To find the molar mass of a weak acid, the most common and effective method is through acid-base titration using a strong base of known concentration. This technique allows for the precise determination of the amount of acid present, which can then be used with its initial mass to calculate its molar mass.
Understanding the Titration Method
Titration is a quantitative chemical analysis method used to determine the concentration of an identified analyte. In the case of a weak acid, you react a precisely measured quantity of the acid with a strong base (the titrant) whose concentration is accurately known. By carefully monitoring the pH during the addition of the strong base, you can generate a pH titration curve.
This curve, created by plotting pH against the amount of strong base added, is essential. It allows you to determine both the acid's ionization constant (Ka) and its molar mass. Weak acids react with water to produce small concentrations of ions, and the degree of this ionization at equilibrium is described by the equilibrium constant Ka.
Steps to Determine Molar Mass and Ka
Follow these steps to accurately determine the molar mass of a weak acid:
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Prepare the Weak Acid Sample:
- Accurately weigh a known mass of the unknown weak acid using an analytical balance. Record this mass precisely.
- Dissolve the weighed acid in a known volume of distilled water in an Erlenmeyer flask or beaker.
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Prepare the Titrant:
- Fill a burette with a strong base solution (e.g., sodium hydroxide, NaOH) of a precisely known concentration (molarity).
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Perform the Titration:
- Place a pH meter probe into the weak acid solution to continuously monitor its pH.
- Slowly add the strong base from the burette to the weak acid solution, stirring constantly.
- Record the pH of the solution after each incremental addition of the strong base. Pay close attention as the pH begins to change more rapidly.
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Plot the Titration Curve:
- Create a graph with the volume of strong base added on the x-axis and the pH of the solution on the y-axis. This plot will reveal the characteristic S-shaped curve of a weak acid-strong base titration.
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Identify the Equivalence Point:
- The equivalence point is the point on the titration curve where the moles of strong base added exactly equal the initial moles of weak acid present. This is typically observed as the steepest part of the S-curve, where the pH changes most dramatically. You can find it precisely by looking for the maximum slope on the first derivative of the curve, or where the second derivative is zero.
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Calculate the Moles of Weak Acid:
- At the equivalence point, assuming a monoprotic acid (one acidic proton), the moles of strong base added are equal to the moles of weak acid initially present.
- Use the following formula to calculate the moles of base:
Moles of Base = Concentration of Base (mol/L) × Volume of Base (L) at Equivalence Point - Therefore,
Moles of Weak Acid = Moles of Base
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Calculate the Molar Mass of the Weak Acid:
- With the known mass of the weak acid and the calculated moles of the weak acid, you can now determine its molar mass:
Molar Mass of Weak Acid (g/mol) = Mass of Weak Acid (g) / Moles of Weak Acid (mol)
- With the known mass of the weak acid and the calculated moles of the weak acid, you can now determine its molar mass:
Determining the Acid Dissociation Constant (Ka)
From the same titration curve, you can also determine the acid dissociation constant (Ka):
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Identify the Half-Equivalence Point:
- The half-equivalence point occurs when exactly half the volume of strong base required to reach the equivalence point has been added.
- At this specific point, the concentration of the weak acid is equal to the concentration of its conjugate base (i.e., [HA] = [A⁻]).
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Determine pKa:
- At the half-equivalence point, the pH of the solution is equal to the pKa of the weak acid. This is because, at this point, the Henderson-Hasselbalch equation (pH = pKa + log([A⁻]/[HA])) simplifies to pH = pKa.
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Calculate Ka:
- Once you have the pKa, you can calculate the Ka using the relationship:
Ka = 10^(-pKa)
- Once you have the pKa, you can calculate the Ka using the relationship:
Summary Table: Key Points of Titration
| Measurement/Point | Significance | Use for Determination |
|---|---|---|
| Initial Mass of Acid | The precisely weighed amount of the weak acid. | Essential for calculating molar mass. |
| Titrant Volume & Molarity | The volume of strong base (titrant) added and its known concentration. | Determines moles of base added. |
| pH Titration Curve | A plot of pH vs. volume of strong base added. This visual representation allows for the identification of critical points. | Enables identification of equivalence and half-equivalence points. |
| Equivalence Point | The point where moles of strong base exactly neutralize the initial moles of weak acid. Identified as the steepest rise in pH on the curve. | Used to calculate moles of weak acid and, subsequently, its molar mass. |
| Half-Equivalence Point | The point where half the titrant volume required for the equivalence point has been added. At this point, the concentrations of the weak acid and its conjugate base are equal. | Used to find the pKa and then the acid dissociation constant (Ka). |
By carefully performing a pH-monitored titration, you can gain valuable insights into the properties of a weak acid, including its molar mass and its characteristic ionization constant.
