pKa stands for the power of acid dissociation constant (Ka).
It is calculated by taking the negative logarithm of Ka, as shown in equation (i).
pKa = -log10 Ka…………. Equation (i)
An acid is defined as a chemical substance that breaks down to release H+ ions in an aqueous solution.
The extent of ionization of an acid is determined by its acid dissociation constant (Ka). Higher the Ka value, the stronger the acidic strength and vice versa.
However, as per equation (i) pKa is inversely related to Ka, which implies that the greater the strength of an acid, the higher its Ka value, but it possesses a low pKa value respectively.
What is a titration curve?
Titration is a volumetric analysis method. It is used to find the unknown concentration of an acid or a base by titrating it against a solution of known concentration.
The solution of unknown concentration is known as the analyte or the titrand. Contrarily, the corresponding acid or base solution of known concentration is referred to as the titrant in an acid-base titration.
The titrand is taken in a titration flask, and a few drops of the indicator are added.
The titrant is then dropwise added from the burette into the analyte mixture present in the titration flask.
A titration curve is plotted, keeping the pH of the analyte solution/ tirand on the y-axis versus the volume of the titrant on the x-axis.
For instance, if we consider determining the unknown concentration of HCl against a 0.1 M solution of NaOH. In this case, HCl is the titrand while 0.1 M NaOH solution is the titrant.
It is an example of a strong acid versus strong base titration. Phenolphthalein is most commonly used as an indicator in such titrations.
In this case, as the titration flask initially contains a strong acid completely dissociated to release a large number of H+ ions, therefore the titration curve shows a very low initial pH value (< 1).
The changes in pH are recorded using a pH meter, while the volume of titrant added is measured as per burette readings.
The pH increases as more NaOH is added from the burette. OH– ions of NaOH readily neutralize H+ ions present in the titration flask, and the pH of the analyte solution increases progressively.
An equivalence point is reached as all H+ ions present in the titration flask get completely neutralized by OH– ions provided by the titrant.
The indicator marks the endpoint of the titration by immediately changing color (from colorless to light pink).
The endpoint of the indicator must coincide with the equivalence point of the acid-base titration for the most accurate results.
A steady state is reached at this point in the titration curve. The equivalence point of the titration lies at exactly the middle of this steady state.
If the volume of titrant at the equivalence point = x mL. Then we can find pH at half-equivalence point i.e., x/2.
The pH of the solution at the half-equivalence point is exactly equal to the pKa of the given acid.
Further increase in titrant volume makes the solution alkaline by an excess of OH– ions in the titration flask, so the pH rapidly increases (> 10), as shown in the titration curve drawn above.
How to find pKa from the titration curve?
As mentioned above, pKa of an acid = pH at the half-equivalence point of the titration curve.
As per Henderson Hasselbalch equation (equation ii), pH is related to the pKa of acid as follows:
where;
[HA] represents the concentration of the acid, while [A–] denotes the concentration of the conjugate base of the acid.
For instance, if HCl is acid, then Cl– ions are its conjugate base formed by the loss of 1 proton (H+) per acid molecule.
At the half-equivalence point, [A–] = [HA]. So the ratio [A–]/[HA] = 1 and the equation (ii) transforms into:
pH = pKa + log10(1)
log10(1) = 0
∴ pH = pKa…………Equation (iii)
Therefore, for the above example, we can find the pKa of HCl by tracing the half-equivalence point on the HCl-NaOH titration curve.
We primarily use this concept of finding pKa from a titration curve for two main types of titrations:
Strong acid-strong base titration
Weak acid-strong base titration
In either case, the acid is the analyte solution or titrand, while the corresponding base is the titrant.
You will understand this concept better by going through the solved examples given below. So let’s begin.
Solved examples for finding pKa from the titration curve
Example # 1:The following titration curve is obtained at the end of a strong acid-strong base titration experiment in which 50 mL HCl was titrated against 0.100 M NaOH solution. The exact concentration of HCl is determined to be 0.100 M.
Use this titration curve to find the pKa of the acid.
The net ionization equation for the above neutralization reaction can be represented as:
As shown in the titration curve, the analyte solution initially had a pH = 1 when only HCl was present in the titration flask. As it was titrated against NaOH from the burette, the pH of the analyte solution increased.
