Acid Base Equilibria 2

Introduction

At this point, you're well familiar with acids and bases and how they affect the water equilibrium (how they change the pH of a solution). Now, we need to consider other materials - things we don't normally think of as being acidic or basic - and how they affect the pH of a solution. In short, we will discuss salts and their effect on pH.

Salts - a review

What is a salt? You probably know the old reaction scheme for a neutralization reaction:

acid + base --> salt + water

So, a salt is an ionic compound formed by an acid/base reaction. A good working definition of a salt for you to use is a salt is an ionic compound that doesn't contain the hydroxide ion, OH^-. (Ionic compounds containing hydroxide are typically strong bases, like NaOH.)

Salts in water

Some salts are soluble. When a salt dissolves in water, it breaks up and forms a solution of its component ions. For example, let's look at the salt ammonium chloride, NH₄Cl.

NH₄Cl(s) --> NH₄⁺(aq) + Cl^-(aq)

So far, so good. But what does this tell us about the acidic or basic characteristics of ammonium chloride? The answer lies in the ions - do the ions function as acids or bases?

We've seen ammonium ion before. We know it as the conjugate acid of ammonia, NH₃ (which means that ammonia is the conjugate base of ammonium):

Ammonia is a weak base (K_b = 1.8x10^-5), so we know that it can exist in solution as a molecule. Since the product of this acid/base reaction is a relatively stable species, ammonium can donate the proton and it is acidic.

Let's consider the chloride ion. Conceivably, chlorine ion could accept a proton (it can't donate one):

The conjugate acid of the chloride ion is HCl, which we commonly know as hydrochloric acid - a strong acid . Hydrochloric acid completely dissociates (breaks up) in aqueous solution. This means that chloride ion will not readily accept a proton (the product is unstable!), and chloride ion is neutral .

The overall pH of the salt, then, would be acidic.

Consider another salt - potassium acetate, KC₂H₃O₂. When it dissolves in water, it breaks up like this:

KC₂H₃O₂(s) --> K⁺(aq) + C₂H₃O₂^-(aq)

Do either (or both) of these ions behave as acids or bases?

Potassium ion, obviously, cannot donate a proton. It's not very likely to accept a proton either. Potassium has no electrons to spare to share with a hydrogen ion and it has a positive charge. So, potassium is neither an acid nor a base by the Bronsted-Lowry definition. It's neutral.

What about the acetate ion, C₂H₃O₂^-? We've seen acetate ion before - as the conjugate base of acetic acid, a common weak acid. Acetic acid is the conjugate acid, then, of acetate ion:

Acetic acid is a weak acid (K_b = 1.7x10^-5), so we know that it can exist in solution as a molecule. Since the product of this acid/base reaction is a relatively stable species, acetate ion can (and does) accept a proton and it is basic.

Potassium acetate, then, is basic.

So, how can you tell if an ion has acidic or basic character? Here are some simple rules:

1. If an ion is the conjugate of a strong acid or a strong base, it is neutral. Chloride ion and nitrate ion are good examples of "neutral" ions. Note that "neutral" in this context refers to acid/base properties, not to charge.

2. If an ion is the conjugate of a weak base, it is acidic. Ammonium ion is a good example.

3. If an ion is the conjugate of a weak acid, it is basic. Acetate ion, fluoride ion, and phosphate ion are good examples.

4. For metal cations like K⁺, Ag⁺, Fe³⁺, Ca²⁺, etc.: Group IA and IIA cations tend to be neutral, while the others tend to be acidic Many transition metal cations are acidic in the Lewis sense - they accept pairs of electrons from Lewis bases.

Calculations: What is the pH of a salt solution?

We've just discussed how to tell whether a salt, when dissolved in water, will form an acidic or a basic solution. That's useful information, but what if you'd like to know something more quantitative - like the pH?

It's rather simple to calculate the pH of most salt solutions if you realize that what you're actually doing is calculating the pH of a weak acid or a weak base. The only tricky bit is actually identifying the weak acid or base you're dealing with. An example:

Calculate the pH of a 0.42 M solution of sodium acetate.

