{\mu} - 0.3 \mu}$$

This equation simplifies the calculation of activity coefficients for ions with the same charge magnitude, indicating that ions like +1 and -1 or +2 and -2 will exhibit the same activity coefficient due to the absence of the size parameter. As ionic strength increases, the activity coefficients tend to decrease, reflecting the diminishing effective concentration of ions in solution.

For practical application, consider a scenario where you need to determine the activity coefficient of calcium ions in a 0.025 M solution of calcium phosphate. Since the size parameter is not available, the Davies equation should be utilized to find the activity coefficient for the calcium ion, which has a charge of +2. This exercise reinforces the understanding of how ionic strength and charge influence the behavior of ions in solution.

Davies Equation

To calculate the activity coefficient of calcium ions in a 0.025 molar solution of calcium phosphate, we first need to determine the ionic strength of the solution. The ionic strength (\(I\)) can be calculated using the formula:

\[ I = \frac{1}{2} \sum c_i z_i^2 \]

where \(c_i\) is the concentration of each ion and \(z_i\) is the charge of each ion. In this case, calcium phosphate dissociates into 3 calcium ions (\(Ca^{2+}\)) and 2 phosphate ions (\(PO_4^{3-}\)). Therefore, the concentrations are:

For calcium ions: \(3 \times 0.025 \, \text{mol/L} = 0.075 \, \text{mol/L}\)

For phosphate ions: \(2 \times 0.025 \, \text{mol/L} = 0.050 \, \text{mol/L}\)

Now, substituting these values into the ionic strength formula gives:

\[ I = \frac{1}{2} \left(0.075 \times 2^2 + 0.050 \times 3^2\right) \]

Calculating this results in an ionic strength of \(0.375 \, \text{mol/L}\).

Next, we can use the Davies equation to find the activity coefficient (\(\gamma\)) of the calcium ion. The Davies equation is expressed as:

\[ \log(\gamma) = -0.51 + \frac{z^2 \sqrt{I}}{1 + \sqrt{I}} - 0.3I \]

For calcium ions, where \(z = 2\), substituting the ionic strength into the equation yields:

\[ \log(\gamma) = -0.51 + \frac{2^2 \sqrt{0.375}}{1 + \sqrt{0.375}} - 0.3 \times 0.375 \]

Calculating this step-by-step gives:

\[ \log(\gamma) = -0.51 + \frac{4 \times 0.612372}{1 + 0.612372} - 0.1125 \]

Continuing with the calculations results in:

\[ \log(\gamma) = -0.545283 \]

To find the activity coefficient, we take the antilogarithm:

\[ \gamma = 10^{-0.545283} \approx 0.28 \]

This indicates that the activity coefficient of the calcium ion in this solution is approximately 0.28. It is important to note that this value is an estimate and may vary, especially when dealing with divalent ions like calcium, as opposed to monovalent ions. When the size parameter of the ion is known, one can use the extended Debye-Hückel equation or interpolation methods to determine the activity coefficient more accurately. However, in cases where the size parameter is unknown, the Davies equation is a reliable approach.

Ionic Salts & Solubility

When acids and bases react, they produce water and a salt, which is an ionic compound made up of a cation (positive ion) and an anion (negative ion). The nature of these ions determines whether the resulting solution is acidic, basic, or neutral. Understanding the role of pH in the solubility of these ions is crucial.

Cations can be categorized into transition metals, main group metals, and positive amines. Transition metals must have a charge of +2 or higher to be considered acidic; those with a charge lower than +2 are neutral. For example, manganese (V) iodide contains a transition metal with a +5 charge, making it acidic. Main group metals require a charge of +3 or higher to be acidic; aluminum fluoride, with aluminum at +3, is therefore acidic. Positive amines, such as the methyl ammonium ion, are inherently acidic.

