Acid-Base Titration Lab Report

Madison Guido

Determination of Ka : Titration of Weak Acid

Introduction/Theory:

The purposed of this experiment is to use a LoggerPro and LabPro to follow the pH changes during an acid-base titration, and ultimately determine the Ka, through calculation, of the weak-acid (acetic acid or vinegar, HC2H3O2) being titrated. Ka can be defined as a constant for a given acid at any temperature. Generally, in water solutions, weak acids react with water to establish equilibrium, for example:

HA + H2O ⇄ H3O+ + A-

This equilibrium is represented by Ka, or the acid dissociation constant, in which:

Ka = [H3O+]aq x [A-]aq/ [HA]aq

The Ka of an acid can be calculated in two ways, including (1) the measurement of the pH of a solution containing a know concentration of a weak acid, and (2) measurement of the pH at the

half-neutralization point in the titration of the weak acid with a strong base. Following the pH during the titration of a weak acid and strong bases, data can be obtained that allows for calculation of Ka using both methods (1) and (2), and also shows why only some indicators are reliable in the titration of a weak acid and strong base.
Generally, in the titration of a weak acid and strong base, the plot of pH against milliliters of base added will look like the graph below:
The graph forms the curve shown because after each addition of base, the equilibrium between the weak acid and it’s ion (HA and H3O+ and A-) is reestablished according to the Ka equation (Ka = [H3O+]aq x [A-]aq/ [HA]aq). If this equation is rearranged and the logarithm of both sides is taken and multiplied by -1, a subsequent equation is established that gives the pH at any [A-]/[HA] ratio, in which pKa is equal to the -logKa:
pH = pKa + log([A-]aq/[HA]aq)
The ratio of [A-]/[HA] changes with each addition of the base to the acid because the reaction is being pushed further to the right. At the beginning of the reaction, only small concentrations of the ions (H3O+ and A-) are present, but as the base is added, the acid begins to neutralize, thus decreasing its concentration, while salt is formed and increases the concentration of [A-]. Therefore, throughout the titration, [HA] decreases and [A-] increases until all of the weak acid is neutralized, and as this happens and the ratio of [A-]/[HA] increases from a low to high value the pH of the solution of weak acid and strong base follows the titration curve shown above.
Finally, during titration of a weak acid and strong base, the first addition of base produces a significant rise in pH. This is followed by a region in which the pH then only changes slightly. In this region of slight change, the solution is being buffered by the presences of the weak acid and its salt. As the addition of base continues, the acid concentration decreases so much that the solution is no longer buffered and the pH rises rapidly through neutralization, equivalence point, which is the point at which chemically equivalent quantities of acid and base have been mixed, and beyond. Beyond this region, the acid has been neutralized and the pH of the solution changes only slightly as more base is added (all seen in titration curve shown above).

Procedure:
Assemble the LabPro and LoggerPro equipment according to the Figure 1:
Figure 1
Add 20.0 mL of weak acid solution to a 100 mL beaker. Do NOT dilute. ← ( HC2H3O2 [acid] and NaOH [base] are located in the hood)
Lower the Drop Counter plate on the ring stand and clamp into position. Connect the Drop Counter to DIG/SONIC 1 of the Vernier computer interface and connect the pH Sensor to CH 1 of the computer interface.
Run the Logger Pro programs on computer. Open the file “07b Acid-Base (Drop Count)” from the Advanced Chemistry with Computers folder.
Obtain the plastic 60 mL reagent reservoir. Close both valves by turning the handles to a horizontal position. Set up the reagent reservoir for titration, making sure the drop rate is under one per second and calibrate the drip rate, and running NaOH through it.
Assemble the apparatus by inserting the pH center through the large hole in the Drop Counter, lining up the Drop Counter and reagent reservoir with he magnetic stirrer, placing the stirrer in the beaker of HC2H3O2 solution, and adjusting the reagent reservoir so its tip is above the drop counter.
Turn the magnetic stir bar on so that it is stirring at a moderate rate.
Click collect on the computer to start collecting data and fully open the top valve on the reagent reservoir, while making sure the bottom valve is adjusted so that the drop drip at a rate of one drop per second.
Watch the graph to see when a large increase in pH takes place - this will be the equivalence point of the reaction. When this jump in pH occurs, add about 7 more milliliter of NaOH solution and then click stop. Turn the bottom valve of the reagent reservoir to its close horizontal position.
Dispose of the beaker contests as directed.
Open Page 3 by clicking the Page window on the menu bare and analyze the second derivative plot and record the volume of NaOH, this indicates equivalence point.
Clean up lab station and return lab equipment.
Data Collected:
Equivalence volume was the average of 28.09 and 28.13 mL because the second derivative switches from positive to negative.

