Dependence of Solubility on pH - Online Tutor, Practice Problems & Exam Prep

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

So in the past, we learned that our activity coefficient, which is represented by gamma, and ionic strength, which is represented by mu, of a solution could be closely and accurately related by using the extended Debye-Hückel equation. Here, we'd say that logγ1+α/1α×√μ305 . When the size parameter of the ion, which is alpha, is unknown, we're going to use instead the Davies equation. Here, because of the lack of a size parameter, this formula is most useful for monovalent ions. So ions with a charge of 1, plus or minus. Examples would be sodium or chloride ions. Now, you could also use larger charges, but there tends to be greater deviation from a credible value, but you can still use larger charged ions as well.

Here, the equation is reformatted into logγ=-0.51z2√μ1+√μ-0.3×μ. Here we have our ionic strength values. They're increasing as we go down. Here, we have our charges, plus or minus 1, plus or minus 2, plus or minus 3, and our activity coefficients. Notice that as your ionic strength is increasing, your activity coefficients are decreasing.

Now, we're going to say here from the Davies equations, all ions with the same magnitude in charge. So if 2 ions, one is plus 1 and the other one is minus 1 or plus 2 and minus 2, they will have the same activity coefficient, which is what we're seeing here. Plus or minus, it really doesn't matter. Again, that's because of the lack of an alpha value. We can group things together and make our list overall smaller. Traditionally, when we're using the extended Debye-Hückel equation, we segregate ions based on their charge as well as the value of their charge.

Now that we've seen this, attempt to do the practice question that's left here at the bottom of the page, where we're asked to determine what the activity coefficient is of calcium ion when we have 0.025 molar of calcium phosphate. Here, we don't have the size parameters, so we're not going to be able to use our typical extended Debye-Hückel equation. Try this question out. If you get stuck, don't worry. Come back and see how I answer the same question.

Davies Equation

So here it says calculate the activity coefficient of calcium ion in 0.025 molar of calcium phosphate. We're going to have to utilize the Davies equation at some point. But first, we need to understand what our ionic strength will be. We're going to say here ionic strength equals half concentration 1 times charge 1 squared plus concentration 2 times charge 2 squared. We're going to say that this breaks up into 3 calcium ions plus 2 phosphate ions. Because there are 3 calcium ions, it's 3 times 0.025 molar, which is going to give me 0.075 molar. There are 2 phosphates, so that's 2 times 0.025 molar to give me 0.050 molar. We're going to say our ionic strength equals half. So the concentration of calcium ions times the charge squared of calcium plus the charge number. The concentration of phosphate ions times the charge squared. When we do all that, we get an ionic strength of 0.375 molar. Now with that ionic strength, we can plug it into each one of these ionic strengths here. We use the charge of the calcium ion to find the log of our activity coefficient.

log y = - 0.5 1 + 2 2 √ 0.375 1 + √ 0.375 , 0.3 · 0.375

Then we're going to say log of our activity coefficient equals negative 0.545283. We don't want the log of our activity coefficient, we just want the activity coefficient. So, activity coefficient equals 10 to the negative 0.545283, which is going to give me 0.28 as my activity coefficient. So here, utilizing the equation, we're able to find the activity coefficient of calcium ion. Here, these values are just estimates. There will be deviations from it if we venture away from monovalent ions. So here, our charge is plus 2, so it's not monovalent. It's divalent because its charge is 2. This is how we get this activity coefficient of 0.28. Remember, we rely on the Davies equation if we don't know what the size parameter for the ion is. If we do know the size parameter, then we'd rely on things such as interpolation or the extended Debye-Hückel equation to help us find the activity coefficient for a specified ion. Remember the 2 equations, the extended Debye-Hückel equation is when we know what the size parameter is, we can use interpolation as well to help us determine what the activity coefficient.

Ionic Salts & Solubility

Remember when we talked about acids and bases reacting with one another, they help to create water and a salt. That salt represents an ionic compound that's composed of a positive ion, which is our cation, and a negative ion, which is our anion. Remember, based on the identities of these, we can make either an acidic, basic or neutral solution. Now we're going to see through the creation of these ions how pH plays a factor in their solubility.

So if we take a look at cations which are positive ions, remember they're grouped as transition metals, main group metals as well as positive amines. Remember for transition metals, they have to be plus 2 or higher in charge to be acidic. If they're less than plus 2, then they are neutral. Here we have manganese(II) iodide and we have 5 iodides. Remember, we're only concerned with the positive ion for now. Since it's a transition metal with a charge of plus 2 or higher, it is acidic. The main group metals, they have to be plus 3 or higher in charge to be acidic. If they're less than plus 3, then they would be neutral. Here we have aluminum fluoride, aluminum is in group 3A so it's plus 3, and then we have our 3 fluoride ions. Because aluminum is plus 3, it is high enough that it is acidic. Finally, remember, positive amines are automatically acidic. Here, we have the methylammonium ion as our positive ion and we have the chloride ion. This would be acidic.