The relationship between cations, pH, and solubility is significant. Increasing the pH of a solution enhances the solubility of acidic salts. This occurs because a higher pH indicates a more basic solution, which can lead to the formation of more soluble compounds. For instance, when aluminum ions (Al³⁺) are present in a solution, increasing the pH by adding hydroxide ions (OH^-) reduces the concentration of hydrogen ions (H⁺). According to Le Chatelier's principle, this decrease in H⁺ concentration shifts the equilibrium to the right, promoting the dissolution of the salt and increasing its solubility.

In summary, the identity of ionic salts and their solubility in relation to pH is a dynamic interplay that highlights the importance of understanding acid-base chemistry in predicting the behavior of ionic compounds in solution.

Ionic Salts & Solubility

When discussing anions, it's important to understand their behavior when combined with hydrogen ions (H⁺). If an H⁺ ion is added to an anion and results in a weak acid, the anion is classified as basic. For example, when the nitrite ion (NO₂^-) from sodium nitrite reacts with H⁺, it forms nitrous acid (HNO₂), which is a weak acid. This indicates that the nitrite ion is basic.

Conversely, if the addition of H⁺ to an anion produces a strong acid, the anion is considered neutral. In the case of potassium chloride, the chloride ion (Cl^-) reacts with H⁺ to form hydrochloric acid (HCl), a strong acid. Since strong acids have very weak conjugate bases, the chloride ion is deemed neutral.

This understanding of anions ties into solubility and pH. Basic anions are more soluble in acidic solutions, which means that lowering the pH (increasing acidity) enhances their solubility. This occurs because a basic ion will react with water, causing the water to donate an H⁺ ion, resulting in hydroxide ions (OH^-) being produced. By decreasing the pH, the added H⁺ ions neutralize the OH^- ions, shifting the equilibrium according to Le Chatelier's principle. This shift encourages the dissolution of more of the basic ion, thereby increasing its solubility.

For acidic salts, the solution should be made more basic to enhance solubility, while for basic salts, the solution should be made more acidic. Amphoteric species, which can act as either acids or bases, follow similar principles. Acidic amphoteric species require an increase in pH to enhance solubility, while basic amphoteric species benefit from a decrease in pH to increase their solubility.

Ionic Salts & Solubility Calculations 1

Barium carbonate (BaCO₃) is a slightly soluble ionic salt formed from the reaction between barium hydroxide (Ba(OH)₂) and carbonic acid (H₂CO₃). Understanding the solubility of barium carbonate in relation to acidity involves examining its dissociation into barium ions (Ba²⁺) and carbonate ions (CO₃^2-). Barium, being a main group metal, does not exhibit acidic properties as it has a charge of less than +3, making it neutral. The carbonate ion, on the other hand, is a basic ion, as it can react with water to form bicarbonate (HCO₃^-) and hydroxide ions (OH^-).

When acidity increases, meaning more hydrogen ions (H⁺) are added to the solution, these hydrogen ions will react with the hydroxide ions present. This reaction reduces the concentration of hydroxide ions, leading to a shift in equilibrium according to Le Chatelier's principle. To counteract the decrease in hydroxide ions, the equilibrium will shift to the right, promoting the dissociation of barium carbonate into its constituent ions. As a result, the solubility of barium carbonate increases in more acidic conditions.

In summary, for basic ionic salts like barium carbonate, an increase in acidity (or a decrease in pH) enhances solubility. This principle is crucial in understanding how the solubility of certain compounds can be manipulated through changes in the acidity of the solution.

Ionic Salts & Solubility Calculations 1

In the context of solubility, certain salts exhibit increased solubility in acidic solutions compared to pure water, particularly when they contain basic ions. Basic ions, which are negatively charged, tend to react with hydrogen ions (H⁺) present in acidic solutions, leading to their enhanced solubility. Examples of basic ions include bromide (Br^-), sulfate (SO₄^2-), sulfite (SO₃^2-), hydroxide (OH^-), and perchlorate (ClO₄^-).