Graphs:
Graph of Titration Curve: pH vs. Volume (mL)
Graph of Second Derivative
Observations:
During the titration of the weak acid (HC2H3O2) and strong base (NaOH), it was observed that our titration curve (pH vs. Volume [mL]) followed a standard form. As seen in the graph, the first addition of base caused a significant increase in pH, which was followed by a region of slight change, and then as the addition of base continued the pH rose rapidly again, which is where the neutralization and equivalence point can be found. The pH then rose only slightly, as more base was added after neutralization. In this graph shown there is a gap in the measurement of pH which is due to human error as there was an error with or Drop Counter and LoggerPro equipment.
Calculations:
Equivalence Volume: 28.11 mL
28.09 = 138.187 (second derivative)
← average the two volumes (28.09 + 28.13)/2 = 28.11 mL
28.13 = -135.820 (second derivative)
[HA] Original: 0.138 M H
[NaOH] = 0.0982 M
Equivalence Point = 28.11 mL
Initial Volume of NaOH = 20.0 mL ← 1000 mL = 1L ← 20 mL/1000mL = 0.020 L NaOH
Mols of NaOH = (M of NaOH/1000 mL) x mL of NaOH
Mols of NaOH = (0.0982 M/1000mL) x 28.11 mL
Mols of NaOH = 2.76 x 10-3 mol
Mols of NaOH = Mols of HA because of equation NaOH + HA → NaA + H2O
mols HA = 2.76 x 10-3 mol
molarity of HA = mols HA/liters HA
molarity of HA = 2.76 x 10-3 mol HA/0.020 L = 0.138 M HA
Ka from pH of original solution: 6.92 x 10-6
Initial pH of HA = 3.01
Concentration of HA = 0.138 M
Ka = [H3O+]aq x [A-]aq/ [HA]aq
[H3O+] = 10pH = 10-3.1= 0.000977 M

→ Ka = [H3O+]aq x [A-]aq/ [HA]aq = (0.000977 M)2/0.138M = 6.92 x 10-6

Ka from pH of half-neutralization point pH1/2 = pKa: 1.23 x 10-5
Equivalence Point: 28.11 mL
Half-Neutralization Point = 28.11 mL/2 = 14.055 mL
pH at Half-Neutralization Point = 4.91
pH = pKa at Half-Neutralization Point
pKa = 4.91
pKa = 10-4.91= 1.23x10-5

5.

Error:

Theoretical Ka of HC2H3O2: 1.75 x 10-5

Error of Ka from pH of original solution: 60.5%

% Error = [|Theoretical Ka - Experimental Ka |/Theoretical Ka] x 100

% Error = [|6.92 x 10-6- 1.75 x 10-5 |/1.75 x 10-5] x 100

% Error = 60.5%

Error of Ka from pH of Half-Neutralization Point: 29.7%

% Error = [|Theoretical Ka - Experimental Ka |/Theoretical Ka] x 100

% Error = [|1.23x10-5- 1.75 x 10-5 |/1.75 x 10-5] x 100

% Error = 29.7%

Discussion:

Based on the results obtained from the experiment, the equivalence volume of the titration of the weak acid (HC2H3O2) and strong base NaOH was 28.11 mL, the calculated Ka from the pH of the original solution was 6.92 x 10-6, and the calculated Ka from the pH of the Half-Neutralization point was 1.23x10-5. There was a 60.5% error in the calculated Ka from the pH of the original solution and 29.7% error in the calculated Ka from the pH of the Half-Neutralization point, indicating that there could have been numerous sources of

error.
To begin, the most critical source of error in titration of a weak acid and strong base is the fact that the pH Sensor could have been faulty and was recording the values of pH incorrectly. It is extremely common that equipment does not work properly, or is set up incorrectly; therefore, the Sensor can malfunction. This possible malfunctioning is indicated by the resulting graph, in which there is a gap in the titration curve, along with the percent error of the value of Ka. An additional source of error could have been incorrect calibration of the drip rate, as an incorrect volume would lead to incorrect calculation of pH. Other sources of error include, improper calculation of the concentration of the HA, failure to properly measure volumes, failure to titrate beyond the equivalence point, contamination of the solutions, and human error.
Possible improvements that one could make to the experiment include using a more accurate pH Sensor, being more accurate and precise when measuring out volumes, using a more accurate titrator (the syringe could be made more accurate), and repeating the experiment multiple times (to minimize the impact of an anomalous result).

Conclusion:
Ultimately it is evident that the two Ka values (6.92 x 10-6 and 1.23x10-5) calculated did not match the theoretical value of Ka for acetic acid (1.75 x 10-5). However, the experiment was still a success, as the purpose of the experiment was to complete the various techniques involving the titration of a weak acid with a strong base, not to specifically obtain accurate results. Therefore, since all of the procedures were completed to the best of ability, the overall experiment and results obtained were successful, despite the possible sources of error.