How to calculate Ka from the titration curve? – (Ka from titration curve), Formulas, Equations
The completion of an acid-base titration is marked when the acid completely neutralizes a base or vice versa. Ka stands for acid dissociation constant. The greater the Ka value, the more H+ ions are released in the titration flask; thus, more OH– ions are required to neutralize it.
Can we use the acid-base titration curve to find Ka? Well, the simple answer to this question is yes, but the tricky part is how?
If you are curious to know how to find Ka from the titration curve, then continue reading the article.
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.
Weak organic acids such as CH3COOH usually possess low Ka values (less than 1) as compared to strong mineral acids.
Ka can be converted to another useful chemical parameter called pKa by taking the negative logarithm of Ka, as shown in equation (iii).
pKa = -log10 Ka………….Equation (iii)
pKa is inversely related to Ka. Therefore, the greater the strength of an acid, the lower its pKa value and vice versa.
If the pKa of an acid is given, we can find its Ka by taking the antilog of pKa, as shown in equation (iv).
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 Ka from the titration curve?
As we discussed above, the pKa of an acid = pH is recorded at the half-equivalence point of the acid-base titration curve.
Once we have identified the pKa of acid from the titration curve, we can easily find its acid dissociation constant (Ka) by substituting the known value into equation (iv).
Ka = 10-pKa…………….Equation (iv)
Now let’s apply this concept and solve some questions in the next section so that we can improve our understanding of finding Ka from a given acid-base titration curve.
Solved examples for finding Ka from the titration curve
Example # 1:An HCl solution of unknown concentration was titrated against a 0.1 M aqueous solution of NaOH using a phenolphthalein indicator. The following titration curve is obtained for this acid-base titration.
Use this curve to find the Ka of the respective HCl solution.
The net ionization equation for the above neutralization reaction can be represented as:
An equivalence point is reached in the acid-base titration curve as [H+] = [OH–] in the titration flask.
The following steps can be used to find the Ka of HCl from the given titration curve.
Step i): Identify the steady region in the titration curve i.e., the region when pH changes abruptly at a specific titrant volume.
A steady region in the above curve is approached at titrant volume = 50 mL when pH abruptly increases from 3 (acidic pH) to 11.5 (alkaline pH).
Step ii): Find the half-equivalence point.
As the equivalence point is reached at titrant volume = 50 mL, so half-equivalence point lies at 50/2 = 25 mL.
Now if we trace 25 mL at the titration curve, it corresponds to a pH = 0.8.
Step iii): Find pKa
As pKa = pH at the half-equivalence point
∴ pKa = 0.8
Step iv): Find Ka by applying equation (iv) as shown below.
Ka = 10-pKa…………….Equation (iv)
Ka = 10-0.8= 0.158
Result: The Ka of the HCl of unknown concentration provided in this example is 1.58 x 10-1.
Example # 2:An unknown concentration of acetic acid (CH3COOH) was titrated using a 1.5 M NaOH solution in the presence of a phenolphthalein indicator. Find Ka using the acid-base titration curve given below.
CH3COOH reacts with NaOH to form CH3COO–Na+ and H2O. It is an example of a weak acid versus strong base titration; therefore, the titration curve begins at a pH above that seen in example 1.
The net ionization equation for the above neutralization reaction can be represented as:
An equivalence point is reached in the acid-base titration curve as [H+] = [OH–] in the titration flask.
The following steps can be used to find the Ka value from the given titration curve.
Step i): Identify the steady region in the titration curve i.e., the region when pH changes abruptly at a specific titrant volume.
A steady region in the above curve is approached at titrant volume = 10 mL.
Step ii): Find the half-equivalence point.
As the equivalence point is reached at titrant volume = 10 mL, so half-equivalence point lies at 10/2 = 5 mL.
Now if we trace 5 mL at the titration curve, it corresponds to a pH = 6.3.
Step iii): Find pKa
As pKa = pH at the half-equivalence point
∴ pKa = 6.3
Step iv): Find Ka by applying equation (iv) as shown below.
Ka stands for acid dissociation constant. It measures the extent of ionization of an acid in an aqueous solution. The greater the strength of an acid, the more rapidly it dissociates in an aqueous solution. Thus it possesses a high Ka value and vice versa.
What is pKa?
pKa denotes the negative logarithm of Ka.
pKa = -log10 Ka
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 Ka 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 Ka from the titration curve:
i) Identify the equivalence point at the steady state of the titration curve.
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 at x/2.
iv) As pH = pKa so, find the Ka of the acid as follows:
Ka = 10-pKa.
Summary
Ka stands for acid dissociation constant. It determines the extent of ionization of an acid in an aqueous solution.
The greater the strength of an acid, the higher its Ka However, it has a low pKa value.
pKa is calculated by taking the negative logarithm of Ka. pKa = – log10 Ka.
Titration is a volumetric analysis method. Acid-base titrations are performed to find the unknown concentration of an acid or base against a corresponding base or acid of known concentration.
A titration curve is plotted, taking the pH of the analyte solution (titrand) on the y-axis versus the volume of titrant added on the x-axis.
An equivalence point is achieved in a titration mixture when the acid and base are completely neutralized; [H+] = [OH–].
An indicator marks the completion of the titration by giving a color change near the equivalence point. This is known as the endpoint of the titration.
The equivalence point can be identified as a steady state on the titration curve.
pKa of the respective acid = pH of the titration mixture at half-equivalence point.
Once we know pKa from the titration curve, we can easily find Ka by applying Ka = 10-pKa.
In this way, Ka can be determined from the titration curve typically for strong acid vs strong base or weak acid vs strong base titrations.
References
University of Massachusetts Amherst. (n.d.). Experiment 5: Acid-Base Titration. Retrieved March 28, 2023, from https://genchem.chem.umass.edu/chem112/112_Experiment_5.htm
Khan Academy. (n.d.). Acid-base titration curves. Retrieved March 28, 2023, from https://www.khanacademy.org/test-prep/mcat/chemical-processes/titrations-and-solubility-equilibria/a/acid-base-titration-curves
Study.com. (n.d.). How to Calculate pKa from the Half-Equivalence Point in a Weak Acid-Weak Base Titration: Explanation. Retrieved March 28, 2023, from https://study.com/skill/learn/how-to-calculate-pka-from-the-half-equivalence-point-in-a-weak-acid-weak-base-titration-explanation.html
Libretexts. (n.d.). Titration of a Weak Base with a Strong Acid. Retrieved March 28, 2023, from https://chem.libretexts.org/Ancillary_Materials/Demos_Techniques_and_Experiments/General_Lab_Techniques/Titration/Titration_of_a_Weak_Base_with_a_Strong_Acid
Chemguide. (n.d.). pH curves and indicators. Retrieved March 28, 2023, from https://www.chemguide.co.uk/physical/acidbaseeqia/phcurves.html
Easy Biology Class. (n.d.). Titration Curve of a Weak Acid and its pKa – Biochemistry Notes. Retrieved March 28, 2023, from https://www.easybiologyclass.com/titration-curve-of-a-weak-acid-and-its-pka-biochemistry-notes/
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