# How to calculate pKa from pKb? - pKb to pKa, Conversion, Formulas, Equations

Home > Chemistry > How to find pKa from pKb? – (pKb to pKa)

pKa determines the acidic strength of an aqueous solution, while pKb marks the basicity present in an aqueous solution. In this way, pKa and pKb are two oppositely contrasting chemical attributes.

In this article, you will learn how to find pKa from pKb i.e (pKb to pKa conversion) through several solved examples.

But before that, let us introduce you to what is pKa and pKb and what their importance is in chemistry.

Page Contents

## What is pKa?

The prefix p in pKa stands for power. Just like pH determines the power of hydrogen ions present in an aqueous solution, pKa measures the strength of an acidic solution as the power of the acid dissociation constant (Ka).

Ka measures the extent of ionization of an acid in an aqueous solution. A weak acid (HA) partially ionizes to release H+ and A ions in water, as shown by the reversible reaction below.

Ka for the above reaction is calculated at the equilibrium point using equation (i).

$Ka = \frac{[H^{+}][A^{-}]}{[HA]}$……….Equation (i)

Where;

• [H+] = concentration of hydrogen ions released in the aqueous solution
• [A] = concentration of conjugate base of the acid
• [HA] = acid concentration at equilibrium

pKa is calculated by taking the negative logarithm to the base 10 of the Ka value for acid, as shown in equation (ii).

pKa = -log10 Ka…………. Equation (ii)

pKa is inversely related to the strength of an acid, just like pH.

The greater the strength of an acid, it undergoes dissociation to a large extent. Thus, a large number of H+ ions are released in the aqueous solution. This implies that the acid possesses a high Ka value; however, it has a low pKa value as per equation (ii).

Strong mineral acids such as HCl that completely ionize in water have Ka above 1 and pKa below 1.

Weak organic acids, such as acetic acid and benzoic acid, have Ka values below 1, while their pKa values lie above 1.

## What is pKb?

pKb denotes the power of the base dissociation constant (Kb). It measures the strength of a basic solution by taking the negative logarithm of Kb.

Kb measures the extent of ionization of a base in an aqueous solution. A base is defined as a chemical substance that liberates OH ions in water. It is also defined as a proton acceptor as per the Bronsted-Lowry theory.

A strong base completely ionizes in water, while a weak base (B) partially dissociates in an aqueous solution to yield OH ions and B+ ions. The B+ ion accepts a proton from water to form a BH+ ion, as shown by the reversible reaction below.

Kb for the above reaction is calculated at the equilibrium point using equation (iii).

$Kb = \frac{[BH^{+}][OH^{-}]}{[B][H2O]}$……….Equation (III)

Where;

• [BH+] = concentration of conjugate acid of the base
• [OH] = hydroxide ion concentration in aqueous solution
• [B]= concentration of base at equilibrium
• [H2O] = concentration of water

Considering the water concentration [H2O] constant throughout the reaction, equation (iii) can be rearranged as equation (iv), shown below.

$Kb = \frac{[BH^{+}][OH^{-}]}{[B]}$……….Equation (iv)

pKb is then calculated by taking the negative logarithm of Kb as shown in equation (v).

pKb = -log10 Kb…………. Equation (v)

Kb is directly related to the strength of a base. Greater the Kb value, the base undergoes dissociation to a greater extent thus, more OH ions are released in the aqueous solution.

However, a strongly basic solution has a low pKb value as per equation (v), so pKb is inversely related to the strength of a basic solution.

## What is the relationship between pKa and pKb?

pKa and pKb are inversely related to each other.

The greater the acidic strength of an aqueous solution, the lower its pKa value; however, it has a high pKb value.

Conversely, the greater the basic strength of an aqueous solution, the lower its pKb; however, it possesses a higher pKa value.

## How to find pKa from pKb? – (pKb to pKa conversion)

Equation (vi) gives the formula that relates pKa to pKb.

pKa + pKb = pKw …………. Equation (vi)

In the above equation, pKw refers to the water dissociation constant.

A water (H2O) molecule undergoes autoionization at room temperature (25°C) to release H+ and OH ions, as shown below.

The water dissociation constant (Kw) can be determined as per equation (vii).