An equivalence point was reached where [H+] = [OH–], represented by a steady state on the graph.
Further NaOH addition increased the pH to 12, representing an alkaline solution.
The following steps will guide you on how to find the pKa of the given acid from this titration curve.
Step i): Identify the equivalence point in the graph.
The equivalence point lies at the steady state of the titration curve i.e., at volume = 50 mL, where there is a sharp rise in pH without any further change in volume.
Step ii):Locate the half-equivalence point.
If the equivalence point occurs at volume = x = 50 mL, then the half-equivalence point of the titration curve is located at x/2 = 50/2 = 25 mL.
Step iii):Find the pH corresponding the half-equivalence point.
Reading pH at the y-axis, corresponding to V= 25 mL on the x-axis, gives us:
∴ pH = pKa = 1.8.
Result: The pKa of 0.100 M HCl solution as per the above data is 1.8.
Example # 2:An acetic acid solution of unknown concentration was titrated against 0.1 M NaOH. It is an example of a weak acid-strong base titration. Use the titration curve shown below to find the pKa of acetic acid.
The acid-base neutralization reaction of acetic acid (CH3COOH) with NaOH produces CH3COO–Na+ (sodium acetate) and water (H2O).
The net ionization equation for the above neutralization reaction can be represented as:
Let’s find out the pKa of the acid using the given titration curve and the following series of steps.
Step i): Identify the equivalence point in the graph.
The graph starts at a comparatively higher pH than the initial pH recorded in example 1, as the former involves a weak acid.
A steady state is obtained in the graph at titrant volume = 50 mL.
You may note here that there is a small rise in pH as the equivalence point is achieved as opposed to a very sharp rise, witnessed in strong acid-strong base titrations (example 1).
Step ii):Locate the half-equivalence point.
If the equivalence point occurs at volume = x = 50 mL, then the half-equivalence point of the titration curve is located at x/2 = 50/2 = 25 mL.
Step iii):Find the pH corresponding the half-equivalence point.
Reading pH at the y-axis, corresponding to V= 25 mL on the x-axis, gives us:
∴ pH = pKa = 4.7
Result: The pKa of the given acetic acid solution as per the above data is 4.7
Example # 3:The titration curve for the weak acid-strong base titration of propanoic acid (CH3CH2COOH) with 0.1 M NaOH is given below.
How will you find the pKa of the propanoic acid using this titration curve?
An acid-base neutralization reaction occurs when CH3CH2COOH reacts with NaOH to form CH3CH2COO–Na+ (sodium propanoate) and H2O.
The net ionization equation for the reaction is:
We can follow the following simple steps to find the pKa of the acid from the given titration curve.
Step i): Identify the equivalence point in the graph.
You may note that, in this case, there is no definite steady state. This is because propanoic acid is a very weak acid.
The titration curve starts from a comparatively higher pH (2.5). The pH does not rise sharply at the equivalence point in a weak acid vs strong base titration. We identify the equivalence point where the slope of the curve decreases.
This is the point where OH– ions start to overpower H+ ions present in the analyte solution.
The equivalence point (at which [H+] = [OH–]) is marked between V1 = 22 mL to V2 = 42 mL. Let’s calculate the average of the two values:
Equivalence point = (22 + 42)/2 = 32 mL
Step ii):Locate the half-equivalence point.
If the equivalence point occurs at volume = x =32 mL, then the half-equivalence point of the titration curve is located at x/2 = 32/2 = 16 mL.
Step iii):Find the pH corresponding to the half-equivalence point.
Reading pH at the y-axis, corresponding to V= 16 mL on the x-axis, gives us:
∴ pH = pKa = 4.9
Result: The pKa of propanoic acid, as per the above data, is 4.9.
Example # 4: How can we compare the strength of acids used in examples 1, 2, and 3 as per their pKa values obtained from the respective titration curves?
In all the above examples, 0.1 M NaOH was used as the titrant. As per the data obtained from the respective titration curves, pKa (CH3CH2COOH) > pKa (CH3COOH) >>> pKa (HCl).