Now, how does this tie into solubility and pH? Well, we're going to say remember cations make either an acidic or neutral solution. We're going to say here, if we increase the solubility, that's a direct result of increasing your pH. If you make the solution more basic, it makes your acidic salt more soluble. That's because if we think about it, let's say we have here aluminum 3 plus which is an acidic ion. An acidic ion would help to form acidic ions in solution. If I increase the pH, that means I'm adding OH^-. OH^- here is going to consume this H⁺ ion and decrease its amount. If we decrease its amount according to Le Chatelier's principle, our reaction would shift to the right in order to replenish the ion that we just lost. That's how the identity of our ionic salt can be affected by the presence of our pH.

Now that we've seen cations, click on to the next video to look at anions.

Ionic Salts & Solubility

Now, for anions, we're going to say here for an anion, we're going to add H⁺ ion to it. If you add any H⁺ ion to an anion and you create a weak acid, then your negative ion is basic. Here, we have sodium nitrite. Nitrite ion is our negative ion. We add an H⁺ to it to give us nitrous acid. Nitrous acid is a weak acid. Because it's a weak acid, that means that the negative ion is basic. If we add an H⁺ ion to the anion and you create a strong acid though, that means your negative ion is neutral. Here, our negative ion in potassium chloride is the chloride ion. Add an H⁺ to it, gives us HCl. Now, HCl is a strong acid. Remember, if you're strong as an acid, that means your conjugate base is incredibly weak, so weak that we just say that you're neutral.

Now, how does this tie into solubility and pH? Again, remember anions are basic or neutral. Here to increase the solubility of a basic ion, we want the solution to be acidic, so we want decreasing the pH because remember, what's happening here is, an anion that is basic would react with water and because it's basic, that means water would act as an acid and donate an H⁺ to the basic ion. Here, we would get this plus OH^-. If you decrease the pH of a solution, that means that you're making it more acidic by adding H⁺. That H⁺ would actually counteract or neutralize this OH^-. We're losing product. According to Le Chatelier's principle, to replenish that ion, we'd have to move in the forward direction to make more. This means that more of this ion would have to break up in order to form that product and thereby increase the solubility of that particular ion.

Remember, for acidic salts, we want to make the solution more basic to make it more soluble. Basic salts, you want to make the solution more acidic to increase solubility. And remember for amphoteric species, we have our acidic amphoteric species and our basic amphoteric species. They themselves also follow the same type of guidelines. Since they're acidic, you would want to increase the pH to make it more basic in order to increase their solubility. And these guys which are basic, you'd want to decrease the pH to make it more acidic and thereby increase their solubility.

Ionic Salts & Solubility Calculations 1

So, here it states that barium carbonate is the slightly soluble ionic salt that results from the reaction between barium hydroxide and carbonic acid. Identify the effect of increasing acidity on the solubility of the given compound. Well, here we have barium carbonate and it breaks up into barium ion and your carbonate ion. Here, barium is a main group metal. Remember, main group metals have to be plus 3 or higher in order to be acidic. Because it's less than plus 3 or higher, it is neutral. Carbonate ion itself is a negative ion. Here, it's going to be a basic ionic salt. That's because if hydrogen carbonate or bicarbonate is basic in terms of amphoteric species, this which has even one less hydrogen would also be basic. Because it's basic, it would react with water. It would act as the base. Water would act as the acid donating an H⁺ to it. We would create HCO₃^- + OH^-. If we're increasing the acidity, that means we're adding H⁺ which does what? It's going to neutralize this hydroxide ion. Because it's going to neutralize that hydroxide ion, it's going to decrease in amount and according to Chatelier's principle, we have to shift to the right to replenish it, thereby making this compound overall more soluble because it's going to break up to form more of these products. Now, in this question, we're increasing the acidity of the compound. Technically, this is basic and OH^- is basic, but OH^- is a stronger base and therefore would react even quicker and more so with any H⁺ that's added to my solution. So that's why we're focusing on the effect of OH^- in terms of increasing acidity. So just remember, if you're a basic ionic salt, your solubility will increase as the pH decreases and the solution overall becomes more acidic. Now that you've seen this, attempt to do the example question left on the bottom.

Ionic Salts & Solubility Calculations 1

So here it states which salts will be more soluble in an acidic solution than in pure water. If you're in an acidic solution, remember that you'll be affected by that if you are a basic ion. Basic ions become more soluble in an acidic solution. Remember, your basic ions are your negative ions. So, here, these are Br^-, SO₄^2-, SO₃^2-, OH^-, and ClO₄^-. First of all, the bromide ion, when you add an H⁺ to it, gives you HBr, which is a strong acid. So that means this negative ion is neutral. So that's out. For the perchlorate ion, the same thing, add an H⁺ to it. You create perchloric acid, which is a strong acid, so the negative ion is neutral.

If we look at the other options, OH^- is a basic ion, so of course, it's going to be affected by an acidic solution. Thus, when you add H⁺ to it, you create water, which is amphoteric and therefore weak. So this would be one answer. Here, you add an H⁺ to it. You're going to create HSO₃^-, which is a basic amphoteric ion. Since it's basic, it will be affected. Then here, add an H⁺ to this. This hydrogen sulfate or bisulfate is actually an acidic amphoteric ion, so it will not be affected in the same way. Since it's an acidic amphoteric ion, it won't become more soluble; it'll become less soluble in an acidic solution.

So, out of the choices given, only options C and D are the correct choices.

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.