Kw = [H+][OH]…………Equation (vii)

Kw has a fixed value at r.t.p i.e., Kw = 1 x 10-14. So, pKw can be calculated by taking the negative logarithm of this value as shown in equation (viii).

pKw = -log10Kw…………. Equation (viii)

pKw = -log10 (1 x 10-14) = 14

Thus, putting the above-determined value of pKw into equation (vi) and making pKa the subject of the formula gives us the final equation ix, which we can use to find pKa if the value of pKb is known.

pKa + pKb = 14

pKa = 14 – pKb…………. Equation (ix)

Now let’s see through the solved examples given below; how to apply equation (ix) and find pKa from pKb.

## Solved examples of determining pKa when pKb given

 Example #1: The pKb for an acetic acid (CH3COOH) solution is 9.23. What is its pKa? The pKb value for acetic acid is given in the question statement, so we can use equation (ix) to find its relative pKa, as shown below.pKa = 14 – pKb…………. Equation (ix)                                                     pKa = 14 – 9.23pKa = 4.77Result: The pKa of the given acetic acid solution is 4.77.
 Example #2: What is the relative pKa for hydrofluoric acid (HF) if the pKb is 10.9? The pKb value for hydrofluoric acid (HF) is given in the question statement, so we can easily apply equation (ix) to find the relative pKa, as shown below.pKa = 14 – pKb…………. Equation (ix)                                                     pKa = 14 – 10.9pKa = 3.1Result: The pKa of the given hydrofluoric acid solution is 3.1.
 Example # 3: Comment using pKa values calculated in examples 1 and 2; which out of the two given acids is stronger? Lower the pKa value for an acidic solution, the greater the strength of the acid. As per the calculations made in the above two examples, pKa (HF) = 3.1 < pKa (CH3COOH) = 4.77. Thus, hydrofluoric acid is stronger than acetic acid. You may also note that pKb (HF) = 10.9 > pKb (CH3COOH) = 9.23. As pKb is directly related to acidic strength, so a higher pKb value denotes hydrofluoric acid is a stronger acid than acetic acid, conforming to what we predicted above using pKa values.
 Example # 4: The Kb value for ammonia (NH3) is 1.74 x 10-5. What is the pKa for an aqueous solution of NH3? The base dissociation constant (Kb) value for ammonia is given so we can use equation (v) to find its pKb value.pKb = -log10 Kb…………. Equation (v)                                                     pKb = -log10 (1.74 x 10-5) = 4.76Now that the pKb value is known, we can easily find pKa using equation (ix), as shown below.pKa = 14 – pKb…………. Equation (ix)                                                      pKa = 14 – 4.76 = 9.24Result: The pKa of the ammonia solution is 9.24.
 Example # 5: Aspartic acid is an acidic amino acid; its pKa value is 4.1. Find its pKb. As the pKa for aspartic acid is given in the question statement, so we can easily find pKb from the given pKa using equation (ix).pKa = 14 – pKb…………. Equation (ix)                                                      pKa = 14 – 4.1 = 9.9Result: The pKa for aspartic acid is 9.9.
 Example # 6: The Kb for a chemical substance X is 1.32 x 10-7. Is the aqueous solution of substance X more acidic or basic in nature? We can determine the acidity or basicity of an aqueous solution by calculating its pKa and pKb values, respectively.The base dissociation constant (Kb) for substance X is given so we can use equation (v) to find its pKb value, as shown below.pKb = -log10 Kb…………. Equation (v)                                                     pKb = -log10 (1.32 x 10-7) = 6.88Now that the pKb value is determined, we can conveniently use equation (ix) to calculate the relative pKa value for substance X.pKa = 14 – pKb…………. Equation (ix)                                                      pKa = 14 – 6.88 = 7.12Result:  pKa = 7.12 > pKb = 6.88 for substance X. This implies that substance X is slightly basic in nature.Interesting fact: You may note from this example that an aqueous solution possesses both pKa and pKb values; however, it depends on the magnitude of these values that determines whether the solution is acidic or basic in nature.

## FAQ

### What is pKa?

pKa measures the acidity present in an aqueous solution. It is calculated by taking the negative logarithm to the base 10 of the acid dissociation constant (Ka).

∴ pKa = -log10 Ka

### What is pKb?

pKb measures the basicity present in an aqueous solution. It is calculated by taking the negative logarithm to the base 10 of the base dissociation constant (Kb).