This reassures what we said at the beginning of the article i.e., the higher the pKa value, the lower the acidic strength and vice versa.
Consequently, propanoic acid is weaker than acetic acid, while HCl is definitely stronger than both CH3CH2COOH and CH3COOH.
It determines the acidity of an aqueous solution. The lower the pKa value, the more strongly acidic the aqueous solution is.
What is titration?
Titration is a wet volumetric analysis method. It is performed to find the concentration of an unknown solution using a solution of known concentration.
What is acid-base titration?
An acid-base titration is performed to find the unknown concentration of an acid or a base against a corresponding base or acid of known concentration respectively.
What is a titrant?
Titrant is a chemical substance whose concentration is known while performing a titration experiment. It is usually taken in a burette.
What is a titrand?
Titrand is a chemical substance whose concentration is to be determined via a titration experiment. It is usually taken in a titration flask, also known as an Erlenmeyer flask.
What is an indicator in an acid-base titration?
The indicator is a chemical substance that gives a visual sign, such as a color change, to mark the endpoint of a titration.
Usually, conjugated organic dyes such as methyl orange, methyl red, phenolphthalein etc, are used as indicators in acid-base titrations.
These absorb visible radiations of the electromagnetic spectrum and exhibit vibrant colors. The color changes quickly with a sudden change in the pH of the titration mixture.
What is the equivalence point in an acid-base titration?
The equivalence point is the point at which the concentration of hydrogen ions [H+] becomes equal to the concentration of hydroxide ions [OH–] in the titration flask.
It is where the acid is completely neutralized by the base.
What is the difference between an endpoint and an equivalence point?
Equivalence point = pH at which [H+] = [OH–] in an acid-base titration.
Endpoint = pH at which indicator gives a color change with a small drop of an acid or base from the burette.
The best choice of an indicator for a titration experiment is the one whose endpoint coincides with the equivalence point of the acid-base titration.
What is a titration curve?
A titration curve is a plot of the pH of the analyte mixture in the titration flask versus the volume of titrant added from the burette.
How to find pKa from the titration curve?
pKa of an acid = pH at half-equivalence point in the acid-base titration curve.
The following simple steps can be applied to find the pKa of acid from its acid-base titration curve:
i) Identify the equivalence point in the titration curve. It is located where there is a sharp change in pH (for strong acid-strong base titrations) or where the graph has a decreasing slope (in weak acid-strong base titrations).
ii) If the volume of the titrant at the equivalence point = x, then the volume at half the equivalence point = x/2.
iii) Trace the pH on the y-axis from volume = x/2 at the x-axis.
∴ pKa = pH at the half-equivalence point of the titration curve.
Summary
pKa measures the strength of an acid. It is calculated by taking the negative logarithm of the acid dissociation constant (Ka).
The greater the strength of an acid, the lower the pKa of its aqueous solution.
Titration is a volumetric analysis method.
Acid-base titrations are used to find the unknown concentration of an acid or a base by titrating it against a corresponding base or acid of known concentration.
An acid-base neutralization reaction forms the basis of an acid-base titration.
The equivalence point of the titration is marked when [H+] = [OH–] in the analyte mixture.
A titration curve is plotted by taking the pH of the analyte solution on the y-axis versus the titrant volume on the x-axis.
A sharp change in pH marks the endpoint of the titration at the equivalence point.
The area lying between the initial point and the equivalence point on the titration curve is known as the buffer region in a titration curve.
If the volume of titrant added = x mL at the equivalence point, then we can find the volume at the half-equivalence point = x/2 mL.
The pH of the solution at half-equivalence point = pKa of the acid. This is because, as per the Henderson Hasselbalch equation, pH = pKa + log10[A–]/[HA] ; [A–] = [HA] at the half-equivalence point. In this way, we can find the pKa of acid using its acid-base titration curve. This method is predominantly used for strong acid vs strong base or weak acid vs strong base titrations.
Study.com. “How to Calculate pKa from the Half Equivalence Point in a Weak Acid-Weak Base Titration.” Study.com, Study.com, 2021, https://study.com/skill/learn/how-to-calculate-pka-from-the-half-equivalence-point-in-a-weak-acid-weak-base-titration-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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