Lesson 5: Hydrolysis of Salts

Part b: K_a and K_b Values of Conjugate Acid-Base Pairs

Part a: Predicting and Explaining the Acidity Level of Salts
Part b: K_a and K_b Values of Conjugate Acid-Base Pairs

 

The Big Idea

This lesson explains how conjugate acid–base pairs are connected through K_a and K_b values.  Learn how to use the values to determine if a salt is acidic, basic, or neutral.

 

Conjugate Acid-Base Pairs

The concept of conjugate acid-base pairs is central to the Brønsted-Lowry model of acids and bases. We have been discussing them since Lesson 1. (See Conjugate Acid-Base Pairs if you need a refresher.) In Lesson 5 we learned that evaluating how the cation and anion of a salt hydrolyzes requires that we identify the ion as being (or not being) the conjugate acid of a weak base or the conjugate base of a weak, monoprotic acid. We presented the ground rules for this in Lesson 5a – review How to Predict the Acidity Level of Salts. On this page, we will learn a mathematical trick that will be useful in evaluating tiebreaker  cases and in evaluating salts whose anion is the conjugate base of a polyprotic acid.
 
 
 

Dissociation Constants – K_a and K_b

Acid and base dissociation constants (K_a and K_b) provide a measure of the degree to which a dissociation reaction occurs. A weak acid with a larger K_a value is a better proton donor and produces a more acidic solution (lower pH) than a weak acid with a smaller K_a value. Similarly, a weak base with a larger K_b value is a better proton acceptor and produces a more basic solution (higher pH) than a weak base with a smaller K_b value. Thus, knowing K_a and K_b values provides a meaningful indicator of the degree to which a reaction will occur.
 
Every weak acid has a K_a value. The conjugate base of the weak acid has a K_b value. The K_a and K_b values for a conjugate acid base pair are related by the equation:

K_a • K_b = 1.0 x 10^-14

The 1.0x10^-14 is the ion product constant (K_w) of water. Using this equation, the K_b value of the conjugate base of any weak acid can be calculated. Similarly, the K_a value of the conjugate acid of any weak base can be calculated. We have organized a collection of K_a and K_b values for acids and bases on our Reference page. Here are two examples:
 
 

Example 1 – Calculating the K_b of a Conjugate Base

Hydrofluoric acid, HF, is a weak acid with a K_a value of 6.6x10^-4. It dissociates in water to form F^- ions. The F^- is the conjugate base of HF. As a base, it has a K_b value. The K_b value of F^- is calculated as follows:

K_b = K_w/K_a = (1.0x10^-14)/(6.6x10^-4) = 1.5x10^-11

 
 
 

Example 2 – Calculating the K_a of a Conjugate Acid

Ammonia, NH₃, is a weak base with a K_b value of 1.8x10^-5. It dissociates in water to form NH₄⁺ ions. The NH₄⁺ is the conjugate acid of NH₃. As a base, it has a K_b value. The K_b value of NH₄⁺ is calculated as follows:

K_a = K_w/K_b = (1.0x10^-14)/(1.8x10^-5) = 5.6x10^-10

 

 

Evaluating the Acidity Level of Salts Using K_a and K_b Values

Sometimes a salt contains an acidic cation and a basic anion. In Lesson 5a (See What if a Salt Contains an Acidic and a Basic Ion?), we referred to these situations as tiebreaker cases.  Tiebreaker cases occur when the two ions of a salt are the conjugate base of a weak acid and the conjugate acid of a weak base
 
For tiebreaker cases, the K_a and K_b values can be calculated as done in Examples 1 and 2. K_a indicates the degree to which the conjugate acid hydrolyzes to produce H₃O⁺ ions. The K_b indicates the degree to which the conjugate base hydrolyzes to produce OH^- ions. The most powerful of the two ions is the one that influences the pH level the most and wins the tiebreaker.
 
The following three rules could be used to make the decision as to whether the salt is acidic, basic, or neutral.

• If the K_a of the conjugate acid is larger than the K_b of the conjugate base, then the salt solution is acidic.
• If the K_a of the conjugate acid is smaller than the K_b of the conjugate base, then the salt solution is basic.
• If the K_a of the conjugate acid is equal to the K_b of the conjugate base, then the salt solution is neutral.

 
We’ll apply these rules in the next three examples.
 
 

Example 3 - Is NH₄F Acidic, Basic, or Neutral?

Ammonium fluoride, NH₄F, is an example of a tiebreaker case. It is a salt consisting of ammonium ions (NH₄⁺) and fluoride ions (F^-). Since the NH₄⁺ ion is the conjugate acid of a weak base and F^- is the conjugate base of a weak acid, the task of determining the acidity level requires a comparison of K values. By calculating the K_a and the K_b of NH₄⁺ and F^-, one can evaluate which ion wins the tiebreaker. These K values were calculated in Example 1 and Example 2 above.
 
