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In this experiment, the pKa of acetic acid (HC2H3O2) was determined by titrating it with sodium hydroxide (NaOH). The point of half-titration was used to calculate the pKa. By adding half as many moles of acetic acid as NaOH, a solution with equal moles of HC2H3O2 and C2H3O2- was obtained. The Henderson-Hasselbalch equation was used to calculate the pKa. Two methods were employed, and the results were compared. Method 2, involving titration curve analysis, provided a more accurate pKa value compared to Method 1, which relied on qualitative observations.
The determination of the acid dissociation constant (pKa) of acetic acid (CH3COOH) is a fundamental experiment in chemistry. The pKa value indicates the strength of an acid, with lower pKa values indicating stronger acids. In this experiment, the pKa of acetic acid was determined by titrating it with sodium hydroxide (NaOH) to the point of half-titration, which allowed for the calculation of the pKa.
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The reaction between acetic acid and sodium hydroxide can be represented as follows:
CH3COOH + NaOH → H2O + NaCH3COO
The point of half-titration is reached when half as many moles of acetic acid have reacted with NaOH. At this point, the solution contains equal moles of HC2H3O2 and C2H3O2-. The Henderson-Hasselbalch equation is used to calculate the pKa:
\[pKa = -\log\left(\frac{{[\text{C2H3O2-}]}}{{[\text{HC2H3O2}]}}\right)\]
Materials:
1 uncertainty
Procedure:
Results obtained from the titration of 1M acetic acid with 1M NaOH are summarized in the table below:
| PH ±0.1 | Qualitative Observations |
|---|---|
| At ½ Equivalence (5.0) | Color change from colorless to very slight pink as the Phenolphthalein indicator changed color. |
| At Equivalence (8.9) | No color change observed during the addition of acetic acid. Rapid PH change and pink coloration occurred at equivalence. |
To calculate the pKa, we will use the Henderson-Hasselbalch equation:
\[pKa = -\log\left(\frac{{[\text{C2H3O2-}]}}{{[\text{HC2H3O2}]}}\right)\]
At half equivalence, the concentration of acetic acid and its salt ion are equal, simplifying the equation:
\[pKa = -\log\left(\frac{1}{1}\right) = -\log(1) = 0 ± 2\%\]
This result can be expressed as \(10^{-5} ± 2\%\).
To determine the error, a titration curve was generated, and the PH at half equivalence was measured. The PH of acetic acid (1M) was calculated using the formula:
\[Ka = 10^{-4.76} = \sqrt{(1 \times 10^{-4.76})}\]
So, PH of acetic acid = 2.38
The PH of NaOH (1M) was calculated as follows:
Concentration of NaOH = 1M
\[PH = -\log(1) = 0 ± 0.2\%\]
Thus, PH = 14 ± 0.2%
The following titration curve data was obtained:
| Volume of NaOH (0.2%) | PH of Solution (±0.2) |
|---|---|
| 0 cm³ | 2.38 |
| 45 cm³ | 14 |
| 48 cm³ | 14 |
| 50 cm³ | 14 |
Based on the titration curve, the equivalence point occurred at 28 cm³ of NaOH, where the steepest gradient was observed. Therefore, the half-equivalence point was at half of this volume, 14 cm³, with a PH of 4.8 ± 0.2.
Using this value in the Henderson-Hasselbalch equation:
\[pKa = -\log\left(\frac{[\text{C2H3O2-}]}{[\text{HC2H3O2}]}\right)\]
\[pKa = -\log\left(\frac{10^{-4.8}}{1}\right) = 4.8 ± 0.2\]
The pKa of acetic acid was determined by two methods:
The experiment aimed to determine the pKa of acetic acid using two different methods. Method 1 relied on qualitative observations at half-titration, while Method 2 involved titration curve analysis.
Comparing the results obtained from both methods, it is evident that Method 2 provided a more accurate pKa value (4.8 ± 0.2%) compared to Method 1 (5.0 ± 2%). The higher precision of Method 2 can be attributed to the use of quantitative data and calculations, which reduce subjectivity and random errors associated with visual color changes.
The systematic error in Method 1 was limited, contributing to only 2% of the total error. The main source of error in this method was random error, arising from the difficulty in discerning the exact point of half-titration by visual color change. Pipette inaccuracies also played a minor role in the error. The % error of Method 1 was 5%, with 3% attributed to random error.
In contrast, Method 2 demonstrated higher accuracy, with a total % error of 0.84%. Systematic errors in Method 2 accounted for 2% of the error, primarily due to the ±0.2% uncertainty associated with the PH probe readings. However, random errors played a more significant role in this method, particularly during the estimation of the half-equivalence point from the titration curve. The subjectivity in identifying the steepest gradient contributed to the remaining 0.84% error.