Where do we start? Look at what you get when sodium acetate dissolves in water:

NaC₂H₃O₂(s) --> Na⁺(aq) + C₂H₃O₂^-(aq)

Qualitatively, we can say this:

• Sodium ion is a Group IA cation - it's neutral.

• Acetate ion is the conjugate base of acetic acid - it's basic.

• Therefore, sodium acetate forms a basic solution.

We will ignore the sodium ion , as it is neutral. We will calculate the pH, then, of a solution of 0.42 M acetate ion just like we would any other weak base. First, we write the equilibrium and equilibrium expression

But what's the actual value of K_b? If you try to find K_b for acetate ion in the tables, you won't likely succeed. But you can find the value for the K_a of acetic acid (the conjugate acid of acetate ion). These two are related simply, as the two species differ only by a proton. If you add up the equilibrium of the weak acid and the weak base of any conjugate pair, you end up with the water equilibrium. From this, it's possible to find this relation (which is valid for any conjugate pair):

Plugging in, we can solve for K_b:

K_b = 5.9x10^-10

Now that we know Kb, we have a simple equilibrium problem to solve. As in all of these problems, first express everything in the equilibrium constant expression in terms of one variable:

• [OH^-] = x

• [HC₂H₃O₂] = x

• [C₂H₃O₂^-] = 0.42 - x

Since 0.42 is much larger than the equilibrium constant (5.9x10^-10), we can safely assume that 0.42 - x is approximately equal to 0.42. Now, we plug into the equilibrium expression and solve

x = 1.574x10^-5

Remember that x is equal to the concentration of hydroxide ion . To find the pH, we must use the water equilibrium to find the concentration of hydronium ion .

Plugging in and solving,

[H₃O⁺] = 6.35x10^-10

pH of the 0.42 M NaC₂H₃O₂ solution = 9.20

Practice problem

Find the pH of a solution of 0.42 M ammonium nitrate, NH₄NO₃. The K_b of ammonia (NH₃) is 1.8x10^-5.

Try this one on your own before reading the next line.

The pH of the 0.42 M solution of ammonium nitrate is 4.82 .

Here is the solution to this problem:

Our overall goal is to determine pH. This means that we'll need to calculate the [H₃O⁺] in solution. Our first priority is to determine which of the species present actually influences pH. There are two candidates:

1. Ammonium ion: This ion is the conjugate acid of ammonia, a weak base. We expect this ion to act as an acid. Ammonium ion will readily donate protons to water to form ammonia and lower the pH.

2. Nitrate ion: This ion is the conjugate base of nitric acid, a strong acid. We expect this ion to be neutral. Hydrogen ion will not readily combine with nitrate ion, as the product is unstable and breaks apart immediately. We do not expect the presence of nitrate ion to have a great effect on pH.

The equilibrium we are dealing with in this problem is the equilibrium of ammonium ion:

The only problem is that we're not given the K_a for ammonium ion. Since we do know the K_b of its conjugate base, we can use the water equilibrium to figure out the value of K_a and get on with our solution.

K_a = 5.56x10^-10

Now that we know the value of K_a, we can solve this equilibrium and find [H₃O⁺]. We'll express all concentrations in terms of one variable:

• [NH₄⁺] = 0.42 - x

• [NH₃] = x

• [H₃O⁺] = x

Note that the equilibrium constant is very small, so we don't expect a lot of dissociation of NH₄⁺ here. We'll assume that 0.42 - x = 0.42 as we have done previously.

Plugging into the equilibrium expression, we get:

x = 1.53x10^-5

Since x = [H₃O⁺], the pH is equal to -log(1.53x10^-5). The pH of the solution is 4.82 .

Summary

We have discussed salt solutions and their role as acids or bases in solution. Salts may be acidic, basic, or neutral. You can tell whether a salt is acidic, basic, or neutral based on the ions it contains - are those ions acidic, basic, or neutral? You have also learned that the pH of a salt solution can be easily found once you identify whether the salt is acidic or basic (if it's neutral, the pH is of course 7!). You should be able to calculate the pH of a simple salt solution with ease - if you have trouble, practice on the problems on pages 762 and 763 of your text. See pages 741-744 for some more worked-out examples.

All original site content ©2007 Charles Taylor. Page updated: December 12, 2007.