If a chemist wants to know the acidity of an aqueous solution, then he or she can find it using different chemical parameters. Two of the most important ones are pKa and pH.
Where pH tells us whether an aqueous solution is acidic or basic in nature, pKa, on the other hand, determines whether the solution is strongly or weakly acidic.
These two parameters are inconvertible. If we know one, we can definitely find the other. This article will teach you all the tips and tricks to do so.
So without any further delay, dive into the article and start learning!
pKa is the negative logarithm of Ka to the base 10.
Ka stands for acid dissociation constant, which measures the extent of ionization of an acid in an aqueous solution.
A weak acid (HA) partially dissociates to produce H+ and A– ions in water. H+ ions combine with H2O molecules to form hydronium (H3O+) ions. A– is known as the conjugate base of the acid. HA and A– together are known as a conjugate acid-base pair.
The ionization equilibrium for the dissociation of HA in an aqueous solution can be represented as follows:
The equilibrium constant (Ka) for the above reaction can be represented as equation (i)
Ka = \frac{[H_{3}O^{+}][A^{-}]}{[HA][H_{2}O]}………. Equation (i)
Where;
[H3O+] = concentration of hydronium ions formed in the aqueous solution
[A–] = concentration of conjugate base of the acid
[HA] = acid concentration at equilibrium
[H2O] = concentration of water
As water concentration stays constant throughout the reaction, while [H3O+] = [H+], i.e., the concentration of H+ ions released in the aqueous solution. So, equation (i) can be rearranged as equation (ii).
Ka = \frac{[H^{+}][A^{-}]}{[HA]}……….Equation (ii)
pKa is calculated from Ka by taking the negative logarithm of the latter, as shown in equation (iii).
pKa = -log10 Ka ……….Equation (iii)
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 (iii).
In this way, pKa is inversely related to the strength of an acid, just like pH.
Weak organic acids, such as acetic acid, benzoic acid, lactic acid, etc., have Ka values below 1, while pKa values above 1.
What is pH?
An acid dissociates to release hydrogen ions (H+) in an aqueous solution. The amount of H+ ions released in the aqueous solution determines the strength of the acid.
The concentration of H+ ions released can be measured against a parameter called pH (power of hydrogen).
The pH of a solution is related to [H+] by the formula given in equation (iv).
pH = -log10 [H+] ….Equation (iv)
The hydrogen ion concentration of a solution usually varies from 1 to 10-14 g eq./L. When converted into pH, it is represented in numbers from 0 to 14. The greater the acidity of a solution, the higher [H+], so as per equation (iv), it has a lower pH.
On the pH scale, acidic solutions have a pH ranging from 0 to 6. pH 7 represents a purely neutral solution such as water, while a pH above 7 denotes the basicity of an aqueous solution.
What is the relationship between pH and pKa?
As discussed above, both pH and pKa are inversely related to acidic strength. This implies that pH and pKa are directly related to each other.
Highly ionizable strong acids possess low pH and pKa values. Contrarily, partially ionizable weak organic acids possess high pH and pKa values.
For extremely strong acids in which [A–] = [HA] after ionization, pKa = pH.
How to find pKa from pH? (pH to pKa)
If the pH of an acidic solution is known, we can find its pKa by applying the Henderson Hasselbalchequation i.e., equation (v) given below.
The above equation is usually applied to find the pKa of a weak acid making up a buffer solution.
Buffers are defined as chemical solutions that resist small changes in pH. A buffer solution is usually made up of a weak acid or base and its highly ionizable salt.
A weak acid (HA) only partially dissociates into H+ and A– ions, while the highly ionizable salt (MA) completely dissociates into M+ and A– ions.
A high concentration of A– ions in the mixture shifts the reversible equilibrium (I) backward by the common ion effect.
This results in a high concentration of the weak acid (HA) and its conjugate base (A–) in the buffer solution.
Therefore, in equation (vii), [HA] and [A–] represent equilibrium concentrations of the acid and its conjugate base, respectively.
For strong acids that completely ionize to yield [HA] = [A–] ∴ [HA]/[A–] = 1. Log10 1 = 0. So now you know how pKa = pH for extremely strong acids, as we mentioned at the beginning of the article.
Now let’s find out through the solved examples given below; how to find pKa from pH under different circumstances.
Solved examples for finding pKa from pH (pH to pKa)
Example # 1: A buffer solution of pH 5.0 consists of the following equilibrium concentrations:
The concentration of weak acid = 0.45 M, and the concentration of conjugate base = 0.32 M. What is its pKa?
