How to calculate Ka from pKa? - pka to ka, Conversion, Formulas, Equations
K_{a} stands for acid dissociation constant. It determines the extent of ionization of a weak acid in an aqueous solution. pK_{a }is a related term. The prefix p stands for the power of the acid dissociation constant. K_{a} and pK_{a} are inconvertible.
You will learn in this article how to calculate the K_{a} value of an acid from its pK_{a} i.e. (pK_{a} to K_{a} conversion) by applying a very simple but useful chemical formula.
So without any further delay, dive into the article, and let’s start reading!
What is K_{a}?
K_{a} stands for acid dissociation constant.
The ionization equilibrium for the dissociation of a weak acid (HA) in an aqueous solution is represented as follows:
The acid dissociation constant (K_{a}) for the above reaction can be represented as equation (i).
Ka = \frac{[H_{3}O^{+}][A^{-}]}{[HA][H_{2}O]}………. Equation (i)
Where;
- [H_{3}O^{+}] = concentration of hydronium ions formed in the aqueous solution
- [A^{–}] = concentration of conjugate base of the acid
- [HA] = acid concentration at equilibrium
- [H_{2}O] = concentration of water
As water concentration stays constant throughout the reaction, while [H_{3}O^{+}] = [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 K_{a} value for its aqueous solution and vice versa.
What is pK_{a}?
pK_{a} stands for the power of K_{a}, 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. pK_{a} compares the strength of one acidic solution with another.
It is calculated as a negative logarithm to the base 10 of the K_{a} value, as shown in equation (iii) given below.
pK_{a} = -log_{10}K_{a}…………. Equation (iii)
Weak organic acids have greater pK_{a} values than strong mineral acids.
pK_{a} for pure neutral water = 14. It is also known as the water dissociation constant (pK_{w}).
So pK_{a} is related to pK_{b} i.e., base dissociation constant for an aqueous solution as shown in equation (iv).
pK_{a} + pK_{b} = pK_{w} ……. Equation (iv)
You may note that K_{a} measures the strength of the acid itself, while pK_{a }is an attribute associated with the strength of the aqueous solution that the acid forms upon ionization.
What is the relationship between K_{a} and pK_{a}?
The equation [pK_{a} = -log_{10}K_{a}] tells us that K_{a} and pK_{a} are inversely related to each other. A higher K_{a} value results in a lower pK_{a} value and vice versa.
This implies that a strong acid that dissociates to a large extent in an aqueous solution possesses a higher K_{a} value; however, it has a smaller pK_{a}.
So pK_{a} is also inversely related to acidic strength.
How to find K_{a }from pK_{a}? – (pK_{a} to K_{a} conversion)
This equation [pK_{a} = -log_{10}K_{a}] can be converted into equation (v) by taking antilog and making K_{a} the subject of the formula:
∴ K_{a} = 10^{-pKa}………Equation (v)
If the pK_{a} for an acidic solution is given, we can easily determine its acid dissociation constant (K_{a}) by putting the value of pK_{a} in equation (v).
Let’s practice together some examples to see how to calculate K_{a} from pK_{a}.