When considering the solubility of these ions in acidic conditions, it is essential to recognize how they interact with H⁺. For instance, the bromide ion (Br^-) reacts with H⁺ to form hydrobromic acid (HBr), a strong acid, which neutralizes the basic character of the bromide ion. Similarly, the perchlorate ion (ClO₄^-) forms perchloric acid (HClO₄), also a strong acid, resulting in a neutralization effect.

On the other hand, the hydroxide ion (OH^-) reacts with H⁺ to produce water (H₂O), which is amphoteric and indicates that OH^- is indeed a basic ion. Therefore, it becomes more soluble in acidic solutions. The sulfite ion (SO₃^2-) also reacts with H⁺ to form hydrogen sulfite (HSO₃^-), which is a basic amphoteric ion, thus increasing its solubility in acidic conditions.

Conversely, the hydrogen sulfate ion (HSO₄^-) is an acidic amphoteric ion. When H⁺ is added, it does not increase in solubility; instead, it may become less soluble due to its acidic nature. Therefore, in summary, the ions that become more soluble in acidic solutions are the hydroxide ion (OH^-) and the sulfite ion (SO₃^2-), while the bromide and perchlorate ions remain neutral and do not increase in solubility.

Here’s what students ask on this topic:

How does pH affect the solubility of acidic and basic salts?

The solubility of acidic and basic salts is significantly influenced by pH. For acidic salts, increasing the pH (making the solution more basic) increases their solubility. This is because the added OH⁻ ions react with H⁺ ions, reducing their concentration and shifting the equilibrium to dissolve more salt. Conversely, for basic salts, decreasing the pH (making the solution more acidic) increases their solubility. The added H⁺ ions react with OH⁻ ions, reducing their concentration and shifting the equilibrium to dissolve more salt. This behavior is explained by Le Chatelier's principle, which states that the system will adjust to counteract changes in concentration.

What is the relationship between ionic strength and activity coefficient?

The activity coefficient (γ) and ionic strength (μ) of a solution are related through the extended Debye-Hückel equation. The equation is given by:

${log}^{\frac{\gamma }{1+\alpha }}=-0.51z^2\mu /(1+\mu -0.3\mu )$

When the size parameter (α) is unknown, the Davies equation is used, particularly for monovalent ions. As ionic strength increases, the activity coefficient generally decreases, indicating that ions are less 'active' in more concentrated solutions.

How do cations and anions affect the pH of a solution?

Cations and anions can significantly affect the pH of a solution. Cations, such as transition metals with a charge of +2 or higher, and main group metals with a charge of +3 or higher, tend to make the solution acidic. Positive amines are also acidic. Anions, on the other hand, can be basic or neutral. If an anion forms a weak acid when combined with H⁺, it is basic. If it forms a strong acid, it is neutral. The pH of the solution can be manipulated to increase the solubility of these ions by making the solution more acidic or basic, depending on the nature of the ion.

What is the Davies equation and when is it used?

The Davies equation is used to estimate the activity coefficient (γ) of ions in a solution when the size parameter (α) is unknown. It is particularly useful for monovalent ions. The equation is:

$log\gamma =-0.51z^2\sqrt{\mu }/(1+\sqrt{\mu })-0.3\mu$

In this equation, z is the charge of the ion, and μ is the ionic strength of the solution. The Davies equation is less accurate for ions with higher charges but provides a good approximation for monovalent ions.

How does Le Chatelier's principle explain the effect of pH on solubility?

Le Chatelier's principle states that a system at equilibrium will adjust to counteract any changes imposed on it. When pH is altered, it affects the concentration of H⁺ or OH⁻ ions in the solution. For acidic salts, increasing the pH (adding OH⁻) reduces H⁺ concentration, shifting the equilibrium to dissolve more salt. For basic salts, decreasing the pH (adding H⁺) reduces OH⁻ concentration, also shifting the equilibrium to dissolve more salt. This principle helps predict how changes in pH will affect the solubility of different salts.