∴ pKb = -log10 Kb

### How is pKa related to the acidity of an aqueous solution?

pKa is inversely related to the acidity of an aqueous solution.

A strong Bronsted acid dissociates to a large extent in an aqueous solution by easily liberating its loosely held proton. It thus possesses a high Ka value.

Consequently, the negative logarithm of Ka i.e., pKa, is lowered.

This implies that the greater the acidic strength, the lower its pKa value and vice versa.

### How is pKb related to the acidity of an aqueous solution?

pKb is directly related to the acidity of an aqueous solution. Greater the acidity, the higher the pKb, and vice versa.

### How is pKa related to the basicity of an aqueous solution?

pKa is directly related to the basic strength of an aqueous solution. Strongly basic solutions have high pKa values and vice versa.

### How is pKb related to the basicity of an aqueous solution?

pKb is inversely related to the basicity of an aqueous solution. Strongly basic solutions possess high Kb values, thus low pKb values, and vice versa.

### What is the relationship between pKa and pKb of an aqueous solution?

pKa and pKb are inversely related to each other as per the formula shown below.

∴ pKa + pKb = pKw

Where pKw = water dissociation constant = 14 (at 25°C, 1 atm).

### What is pKw?

pKw stands for the power of water dissociation constant (Kw). The autoionization of water at room temperature (25°C) liberates H+ and OH ions, as shown below.

The equilibrium constant (Kw) for the above reaction is calculated as follows:

As the concentration of water [H2O] stays constant overall, thus the above equation can be rewritten as:

∴ Kw = [H+] [OH]

pKw is calculated as a negative logarithm of Kw. As the value of Kw = 1.00 x 10-14 is fixed at r.t.p so,

∴ pKw = -log10 Kw

∴ pKw = -log10 (1 x 10-14) = 14.

### Can pKa obtain both positive and negative values?

Yes. A negative pKa value implies extremely strong acidic strength. For instance, pKa for hydrochloric acid (HCl) = -6.30.

### How to find pKa from pKb?

pKa can be calculated from pKb by substituting the given value into the equation shown below:

∴ pKa = 14 – pKb.

## Summary

• pKa is the negative logarithm of the acid dissociation constant (Ka).
• pKa = -log10 Ka.
• pKa measures the strength of an acidic solution. The lower the pKa value, the higher the acidic strength.
• pKb is the negative logarithm of the base dissociation constant (Kb).
• pKb = -log10 Kb.
• pKb measures the strength of a basic solution. Lower the pKb value, the higher the basic strength of an aqueous solution.
• pKa is inversely related to pKb by the formula: pKa + pKb = 14. The number 14 represents pKw, where Kw is the water dissociation constant at room temperature (25°C).
• If the value of pKb for an aqueous solution is known, we can find its pKa by substituting the given value into the formula: pKa = 14 – pKb.

## References

1. “Converting Between pKa and pKb: Explanation.” Study.com, https://study.com/skill/learn/converting-between-pka-and-pkb-explanation.html.
2. Helmenstine, Anne Marie. “pH, pKa, Ka, pKb, and Kb Explained.” ThoughtCo, https://www.thoughtco.com/ph-pka-ka-pkb-and-kb-explained-4027791.
3. “pH, pKa, Ka, pKb, Kb.” Socratic.org, https://socratic.org/organic-chemistry-1/acids-and-bases-1/ph-pka-ka-pkb-kb.
4. “Equilibrium Constants (Ka and Kb, pKa and pKb).” Jack Westin MCAT Prep, https://jackwestin.com/resources/mcat-content/acid-base-equilibrium/equilibrium-constants-ka-and-kb-pka-pkb.
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#### Ammara Waheed

Ammara Waheed is a highly qualified and experienced chemist, whose passion for Chemistry is evident in her writing. With a Bachelor of Science (Hons.) and Master of Philosophy (M. Phil) in Physical and Analytical Chemistry from Government College University (GCU) Lahore, Pakistan, with a hands-on laboratory experience in the Pakistan Council of Scientific and Industrial Research (PCSIR), Ammara has a solid educational foundation in her field. She comes from a distinguished research background and she documents her research endeavors for reputable journals such as Wiley and Elsevier. Her deep knowledge and expertise in the field of Chemistry make her a trusted and reliable authority in her profession. Let's connect - https://www.researchgate.net/profile/Ammara-Waheed

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