Solved examples of determining K_{a }when pK_{a} given
Example #1: The pK_{a} of a moderately acidic solution A is 3.14. Find its K_{a}? |
As the pK_{a} value is given in the question statement so we can find K_{a} by applying the equation given below. ∴ K_{a} = 10^{-pKa} ∴ K_{a} = 10^{-3.14} = 7.24 x 10^{-4}. Result: The acid dissociation constant (K_{a}) for the given acid is 7.24 x 10^{-4}. |
Example #2: What is the acid dissociation constant of an acidic solution B whose pK_{a} value is given to be 11.62? |
As the pK_{a} value is given in the question statement so we can find K_{a} by applying the equation given below. ∴ K_{a} = 10^{-pKa} ∴ K_{a} = 10^{-11.62} = 2.40 x 10^{-12} Result: The acid dissociation constant (K_{a}) for the given acid is 2.40 x 10^{-12}. |
Example # 3: Using the pK_{a} and K_{a }values determined in examples 1 and 2, explain which acid is the stronger one? |
As K_{a} is directly related to the strength of an acid. Therefore, as per the K_{a} values calculated in examples 1 and 2, acid A is stronger than acid B. ⇒ K_{a} = 7.24 x 10^{-4} > K_{a} = 2.40 x 10^{-12} A higher K_{a} value denotes that the acid easily liberates its H^{+} ions in the aqueous solution thus it is a stronger acid. Contrarily pK_{a} is inversely related to the strength of an acid. ⇒ pK_{a }= 3.14 < pK_{a} = 11.62 Thus, solution A is more acidic than solution B, conforming to what we predicted above. |
Example # 4: The pK_{a} for acetic acid is 4.80. Which of the following options gives the correct K_{a} 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 pK_{a} value for acetic acid is given in the question statement. So we can substitute it into the equation given below to find K_{a} as follows. ∴ K_{a} = 10^{-pKa} ∴ K_{a} = 10^{-4.80} = 1.58 x 10^{-5}. So the acid dissociation constant (K_{a}) value for acetic acid is 1.58 x 10^{-5}. |
FAQ
What is K_{a}? |
K_{a} stands for acid dissociation constant. A weak acid (HA) partially dissociates to produce H^{+} and A^{–} ions in water. H^{+} ions combine with H_{2}O molecules to form hydronium (H_{3}O^{+}) 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 + H_{2}O ⇌ H_{3}O^{+} + A^{–} The equilibrium constant (K_{a}) for the above reaction can be represented as equation (i) ⇒ Ka = \frac{[H_{3}O^{+}][A^{-}]}{[HA][H_{2}O]}………. Equation (i) Where;
As water concentration stays constant throughout the reaction, while [H_{3}O^{+}] = [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 K_{a} value. Weak organic acids such as acetic acid and citric acid have K_{a} values below 1. However, strong mineral acids such as HCl and HNO_{3} that completely dissociates to release a large number of H^{+} ions in an aqueous solution have K_{a} values above 1. |
How is K_{a} related to the strength of an acid? |
K_{a} is directly related to the strength of an acid. The greater the strength of an acid, the higher its K_{a} value. Weak acids have K_{a} below 1. Strong mineral acids have K_{a} values above 1. |
What is pK_{a}? |
pK_{a} stands for the power of K_{a}. It is calculated as a negative logarithm of the K_{a} value. |
How is pK_{a} related to the strength of an acid? |
pK_{a} is inversely related to the strength of an acidic solution. The greater the strength of an acid, the lower its pK_{a }value. |
What is the relationship between K_{a} and pK_{a}? |
K_{a} is inversely proportional to pK_{a}. The higher the K_{a} of an acid, it dissociates to a greater extent to release a large number of H^{+} ions in an aqueous solution. However, the pK_{a} value of the acidic solution will be lowered. |
What is the formula that relates pK_{a }from K_{a}? |
pK_{a} is the negative logarithm of K_{a} to the base 10 as shown in the formula given below: pK_{a} = -log_{10}K_{a} |
What is the formula that relates K_{a }from pK_{a}? |
K_{a} can be determined by taking the antilog of pK_{a} as shown below. ∴ K_{a} = 10^{-pKa} |
How to find K_{a} if the pK_{a} of a solution is given? |
If the value of pK_{a} is given, we can easily find the acid dissociation constant (K_{a}) for the respective acid by substituting the given value into the following equation. ∴ K_{a} = 10^{-pKa} |
Summary
- K_{a} stands for acid dissociation constant. It measures the extent of ionization of an acid in an aqueous solution.
- Greater the K_{a} value, the higher the strength of the acid.
- pK_{a }denotes the power of K_{a}. It is calculated as a negative logarithm of K_{a} to the base 10.
- pK_{a }= -log_{10}(K_{a}).
- K_{a} can be calculated from pK_{a} by applying antilog on the above formula.
- If the value of pK_{a} for an acidic solution is given, we can find the K_{a} for the respective acid by applying the formula, K_{a} = 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.
About the author
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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