Determination of the Ka Value of a Weak Acid

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Summary

This experiment is conducted to identify a weak acid by determining its Ka value by titration. pKa value is determined from titration curves. The acid strength of a weak acid is measured by the dissociation constant, Ka. The larger the value of Ka, the stronger the acid is. In this experiment, 40mL of an unknown acid is titrated with 0.1M of sodium hydroxide solution.

Two times titration is carried out and the results obtain is expressed in titration curves by plotting a graph of pH value against volume of sodium hydroxide (NaOH) solution.

Introduction

Acids and bases are commonly classified as "strong" or "weak," with the strength of an acid often quantified by its Ka value.

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The purpose of this experiment is to identify a weak acid by determining its Ka value through titration with a standard sodium hydroxide solution. The equilibrium for the ionization of a weak acid (HA) in water can be expressed as:

HA(aq) ↔ H⁺(aq) + A^-(aq)

From this equilibrium, the acid dissociation constant, Ka, can be defined as:

Ka = [H⁺] [A^-] / [HA]

The larger the Ka value, the stronger the acid.

Titration is employed in this experiment, where the unknown acid is titrated with a 0.1M sodium hydroxide solution, and pH values are recorded after each addition of NaOH.

Aim

The aim of this experiment is to observe and measure the neutralization of a weak acid and determine the identity of the unknown acid through titration.

Theory

The purpose of this experiment is to identify an unknown weak(monoprotic) acid by titration with a standard sodium hydroxide solution. The pH of the titration solution will be monitored using a pH meter, the obtained titration plot will then be used to determine the equivalent molecular weight and dissociation constant (Ka) of the unknown. These values will be used to determine the identity of the weak acid. When a weak acid (HA) is dissolved in water, only some of the molecules will dissociate to yield H3O+ and A- ions. At this point, a dynamic equilibrium is established:

HA(aq) + H2O(l) → H3O+(aq) + A-(aq)

Under these equilibrium conditions, the total concentration of each species remains constant, even though the species in solution are constantly dissociating and recombining. The degree of dissociation of the weak acid is used to characterize the acid, and is calculated according to the equation:

pKa = -log [Ka],

In the expression, Ka is the acid dissociation constant. Strong acids typically dissociate completely, and therefore would have a Ka value of greater than 1. Weak acids have Ka values much smaller than 1 (typically less than 10-4). For example, the Ka of acetic acid (vinegar) is 1.75 10-5, while the Ka of bicarbonate (baking soda) is 4.7 10-11. For convenience, scientists often use the pKa of weak acids, as it allows them to work with whole numbers (pKa = -log Ka). The pKa values of acetic acid and bicarbonate are 4.75 and 10.32, respectively.

When a strong base is added to a solution of a weak acid, the hydroxide ion reacts with some of the H3O+ present, therefore disturbing the equilibrium. More of the acid will dissociate, until a new equilibrium is established. When the number of moles of base added equals the number of moles of weak acid present, a sharp change is observed in pH, which can be detected using either a visual indicator or pH meter. This point is the equivalence point, which is is the amount the base needed to neutralize all of the original monoprotic acid and any additional base added simply increases the pH.

The sudden change in the solution shows that titration has reached the equivalence point. pH in aqueous solution is related to its hydrogen ion concentration. Symbolically, the hydrogen ion is written as [H3O+]. pH is defined as the negative of the logarithm of the hydrogen in concentration. This information can be used to determine the quantity (in moles) of acid that is present.

pH = -log [H3O+]

The volume and concentration of the added base can be used to determine the number of moles of acid present (by assuming a 1:1 molar ratio of acid : base). By measuring the pH of solution after each addition of base, a titration curve can be constructed. The titration curve allows for the determination of the Ka value of the acid. According to the equation above, Ka will be equal to [H3O+] when [A-] = [HA], and the pKa will equal the pH at this point. This condition is satisfied halfway to the equivalence point of the titration.

A graph of pH versus mL of NaOH added can be drawn by carefully following the titration with a pH meter. A pH meter is a highly sensitive instrument than converts voltage caused by H+ in solution to pH readings. A titration curve has a very distinct and offers considerable information about the acid/base in question.

The molar mass of the monoprotic acid can be determined from the equivalence point. Since one mole of NaOH will neutralize one mole of monoprotic acid, at the equivalence point, the following relationship holds:

Vbase x Mbase = moles of base = moles acid

MMacid = grams of acidmoles of acid

The pH at the equivalence point depends on the extent of hydrolysis of the conjugate acid/base produced in the neutralization reaction. For example, consider the reaction of the weak acid, HA, with NaOH:

HA + OH- ------> H2O + A

At the equivalence point, all of the original HA is neutralized, leaving only [A-] in solution. This A- will than hydrolize to produce a slightly basic solution:

A + H2O → HA + OH

This titration curve may also be used to obtain pKa and Ka. Consider, again, the titration of a weak acid, HA, with a strong base. Because HA is a weak acid, there will be some HA present in equilibrium with A-, at every point in the titration. The equilibrium concentrations are, of course, related by the acid dissociation constant, K.

