RetroSynthetiX

Contents

I. Introduction

II. Acidity and Basicity

II.1. Acidity (K_a and pK_a)

II.2. Basicity (K_b and pK_b)

II.3. Seeing a Base Through Its Conjugate Acid: K_aH and pK_aH

II.3.1. Step i

II.3.2. Step ii

II.3.3. Summary and Other Details

III. Conclusion

IV. Try It Yourself!

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I. Introduction

In Acid-Base I, we have learnt what strong and weak acids/bases are. We also learnt the relationship between them and their respective conjugate pairs. So that’s good and all, but here we will move on to the more common way that an organic chemist would do when looking at a reaction.

So now that your memory is, hopefully, refreshed about what acid/base is and what conjugate pairs are, we shall start looking at the concept from an organic chemist’s point of view.

In this post I re-introduce the concept of acidity (K_a and pK_a) and basicity (K_b and pK_b). After that, we learn how to think about the basicity of a base using the K_a of its conjugate acid. This is something that is very useful and is used a lot in organic chemistry.

From my own experience, it was hard for me to think in terms of K_a for bases because in general chemistry, I was more used to using K_b to gauge basicity of a base. I’m guessing that many people also run into the same problem, so I will discuss this important topic in a thorough manner. Here, I introduce the concept of K_aH and pK_aH.

The aims of this post are:

• To refresh your memory about acidity (K_a and pK_a) and basicity (K_b and pK_b)
• To start thinking and seeing bases through their conjugate acids by introducing K_aH and pK_aH

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II. Acidity and Basicity

This is another extension of Brønsted-Lowry acid/base theory. First, let’s address this question: how acidic is an acid and how basic is a base? Let’s look at it the way an organic chemist does.

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II.1. Acidity (K_a and pK_a)

Brønsted-Lowry theory states that an acid is a proton (H⁺) donor. This implies that the strength of an acid is determined by how readily it releases H⁺.

Strong acids release H⁺ more readily, whilst weaker acids, not so much. This implies that strong acids also release their conjugate bases readily. This means that the conjugate bases of strong acids are stable (that’s why it can be released readily). Ultimately, this translates to: strong acids give weak conjugate bases.

Weak acids find it hard to release their H⁺, and do not do it readily. Once a weak acid releases H⁺ and a conjugate base, they quickly get back together to form the acid again. This means that the conjugate bases of weak acids are unstable (so once the conjugate base is released, it quickly goes back to its acid). Ultimately, this translates to: weak acids give strong conjugate bases.

We can determine whether an acid is strong or weak through its K_a (acid dissociation constant) value. I believe that this has been covered in general chemistry, so I will not get into too much detail.

In solution, an acid can dissociate to release proton and a conjugate base in equilibrium. The K for this dissociation reaction is the K_a, and its value is different for every acid.

The value of K_a tend to be very large (10^x) for strong acids and very small (10^–x) for weak acids. Furthermore, there are a lot more weak acids compared to strong acids. Owing to all of these reasons, chemists like to simplify K_a by using its negative log, known as pK_a.

Important note: because pK_a is a negative log function, a large K_a translates to a small pK_a and vice versa. And yes, pK_as can have a negative value.

Let’s have a look at a famous weak acid: acetic acid (HOAc).

In water, HOAc dissociates to release proton (H⁺ which subsequently protonates water and becomes H₃O⁺) and acetate ion (its conjugate base, AcO^– in equilibrium. The K_a value for acetic acid is known to be 1.8 × 10^–5 (pK_a HOAc= 4.74). This means that there are only a very small number of H⁺ and AcO^– ions at any given time in the equilibrium, whilst the majority of them exist as HOAc.

Now let’s compare it to a strong acid: HCl.

In water, HCl releases proton (H⁺, which also protonates water and becomes H₃O⁺) and chloride ion (its conjugate base). It releases proton so easily that we can essentially say that HCl completely ionises. However, it does have a K_a value, which is about 10⁷ (pK_a HCl = –7), so we can look at the ionisation reaction through the perspective of an equilibrium reaction. Such a large K_a value (small pK_a value) means that there’s a large number of H⁺ and Cl^– in the solution at any given time in the equilibrium, and only a very small number exists as HCl.

To summarise:

• Strong acids give weak conjugate bases
  
• Weak acids give strong conjugate bases
  
• The smaller the pK_a value of an acid is, the stronger the acid is, the weaker its conjugate base is
  

We can come to another conclusion after we have a look at the next section: basicity.

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II.2. Basicity (K_b and pK_b)

What about bases?

Brønsted-Lowry theory states that a base is a proton (H⁺) acceptor. This implies that the strength of a base is determined by how readily it accepts H⁺.

