How to calculate Ka from pKa? - pka to ka, Conversion, Formulas, Equations
Ka stands for acid dissociation constant. It determines the extent of ionization of a weak acid in an aqueous solution. pKa is a related term. The prefix p stands for the power of the acid dissociation constant. Ka and pKa are inconvertible.
You will learn in this article how to calculate the Ka value of an acid from its pKa i.e. (pKa to Ka conversion) by applying a very simple but useful chemical formula.
So without any further delay, dive into the article, and let’s start reading!
The ionization equilibrium for the dissociation of a weak acid (HA) in an aqueous solution is represented as follows:
The acid dissociation 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)
The greater the strength of an acid, the higher the Ka value for its aqueous solution and vice versa.
What is pKa?
pKa stands for the power of Ka, just like pH is the power of hydrogen ions in an aqueous solution. Where pH determines whether a solution is acidic or basic in nature. pKa compares the strength of one acidic solution with another.
It is calculated as a negative logarithm to the base 10 of the Ka value, as shown in equation (iii) given below.
pKa = -log10Ka…………. Equation (iii)
Weak organic acids have greater pKa values than strong mineral acids.
pKa for pure neutral water = 14. It is also known as the water dissociation constant (pKw).
So pKa is related to pKb i.e., base dissociation constant for an aqueous solution as shown in equation (iv).
pKa + pKb = pKw ……. Equation (iv)
You may note that Ka measures the strength of the acid itself, while pKa is an attribute associated with the strength of the aqueous solution that the acid forms upon ionization.
What is the relationship between Ka and pKa?
The equation [pKa = -log10Ka] tells us that Ka and pKa are inversely related to each other. A higher Ka value results in a lower pKa value and vice versa.
This implies that a strong acid that dissociates to a large extent in an aqueous solution possesses a higher Ka value; however, it has a smaller pKa.
So pKa is also inversely related to acidic strength.
How to find Ka from pKa? – (pKa to Ka conversion)
This equation [pKa = -log10Ka] can be converted into equation (v) by taking antilog and making Ka the subject of the formula:
∴ Ka = 10-pKa………Equation (v)
If the pKa for an acidic solution is given, we can easily determine its acid dissociation constant (Ka) by putting the value of pKa in equation (v).
Let’s practice together some examples to see how to calculate Ka from pKa.
Solved examples of determining Ka when pKa given
Example #1:The pKa of a moderately acidic solution A is 3.14. Find its Ka?
As the pKa value is given in the question statement so we can find Ka by applying the equation given below.
∴ Ka = 10-pKa
∴ Ka = 10-3.14 = 7.24 x 10-4.
Result: The acid dissociation constant (Ka) for the given acid is 7.24 x 10-4.
Example #2:What is the acid dissociation constant of an acidic solution B whose pKa value is given to be 11.62?
As the pKa value is given in the question statement so we can find Ka by applying the equation given below.
∴ Ka = 10-pKa
∴ Ka = 10-11.62 = 2.40 x 10-12
Result: The acid dissociation constant (Ka) for the given acid is 2.40 x 10-12.
Example # 3:Using the pKa and Ka values determined in examples 1 and 2, explain which acid is the stronger one?
As Ka is directly related to the strength of an acid. Therefore, as per the Ka values calculated in examples 1 and 2, acid A is stronger than acid B.
⇒ Ka = 7.24 x 10-4 > Ka = 2.40 x 10-12
A higher Ka value denotes that the acid easily liberates its H+ ions in the aqueous solution thus it is a stronger acid.
Contrarily pKa is inversely related to the strength of an acid.
⇒ pKa = 3.14 < pKa = 11.62
Thus, solution A is more acidic than solution B, conforming to what we predicted above.
Example # 4:The pKa for acetic acid is 4.80. Which of the following options gives the correct Ka value for acetic acid?
A) 2.58 x 10-3 B) 1.58 x 10-7
C) 3.91 x 10-5 D) 1.58 x 10-5 E) 2.58 x 10-5
Answer: Option D is the correct answer.
Explanation:As the pKa value for acetic acid is given in the question statement. So we can substitute it into the equation given below to find Ka as follows.
∴ Ka = 10-pKa
∴ Ka = 10-4.80 = 1.58 x 10-5.
So the acid dissociation constant (Ka) value for acetic acid is 1.58 x 10-5.
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 equilibrium constant for a reversible reaction is the ratio of the product of the concentration of products to the product of reactant concentrations.
The ionization equilibrium for the dissociation of HA in an aqueous solution can be represented as follows:
⇒ HA + H2O ⇌ H3O+ + A–
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)
The greater the strength of an acid, it undergoes dissociation to a larger extent in the aqueous solution; thus, it possesses a higher Ka value.
Weak organic acids such as acetic acid and citric acid have Ka values below 1. However, strong mineral acids such as HCl and HNO3 that completely dissociates to release a large number of H+ ions in an aqueous solution have Ka values above 1.
How is Ka related to the strength of an acid?
Ka is directly related to the strength of an acid. The greater the strength of an acid, the higher its Ka value.
Weak acids have Ka below 1. Strong mineral acids have Ka values above 1.
What is pKa?
pKa stands for the power of Ka. It is calculated as a negative logarithm of the Ka value.
How is pKa related to the strength of an acid?
pKa is inversely related to the strength of an acidic solution.
The greater the strength of an acid, the lower its pKa value.
What is the relationship between Ka and pKa?
Ka is inversely proportional to pKa. The higher the Ka of an acid, it dissociates to a greater extent to release a large number of H+ ions in an aqueous solution.
However, the pKa value of the acidic solution will be lowered.
What is the formula that relates pKa from Ka?
pKa is the negative logarithm of Ka to the base 10 as shown in the formula given below:
pKa = -log10Ka
What is the formula that relates Ka from pKa?
Ka can be determined by taking the antilog of pKa as shown below.
∴ Ka = 10-pKa
How to find Ka if the pKa of a solution is given?
If the value of pKa is given, we can easily find the acid dissociation constant (Ka) for the respective acid by substituting the given value into the following equation.
∴ Ka = 10-pKa
Summary
Ka stands for acid dissociation constant. It measures the extent of ionization of an acid in an aqueous solution.
Greater the Ka value, the higher the strength of the acid.
pKa denotes the power of Ka. It is calculated as a negative logarithm of Ka to the base 10.
pKa = -log10(Ka).
Ka can be calculated from pKa by applying antilog on the above formula.
If the value of pKa for an acidic solution is given, we can find the Ka for the respective acid by applying the formula, Ka = 10-pKa.
References
“How to Find Ka from pKa.” wikiHow, wikiHow, 26 Aug. 2021, https://www.wikihow.com/Find-Ka-from-pKa.
“How do you calculate a Ka value from pKa?” Socratic, Socratic.org, n.d., https://socratic.org/questions/how-do-you-calculate-a-ka-value-from-pka.
“How to Convert Between Ka and pKa: Explanation & Examples.” Study.com, Study.com, n.d., https://study.com/skill/learn/how-to-convert-between-ka-and-pka-explanation.html.
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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