As per all the data given in the question statement, we can easily find pKa by applying equation (vii).
[HA] = 0.45 M, [A–] = 0.32 M, and pH = 5.0.
pKa = 5.0 + log10(0.45/0.32)
pKa = 5.0 + 0.148 = 5.15
Result: The pKa of the weak acid in this example is 5.15.
Example # 2: A 0.075 M aqueous solution of a weak acid undergoes 50% ionization till it reaches the equilibrium point. The measured pH was 5.12. Calculate its pKa.
50% ionization of the weak acid implies [A–]/[HA] = 50/100 = 1/2 .
∴ [HA]/[A–] = 2/1
The pH of the solution is given in the question statement. So we can substitute all the above data into equation (vii) to find the pKa value.
pKa = 5.12 + log10(2/1)
pKa = 5.12 + 0.301 = 5.42
Result: The pKa of the weak acid in this example is 5.42.
Pro-tip: The original molarity of the acid (0.075 M) is not required to solve this question. It was just given to distract the problem solver. So you need to be extra careful while solving such questions.
Example # 3: What is the pKa of a 0.1 M acetic acid solution having pH = 2.60?
The initial concentration of acetic acid is also given in the question statement i.e., 0.1 M.
So [CH3COOH] equilibrium = 0.1 – (2.51 x 10-3) = 0.097 M
Result: The pKa of the acetic acid solution at pH 2.60 is 4.19.
Example # 4: The pH of a given solution of lactic acid and lactate is 4.30. Calculate the pKa of lactic acid when the concentrations of lactic acid and lactate are 0.020 M and 0.073 M, respectively, at equilibrium.
Lactic acid (CH3CH(OH)COOH) is a weak acid that dissociates to produce lactate (CH3CH(OH)COO–) and hydrogen (H+) ions at equilibrium.
[lactic acid] equilibrium and [lactate]equilibrium is given in the question statement. So we can use these concentrations and the given pH value to find pKa by applying the Henderson Hasselbalch equation i.e., equation (vii).
Result: The pKa of the given lactic acid solution is 3.74.
pKa is the negative logarithm of the acid dissociation constant i.e., Ka.
pKa = -log10 Ka.
How is pKa related to the strength of an acid?
pKa is inversely related to the strength of an acid.
The greater the acidic strength, the higher the Ka value; thus, the negative logarithm of Ka i.e., pKa, decreases.
What is pH?
pH stands for the power of hydrogen. It measures the concentration of hydrogen ions (H+) released in an aqueous solution by the formula: pH = -log10 [H+].
The stronger the acid, the more H+ ions are released in the aqueous solution; therefore, the negative logarithm of [H+] decreases i.e., the pH decreases.
Are pKa and pH the same?
No, pKa and pH are closely related but two different chemical entities.
What is the difference between pKa and pH?
pH determines whether an aqueous solution is acidic or basic in nature. However, pKa tells us whether an acidic solution is strongly acidic or weakly acidic.
How is the pH of a solution related to pKa?
pH is directly related to pKa as per Henderson Hasselbalch’s equation given below.
where [HA]= concentration of the acid and [A–]= concentration of conjugate base of the acid at equilibrium.
How to find pKa from pH?
The Henderson Hasselbalch equation can be rearranged to make pKa the subject of the formula as follows:
If the value of pH and the required concentrations are given, then we can find the pKa of the solution by applying the above formula.
Summary
pKa is defined as the negative logarithm to the base 10 of the acid dissociation constant (Ka). pKa = – log10 Ka.
pH stands for the power of hydrogen. It measures the concentration of hydrogen ions (H+) present in an aqueous solution.
pH is related to [H+] by the formula pH = -log10 [H+].
pH tells us whether an aqueous solution is acidic or basic in nature, while pKa determines the strength of an acidic solution.
pKa is directly related to pH.
Both pH and pKa are inversely related to the strength of an acid.
Greater the acidic strength, the lower the pH and pKa values, and vice versa.
pKa is related to pH by the Henderson Hasselbalch equation: pKa = pH +log10[HA]/[A–] where [HA]= concentration of the acid and [A–]= concentration of conjugate base of the acid at equilibrium. It is usually used for determining the pKa of buffer solutions.
If the pH and required equilibrium concentrations of an aqueous solution are known, we can find pKa from pH by substituting the given values into the Henderson Hasselbalch equation.
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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