Strong bases accept H⁺ more readily, whilst weaker bases, not so much. This implies that strong bases also release their conjugate acids readily. This means that the conjugate acids of strong bases are stable (that’s why it can be released readily). Ultimately, this translates to: strong bases give weak conjugate acids.

Weak bases find it hard to accept H⁺. Once a weak base accepts H⁺ and a conjugate acid, they quickly get back together to form the base again. This means that the conjugate acids of weak bases are unstable (so once the conjugate acid is released, it quickly goes back to its base). Ultimately, this translates to: weak bases give strong conjugate acids.

Similar to the acids, we can determine the strength of a base through its K_b (base dissociation constant) value. In solution, a base can accept a proton and becomes its conjugate acid in an equilibrium. The K for this dissociation reaction is the K_b, and its value is different for every base.

Also similar to the acids, the value of K_b tend to be very large (10^x) for strong bases and very small (10^–x) for weak bases. Furthermore, there are also a lot more weak bases compared to strong bases. Therefore, pK_b can be used to simplify this.

Important note: because pK_b is a negative log function, a large K_b translates to a small pK_b and vice versa. And yes, pK_bs can have a negative value.

Let’s have a look at a famous weak base: ammonia (NH₃).

In water, ammonia readily accepts proton (H⁺) from H₂O to form NH₄⁺ and OH^– in equilibrium. The K for this dissociation reaction is known as K_b, and its value for ammonia is known to be 1.8 × 10^–5 (pK_b NH₃ = 4.74). This means that there are only a very small number of NH₄⁺ and OH^– ions at any given time in the equilibrium, whilst the majority of them exist as NH₃ and H₂O.

Note: the fact that the K_b value of NH₃ is the same as the K_a value of HOAc is just a coincidence.

Now let’s compare it to a strong acid: NaNH₂ (a much stronger base than NaOH).

In water, NaNH₂ completely dissociates to form Na⁺ and NH₂^– ions. The NH₂^– ion accepts proton (H⁺) from H₂O to form NH₃ and OH^– in equilibrium. However, it does have a K_b value, which is about 10²⁴ (pK_b NH₂^– = –24). So we can look at the ionisation reaction through the perspective of an equilibrium reaction. Such a large K_b value means that there’s a large number of NH₃ and OH^– in the solution at any given time in the equilibrium, and only an extremely small number exists as NH₂^–.

To summarise:

• Strong bases give weak conjugate acids
  
• Weak bases give strong conjugate acids
  
• The smaller the pK_b value of a base is, the stronger the base is, the weaker its conjugate acid is
  

Now, we can come up with another conclusion if we combine everything we’ve got so far at the next section.

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II.3. Seeing a Base Through Its Conjugate Acid: K_aH and pK_aH

Organic chemists like myself don’t really use K_b or pK_b that often. We like to see the strength of a base from the strength of its conjugate acid. Why? You shall see.

First, have a look at the reactions below.

I’m sure you’ll see the similarity between the two reactions right away. Both H₃O⁺ and NH₄⁺ lose a proton in the first step (step i), giving H₂O and NH₃, respectively. Both of them subsequently lose another proton in the second step (step ii), giving OH^– and NH₂^–.

In the first step, both H₃O⁺ and NH₄⁺ are acids whilst H₂O and NH₃ are their conjugate bases, respectively. In the second step however, H₂O and NH₃ are acids and OH^– and NH₂^– are their conjugate bases, respectively.

Ok, because of their similarity, let’s just use H₃O⁺, H₂O, and OH^– as our primary example. I included the NH₄⁺ series just as an example so you can see there are other species capable of doing the same thing.

Let’s consider each step (i and ii) in the H₃O⁺ series separately.

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II.3.1. Step i

First, let’s consider both the forward and the reverse reaction in each step separately.

In the forward reaction, H₃O⁺ is an acid and H₂O is its conjugate base. This reaction is the acid dissociation reaction of H₃O⁺, and therefore its K (K_forward) is the K_a of H₃O⁺, which has a value of 10^1.7.

In the reverse reaction, H₂O is a base and H₃O⁺ is its conjugate acid. The K of this reaction (K_reverse) is the reciprocal of K_forward.

Remember the title of this section? Seeing a base through its conjugate acid. So let me introduce you to K_aH:

The K_aH of a base is actually the K_a of its conjugate acid

We know that the K_a of the conjugate acid H₃O⁺ is 10^1.7. If we want to talk about the base (H₂O), we can say that the K_aH of the base H₂O is 10^1.7.

Again, this means that:

K_a of a conjugate acid = K_aH of its base

So, the equilibrium constant of the forward and reverse reactions can be rewritten as follows:

We only say K_aH when we’re talking about a base using the K_a of its conjugate acid. Small K_aH value means weak conjugate acid, which means strong base. Conversely, large K_aH value means strong conjugate acid, which means weak base.