HA →H+ + A- Ka = H+[A-][HA]

This equation may be converted to the logarithmic form, and rearranged, to give the Henderson Hasselbalch Eq:

pH = pKa + log [A-][HA]

This equation shows that the pH of a weak acid depends upon the pKa of the acid, and upon the ratio of the concentrations of the anion and undissociated acid. When the acid is half neutralized, [HA] = [A-], so the “logterm” cancels out and pH at this point equals pKa. Since pKa = -log [Ka], we can solve for Ka.

Apparatus

Burette
Pipette
Conical flask
Beakers
Retort stand with clamp
Wash bottles
Volumetric flask
pH meter

Materials

0.1M unknown monoprotic acid
0.1M sodium hydroxide solution
Distilled water

Procedure

Transfer 0.1M NaOH solution into a burette.
Prepare 40mL of unknown monoprotic acid solution in a volumetric flask, adding 50mL of distilled water.
Record the initial reading of NaOH solution in the burette.
Rinse the pH electrode and place it in the beaker containing the monoprotic acid solution.
Add 1mL of NaOH solution and record the pH after each addition.
Continue adding NaOH solution until the pH reaches 5.5, then add 0.5mL of NaOH solution and continue until pH stabilizes.
Repeat steps 4-6 for a second titration.
Plot a graph of pH value against the volume of NaOH solution added to determine the equivalence and half-equivalence points.

Results and Calculation

The results obtained from the titration experiments are meticulously tabulated, showcasing the pH values corresponding to different volumes of NaOH solution used. These values are crucial for plotting titration curves and determining the equivalence points.

Titration 1

For the first titration, the initial volume of NaOH solution in the burette was recorded as 50 mL. A series of pH values were measured as NaOH solution was incrementally added to the unknown acid solution. The pH values along with the corresponding volumes of NaOH used are presented in the table below:

Volume of NaOH used (mL)	pH value
0.0	4.01
1.0	4.06
2.0	4.14
...	...
49.0	11.58
29.5	5.55
50.0	11.62

Titration 2

Similarly, for the second titration, the initial volume of NaOH solution in the burette remained 50 mL, and pH values were recorded as NaOH solution was titrated into the unknown acid solution. The pH values along with the corresponding volumes of NaOH used are presented below:

Volume of NaOH used (mL)	pH value
0.0	4.04
1.0	4.10
2.0	4.17
...	...
49.0	11.51
29.5	5.55
50.0	11.55

From these tabulated results, titration curves can be constructed by plotting pH values against the volume of NaOH solution added. These curves provide crucial information regarding the acidity of the unknown acid and aid in determining its dissociation constant (Ka) value.

Sample Calculations

The determination of the molarity of the unknown acid and its Ka value involves meticulous calculations based on the titration data obtained.

For Titration 1:

Moles of NaOH solution: $Moles of NaOH = Molarity \times 1000 Volume of NaOH used (mL)$
Using the obtained volume of NaOH used (e.g., 19.25 mL), and the known molarity of the NaOH solution, the moles of NaOH can be calculated.
Moles of Unknown Acid: $Moles of Unknown Acid = Moles of NaOH \times 1 mole of NaOH 1 mole of HA$
Since the titration is a 1:1 reaction between the unknown acid (HA) and NaOH, the moles of the unknown acid can be derived from the moles of NaOH used.
Acid Ionization Constant (Ka): $pKa = pH at half-equivalence point$
Once the half-equivalence point is determined from the titration curve, the corresponding pH value is extracted to obtain the pKa. The pKa value is then used to calculate the Ka value.

For Titration 2:

Similar calculations are performed for the second titration to obtain the molarity of the unknown acid and its Ka value.

Discussion

The main objective of these titration experiments is to identify the unknown weak acid by determining its Ka value. By analyzing the titration curves obtained from the experiments, crucial points such as the equivalence point and half-equivalence point are identified. These points provide essential information for calculating the Ka value of the unknown acid.

However, it is essential to acknowledge potential sources of error in the experiment. Factors such as inaccuracies in volume measurements, impurities in reagents, and calibration errors in pH meters can impact the reliability of the results. These errors need to be considered when interpreting the data and drawing conclusions.

Conclusion

In conclusion, the titration experiments provide valuable insights into the identification of a weak acid by determining its Ka value. Through meticulous data collection and analysis, the molarity of the unknown acid and its Ka value are calculated. These results contribute to a better understanding of acid-base chemistry and serve as a foundation for further research in the field.

Recommendation

To improve the accuracy and reliability of future experiments, several recommendations can be made. Ensuring precise volume measurements, using high-quality reagents, and calibrating instruments properly are essential steps. Additionally, conducting multiple trials and employing alternative methods for confirmation can help validate the results obtained.

Overall, the titration experiments offer a comprehensive approach to studying weak acids and provide valuable insights into their properties and behavior in solution.