            NH₄⁺:              K_a = 5.6x10^-10
            F^-:                    K_b = 1.5x10^-11
 
Since NH₄⁺ has the larger K value, it wins the tiebreaker. The solution is slightly acidic with a pH value a little less than 7.0.
   
 

Example 4 - Is NH₄CN Acidic, Basic, or Neutral?

Ammonium cyanide, NH₄CN,  is a salt consisting of ammonium ions (NH₄⁺) and fluoride ions (CN^-). Since the NH₄⁺ ion is the conjugate acid of a weak base and CN ^- is the conjugate base of a weak acid, the task of determining the acidity level of a NH₄CN  solution lands in the tiebreaker case category once again By calculating the K_a and the K_b of NH₄⁺ and CN ^-, one can evaluate which ion wins the tiebreaker. These K values were calculated in Example 1 and Example 2 above.
 
            NH₄⁺:              K_a = 5.6x10^-10    (See Example 1 above)
            CN ^-:               K_b = K_w/K_a = (1.0x10^-14)/(6.2x10^-10) = 1.6x10^-5
 
Since CN^- has the larger K value, it wins the tiebreaker. The solution is slightly basic with a pH value greater than 7.0.
 
 
 

Example 5 - Is NH₄C₂H₂O₂ Acidic, Basic, or Neutral?

Ammonium acetate, NH₄C₂H₂O₂,  is a salt consisting of ammonium ions (NH₄⁺) and fluoride ions (C₂H₂O₂^-). Since the NH₄⁺ ion is the conjugate acid of a weak base and C₂H₂O₂^- is the conjugate base of a weak acid, the task of determining the acidity level of a NH₄C₂H₂O₂ solution lands in the tiebreaker case category once again. By calculating the K_a and the K_b of NH₄⁺ and C₂H₂O₂^-, one can evaluate which ion wins the tiebreaker. These K values were calculated in Example 1 and Example 2 above.
 
            NH₄⁺:              K_a = 5.6x10^-10    (See Example 1 above)
            C₂H₂O₂^-:         K_b = K_w/K_a = (1.0x10^-14)/(1.8x10^-5) = 5.6x10^-10
 
Since NH₄⁺ and C₂H₂O₂^- have the same sized dissociation constant, there is no winner in the pH battle. This salt solution is neutral with a pH of 7.0.
 
 
 

Dissociation of Polyprotic Acids

Polyprotic acids are acids that have two or more ionizable protons. Examples include H₂CO₃, H₃PO₄, H₂C₂O₄, and H₂SO₄. These acids dissociate in steps, with one proton being donated in each step. Each step has its own dissociation constant, indicating the extent to which that step occurs. For instance, sulfuric acid (H₂SO₄) dissociates in two steps.
   
H₂SO₄ is unique in that it is a strong acid. The first dissociation step has a K_a1 value that is much greater than 1. Its dissociation occurs to completion as denoted by the irreversible reaction arrow (→). This means that the conjugate base – HSO₄^- - will not hydrolyze as a base. It can however act as an acid and dissociated to form SO₄^2-.
   

Dissociation of Carbonic Acid

The behavior of weak acids like carbonic acid, H₂CO₃, is considerably different than the strong acid behavior of H₂SO₄. Each step of the H₂CO₃ dissociation is irreversible as denoted by the irreversible reaction arrow (⇄).
   
The first dissociation step produces the bicarbonate ion (HCO₃^-). This is an amphiprotic ion that could act as either an acid or a base.
 
Let’s ponder an important question: is the bicarbonate ion more likely to donate a proton (i.e., act as an acid) or accept a proton (i.e., act as a base) from water? We now know how to answer that question – determine the K values for each process. Since HCO₃^- is the conjugate base of H₂CO₃, the K_b value for its hydrolysis as a base is equal to
   
The K_a value for its hydrolysis is simply the K_a2 value of the second step as stated above. So, this is what we know:
   
As seen by the two K values for the two hydrolysis pathways, HCO₃^- is a better base than it is an acid. Since the K_b for the base dissociation is greater than the K_a for its acid dissociation, the bicarbonate ion is more likely to gain a proton than it is to lose a proton in the presence of water.
 
 
 

Is NaHCO₃ Acidic, Basic, or Neutral?

This discussion of the dual nature of HCO₃^- sets us up to answer the question as to whether salts containing the bicarbonate ion are acidic, basic, or neutral. Let’s restrict the discussion to the salt commonly referred to as baking soda, bicarbonate of soda, or simply sodium bicarbonate – NaHCO₃. The cation of this salt is the cation of a strong base and therefore neutral. The anion is the bicarbonate ion. It is the weak base of the diprotic acid, H₂CO₃. Our analysis above led to the conclusion that HCO₃^-, while amphiprotic, is a stronger base than it is an acid. Its predominant behavior is to hydrolyze and accept a proton from water and produce hydroxide ions, OH^-. Thus, we conclude that a solution of dissolved NaHCO₃ is basic.
 