For the same reason that has been explained before, pK_aH is more useful than K_aH itself due to the magnitude of K_aH.

Therefore:

pK_a of a conjugate acid = pK_aH of its base

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II.3.2. Step ii

We’ve basically covered all the basics about K_aH and pK_aH. This section is to give you another example for you to ponder about.

Let’s consider both the forward and the reverse reaction in each step separately.

In the forward reaction, H₂O is an acid and OH^– is its conjugate base. This reaction is the acid dissociation reaction of H₂O, and therefore its K (K_forward) is the K_a of H₂O, which has a value of 10^–15.7.

In the reverse reaction, OH^– is a base and H₂O is its conjugate acid. The K of this reaction (K_reverse) is the reciprocal of K_forward.

Remember:

K_a of a conjugate acid = K_aH of its base

Therefore, the equilibrium constant of the forward and reverse reactions can be rewritten as follows:

Since pK_aH is more useful, then:

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II.3.3. Summary and Other Details

Now, you should already know that in the NH₄⁺ series:

• In step i, pK_a NH₄⁺ = pK_aH NH₃
  
• In step ii, pK_a NH₃ = pK_aH NH₂^–

Organic chemists like to use pK_a and pK_aH interchangably, which often leads to confusion, especially to students who are not yet familiar with this. For example, at one time they may say the pK_a of NH₃ is 38, which is correct. However, they may also, at other times and depending on the circumstances, say that the pK_a of NH₃ is 9.2, which is actually the pK_a of NH₄⁺. I believe that to avoid confusion, they should’ve said that pK_aH of NH₃ is 9.2.

Therefore, in my opinion, I think the usage of pK_aH should be popularised.

That being said, pK_aH is still not a common term, so if you write it in an exam paper, your examiner may not accept it. My suggestion is to get used to using pK_aH and only use it in your calculation. But when you actually write it in your exam paper, write ‘pK_a of the conjugate acid’ instead.

You probably ask ‘why should we see a base through its conjugate acid and even go as far as to introduce pK_aH?’. We’ll see the application and importance of using pK_aH in Acid-Base V and Acid-Base VIII. For now, make sure you understand what pK_aH is.

One last thing, I’d like to show you that this is also applicable to organic compounds. Have a look at the protonated methanol (CH₃OH₂⁺) and protonated diisopropylamine (a.k.a. diisopropyl ammonium or protonated DIPA, C₆H₁₄NH₂⁺) series.

To conclude:

• Small pK_aH means strong conjugate acid, which means the base is a weak base
• Large pK_aH means weak conjugate acid, which means the base is a strong base

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III. Conclusion

To conclude this post, let’s put everything we have got so far here:

• Strong acids give weak conjugate bases
  
• Weak acids give strong conjugate bases
  

• Strong bases give weak conjugate acids
  
• Weak bases give strong conjugate acids

• The smaller the pK_a value of an acid is, the stronger the acid is, the weaker its conjugate base is

• Small pK_aH means strong conjugate acid, which means the base is a weak base
• Large pK_aH means weak conjugate acid, which means the base is a strong base

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IV. Try It Yourself!

Let’s try to assign pK_a and pK_aH yourself.

Use the protonated methanol and the protonated DIPA series and assign the pK_a and pK_aH relationships. I’ll put the chemical equations again here:

Highlight text for answer:

1. In the protonated methanol series:

• In step i: pK_a CH₃OH₂⁺ = pK_aH CH₃OH
  
• In step ii: pK_a CH₃OH = pK_aH CH₃O^–

2. In the protonated DIPA series:

• In step i: pK_a C₆H₁₄NH₂⁺ = pK_aH C₆H₁₄NH
  
• In step ii: pK_a C₆H₁₄NH = pK_aH C₆H₁₄N^–

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Page last updated: 09ii17
RP

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Other Posts in Acid, Base, and pK_a Series

Acid-Base Prologue	Acid-Base I What are Acids and Bases?	Acid-Base II What is pKa and Why is It Important?
Acid-Base III The pKa Table and What Information It Tells You	Acid-Base IV Factors Affecting the Acidity of Organic Compounds	Acid-Base V Using pKa to Predict the Course of a Reaction Part 1
Acid-Base VI Using pKa to Predict the Course of a Reaction Part 2	Acid-Base VII Using pKa to Predict the Course of a Reaction Part 3	Acid-Base VIII Acidity, Basicity, and Solvent Part 1
Acid-Base IX Acidity, Basicity, and Solvent Part 2	Acid-Base X Levelling Effect	Acid-Base XI Hard and Soft Acids and Bases (HSAB) Theory in Organic Chemistry