The symbol Keq represents the equilibrium constant for a reversible chemical reaction. The dissociation of a weak acid in water to liberate H+ ions is one such reversible reaction.
So what do you think is the equilibrium constant for acid dissociation called? If we know the pKa of acid, how can we use it to find Keq for its partial ionization?
Continue reading the article to find the answers to all these questions.
Mineral acids such as HCl, H2SO4, HNO3, etc., are strong acids that irreversibly ionize in water to release a large number of H+ ions.
Contrarily, weak carboxylic acids such as formic acid (HCOOH) and acetic acid (CH3COOH) only partially ionize in water to liberate a limited number of H+ ions, giving a reversible chemical change.
A weak acid, generally represented as HA when added to water, breaks down into H+ and A– ions, where A– denotes the conjugate base of the acid.
HA (aq) ⇌ H+ (aq) + A–(aq)
H+ combines with H2O molecules to form hydronium (H3O+) ions. So the overall chemical reaction becomes:
HA (aq) + H2O (aq) ⇌H3O+ (aq) + A–(aq)……Equilibrium (i)
For a reversible chemical change, the equilibrium constant (Keq) refers to the ratio of the product of the molar concentration of products to the product of the molar concentration of reactants.
Where,
Ka = Equilibrium constant for the dissociation of a weak acid
[A–] = Molar concentration of conjugate base of the acid (Units: mol/dm3or M)
[H+] = Molar concentration of hydrogen ions (Units: mol/dm3or M)
[HA] = Molar concentration of the weak acid (Units: mol/dm3 or M)
The greater the Ka value, the higher the strength of the acid, as a higher Ka value implies more H+ ions released in water.
If Keq = Ka > 1: Equilibrium (i) shifts forward
If Keq = Ka < 1: Equilibrium (i) shifts backward
If Keq = Ka = 1: Dynamic equilibrium is maintained
At dynamic equilibrium, the rate of forward reaction is equal to the rate of backward reaction.
What is pKa?
pKa is defined as the negative logarithm to the base 10 of Ka.
The lower the pKa value, the greater the strength of the acid, and vice versa.
pKa = -log10 Ka….Equation (iii)
How to find Keq from pKa? – Examples
For acid dissociation, Keq = Ka; therefore, if the value of pKa of an acidic solution is given, we can find its Keq by taking the antilog of pKa as shown below:
For example,The pKa of acetic acid is 4.76. Find its equilibrium constant (Keq).
Solution:
Acetic acid dissociates in water as follows:
CH3COOH (aq)⇌ CH3COO–(aq) + H+ (aq)……Equilibrium (ii)
As the pKa value is given in the question statement, so we can find Keq by applying the formula Keq = 10-pKa.
⇒ Keq = 10-pKa
Step I: Substitute the given value of pKa.
Keq = 10-4.76
Step II: On your scientific calculator, press 10, then press ^ and insert the value of pKa with the negative sign.
Keq = 10-4.76
∴ Keq = 1.74 x 10-5 mol/dm3.
Result: The equilibrium constant for the dissociation of acetic acid in water is 1.74 x 10-5 mol/dm3.
Further insight: Keq < 0 implies that equilibrium (ii) is largely shifted towards the left (backward); thus, most of the acetic acid stays undissociated.
Let’s see another example- Find the equilibrium constant (Keq) for hydrofluoric acid given that its pKa value is 3.17.
Solution:
Hydrofluoric acid dissociates in water as follows:
HF (aq)⇌ H+ (aq) + F–(aq) ……Equilibrium (iii)
As the pKa value is given in the question statement, so we can find Keq by applying the formula Keq = 10-pKa.
⇒ Keq = 10-pKa
Step I: Substitute the given value of pKa.
Keq = 10-3.17
Step II: On your scientific calculator, press 10, then press ^ and insert the value of pKa with the negative sign.
Keq = 10-3.17
∴ Keq = 6.76 x 10-4 mol/dm3.
Result: The equilibrium constant for the dissociation of hydrofluoric acid in water is 6.76 x 10-4 mol/dm3.
Further insight: Keq < 0 implies that equilibrium (iii) is also largely shifted towards the left (backward).
However, you may notice that Keq (HF) > Keq (CH3COOH) while pKa (HF) < pKa (CH3COOH), which means hydrofluoric acid is a comparatively stronger acid than acetic acid.
FAQ
How do you find Keq from pKa?
pKa refers to the negative logarithm of Ka to the base 10, where Ka stands for the equilibrium constant (Keq) for the dissociation of a weak acid in water.
So Keq can be calculated by taking the antilog of pKa, shown below:
Keq = 10-pKa
When is Keq = Ka?
Keq = Ka when we are determining the equilibrium constant for the dissociation of a weak acid (HA) in water.
As [H2O] stays constant, thus Keq x [H2O] = Ka.
What is the relationship between pKa and the pH of an acid?
The pKa of an acid is directly related to its pH as per the Henderson Hasselbalch equation:
The greater the acidity of an aqueous solution, the lower its pH and pKa values.
How to determine the position of an equilibrium for an acid-base reaction?
The position of an acid-base equilibrium can be determined from its Keq.
For a reversible reaction: Acid + Base ⇌ Conjugate base + Conjugate acid
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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