 
 

Is NaH₂PO₄ Acidic, Basic, or Neutral?

The anion present in NaH₂PO₄ is the dihydrogen phosphate ion (H₂PO₄^-). It is the conjugate base of phosphoric acid. It is also amphiprotic, having two ionizable protons. To make a judgement regarding the pH of a solution of NaH₂PO₄, we need to analyze the dissociation of phosphoric acid, H₃PO₄.
 
Phosphoric acid is a triprotic acid that dissociates in three steps. The steps and their dissociation constants are:
   
As mentioned, dihydrogen phosphate ion (H₂PO₄^-) is the conjugate base of H₃PO₄. It will accept a proton from water and undergo hydrolysis. The K_b value for its hydrolysis is K_w/K_a1:
   
Being such a low K_b value, the tendency of H₂PO₄^- to hydrolyze as a base is very weak. It’s K_a value (K_a2, listed above) is noticeably larger. The two competing reactions for H₂PO₄^- are
     
From this data, it is reasonable to conclude that the dihydrogen phosphate ion is a stronger acid than it is a base.
 
The question Is NaH₂PO₄ Acidic, Basic, or Neutral? can now be answered. This salt contains Na⁺ cations. Being the cation of a strong base (NaOH), sodium ions do not hydrolyze. They act as spectator ions in solution. The anion, H₂PO₄^-, undergoes hydrolysis with water, donating a proton to form H₃O⁺ and HPO₄^2-. This lowers the pH of the solution. Thus, solutions of NaH₂PO₄ are acidic.
 
 
 

Show Me the Math

Much of Chapter 15 has been conceptual in nature. While we have done some calculations (e.g., pH, neutralization stoichiometry, etc.), we have maintained a predominantly conceptual approach. There are Chemistry courses that utilize considerably more mathematics, particularly associated with equilibrium considerations. We have left Lesson 2 of Chapter 16 for that purpose. If you’re needing help and practice on the topic of K_a and K_b problems and related equilibrium problems, tap forward to Chapter 16 of our Chemistry Tutorial where you will find full-blown coverage of acid-base equilibria.
 
 
 

Before You Leave – Practice and Reinforcement

Now that you've done the reading, take some time to strengthen your understanding and to put the ideas into practice. Here's some suggestions.

• Download our Study Card on Analyzing Salt Solutions. Save it to a safe location and use it as a review tool. (Coming Soon.)
• The Check Your Understanding section below includes questions with answers and explanations. It provides a great chance to self-assess your understanding.

 
 
 
 

Check Your Understanding of the Hydrolysis of Salts

Use the following questions to assess your understanding of how to predict whether a salt solution is acidic, basic, or neutral. Tap the Check Answer buttons when ready.
 
1. A salt is a substance that is ______.

1. Acidic
2. Basic
3. Neutral
4. … nonsense! It’s more complicated than that. 

 
2. Fluoroacetic acid (HC₂H₂FO₂) has a K_a value of 2.6×10^-3.  Write the equation for the hydrolysis of its anion. Calculate the K_b for the hydrolysis reaction.

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3. Isoquinoline (C₉H₇N) is a weak base with a K_b value of 2.5x10^-9. Identify the formula of its conjugate acid. Then write the equation for the hydrolysis of its conjugate acid. Calculate the K_a for the hydrolysis reaction.

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4. Benzoic acid (HC₇H₅O₂) has a K_a of 6.3×10^-5. Isoquinoline (C₉H₇N) has a K_b value of 2.5x10^-9. Suppose that there is a salt formed from their conjugates – isoquinolinium benzoate (HC₉H₇NC₇H₅O₂). Will the salt be acidic, basic, or neutral? Perform calculations and/or supply reasoning to support your claim.

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5. Sulfurous acid, H₂SO₃, is a diprotic acid with dissociation constants of

K_a1 = 1.3×10^-2
K_a2 = 6.2×10^-8

The conjugate base, HSO₃^-, is the hydrogen sulfite ion. Will an aqueous solution of potassium hydrogen sulfite, KHSO₃, be acidic, basic, or neutral? Perform calculations and supply reasoning to support your claim.

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6. Ascorbic acid, H₂C₆H₆O₆, is a diprotic acid with dissociation constants of

K_a1 = 7.9x10^-5
K_a2 = 1.6×10^-12

The conjugate base, HC₆H₆O₆^-, is the ascorbate ion. Will an aqueous solution of potassium ascorbate, KHC₆H₆O₆, be acidic, basic, or neutral? Perform calculations and supply reasoning to support your claim.

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