Despite the presence of systematic and random errors in both methods, the results obtained from Method 2 closely matched the expected pKa value of acetic acid (4.76). The titration curve provided a more objective and precise means of determining the half-equivalence point compared to visual color changes, resulting in a smaller % error. Method 2 can be considered more reliable and accurate for determining the pKa of acetic acid.
The pKa of acetic acid was determined using two methods, and the results were compared. Method 2, which involved titration curve analysis, yielded a more accurate pKa value of 4.8 ± 0.2%, while Method 1, relying on qualitative observations, provided a pKa of 5.0 ± 2%. The lower % error in Method 2 demonstrates its higher precision and reliability in determining the pKa of acetic acid.
From the results it is clear error was limited for method 1, 5%. We calculated that uncertainties make up at least 2% of that error. Thus systematic error only makes 2% of the error while random error makes 3% of the error.
Thus the significant error is random errors. This was due to the subjectiveness at seeing the half-titration points. As we relied on the fact that the phenolphatlein made the solution light pink, it was difficult to see such color change. Thus it was very easy to keep adding base, when there was already a color change. Hence our error was that we could overshoot the titration. As we added to much NaOH the color change seen was too much. So when we added the acetic acid, the PH at half-equivalence is higher so we overestimated the PKa. This was reflected directly on our results. Finally another less important random error was that pipettes leaked. Thus more NaOH was added. This while small also explains why we overestimated the PKa, as we overshooted the titration even more.
Finally our less significant errors were systematic error. They only make 2% of our errors. They were mainly caused by inaccuracy of our apparatus. The main systematic error caused was by the PH probe. The PH probe, first of all has great inaccuracy recording PH with a ±0.1 uncertainty. Thus as the PH recorded was small, the %uncertainty calculated is much bigger than it would be with a higher PH. The other uncertainty was caused by the inaccuracy of pipettes. When we measured the volume of the acetic acid, there was a systematic error as Burets have uncertainties of, ±0.10 cm3. Thus at a volume we measured of acetic acid at 25cm3, we had 0.4% error caused.
We can also analyze improvements for method 2. We used this method and generated it from data we had form method 1. However, the titration sketch clearly was much more accurate than method 1, as it yields 0.84% error of which 0.2% was caused by uncertainties. Thus as we got the results for the titration curve from method 1, the error that caused the systematic errors were the same. However the main cause of error is the random error. At calculating the equivalence point, we had to estimate the point with the maximum gradient. As this is subjective, there is human error. Hence, when we then halved that volume, we could overestimate or underestimate the error since we estimated the point with maximum gradient.
To reduce the random error firstly we must do more trials. Just by doing this, we will reduce the random error. Finally as the problem with the color change was that it was a qualitative observation. To improve this we can get a quantitative measurement. To do this we use a colorimeter. This is a device we will put behind the solution. This measures the exact absorbance or transmission of light. Thus as the light absorbance changes when there is a color change, when the colorimeter states such we know that the color change has occurred. Hence we know exactly the equivalence points. The significance of this improvement is that it would enable us to get qualitative results. Thus if the colorimeter very accurate we can decrease random error, as there is no human error. Also, as the colorimeter is accurate, systematic error will also be limited.
Another way we can improve is in the systematic errors. The first problem was measuring accurately volumes. As the pipettes had big uncertainties, the volume recorded had high %uncertainties. If we however use micropipettes, which have ±0.01 cm3 uncertainties, our volumes will be extremely accurate. Hence %uncertainties will be minimal. Also micropipettes allow much easier for drops of base to be dropped. Thus the significance of this improvement is that when we measure volumes, the equivalence point will occur, more exactly as we will be less likely to overshoot the solution.
Finally to solve the inaccurate measurements of PH we can get a PH sensor and data logger. These do real-time measurements and will state the PH with less uncertainty. It will also provide an alternative method for calculating the half-point. As the data logger draws the graph of the titration done, it can calculate the point with the highest gradient. Thus this will be the equivalence point. Hence we can calculate the PH at half the equivalence point of the graph as this is half the volume of base at equivalence. Thus clearly calculating a very accurate PH from the curve. The significance of this will be that it is a major improvement on method 2 and 1 as it is not qualitative. Thus it does not allow for human error. Hence as the sensor is also very accurate systematic error will also be limited as well as random error. Thus this method will get a very accurate PKa with low systematic and random errors.
Experiment Report: Determination of pKa of Acetic Acid. (2017, Nov 11). Retrieved from https://studymoose.com/document/determining-ka-by-the-half-titration-of-a-weak-acid
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