Abstract

The use of an autotitrator for the purpose of studying and the conceration of a sample is widespread in chemistry. In our lab, we used manual titration before to determine the titration curve .In this lab, we used an autotitrator to make our titration curve. In a diprotic titration, the solution reaches two equilibrium points called Ka1 and Ka2, resulting in two distinct points on the titration curve. Understanding these equilibrium points is essential for accurately analyzing diprotic acid solutions and determining their concentration through titration.

For this project we determined many things ,one the most important thing was two Ka values called Ka1 and Ka2. Which we found to be equal to Ka1=\(1.32*10^{-2}\) and Ka2=\(4.84*10^{-5}\), this is within the range of the Ka values of oxalic acid [3].

Expermental Results

Here is the titration curve that was produced via of the use of the autotitrator.

To create this Binding curve, we transformed the data using the following equation \[ \text{Fraction Bound} = 2 - \frac{C_B \cdot V_{\text{add}} + [\text{H}^+] \cdot (V_{\text{ini}} + V_{\text{add}})}{C_B \cdot V_{\text{end}}} \]

Then the nls2 library was used to create a curve that accurately represented the two Ka values. The therotical equation that the nls function used to fit was defined as \(\frac{H/KD1 + 2H^2/(KD1KD2)}{1 + H/KD1 + H^2/(KD1KD2)}\) [1].

##  [1] 2.0000000 1.9990835 1.9981561 1.9957591 1.9900431 1.9755130 1.9391535
##  [8] 1.9026441 1.8657668 1.8318718 1.7967909 1.7607610 1.7262583 1.6921160
## [15] 1.6583216 1.6286983 1.6034837 1.5674117 1.5395387 1.5161454 1.4849963
## [22] 1.4542265 1.4340537 1.4040279 1.3840189 1.3564801 1.3362656 1.3073622
## [29] 1.2915518 1.2660542 1.2686727 1.2356058 1.2317258 1.2200800 1.1979995
## [36] 1.1802340 1.1551750 1.1363830 1.1171876 1.0856693 1.0669590 1.0430751
## [43] 1.0209233 0.9936241 0.9696965 0.9435516 0.9167184 0.8905902 0.8639706
## [50] 0.8373578 0.8108600 0.7831834 0.7565607 0.7297182 0.7022530 0.6755722
## [57] 0.6483293 0.6214499 0.5942779 0.5671980 0.5407022 0.5332503 0.5314778
## [64] 0.5274123 0.5170750 0.4912137 0.4640838 0.4369229 0.4097925 0.3826627
## [71] 0.3554917 0.3283004 0.3013189 0.2997964 0.2991152 0.2974847 0.2932653
## [78] 0.2825056 0.2559741 0.2549538 0.2542725 0.2526396 0.2482940 0.2447533
## [85] 0.2356536 0.2336109 0.2285837 0.2274943 0.2250487
## Loading required package: proto
## 
## Formula: f ~ (H/KD1 + 2 * H^2/(KD1 * KD2))/(1 + H/KD1 + H^2/(KD1 * KD2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## KD1 4.843e-05  5.749e-06   8.423 6.79e-13 ***
## KD2 1.342e-02  1.270e-03  10.572  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1314 on 87 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 3.844e-06

Discussion and Results

The two plots allow us to perform some very useful anlysis on our data. For one thing we can find the Ka1 and Ka2 values which are. And what I find was that was that Ka1 = \(1.32*10^{-2}\) (pKa1 = \(1.87\)) and Ka2 = \(4.84*10^{-5}\) (pKa2 = \(4.34\)). From our lab report I knew that compound we where titration was oxalic acid with a molar mass of 126 g/mol[2]. And the reported for the compound is Ka2 = \(7.24*10^{-5}\) (pKa2 = \(4.14\)) and Ka1 =\(5.6*10^{-2}\) (pKa1 = \(1.25\)).

Althought the Ka’s values differ by very large amount, the pKa of the experminental calculations is within the range of the reported values. So that is how we settled the question as to whether compound was really oxalic aicd.

Their are many possible reasons for the discripancy between the theorotical values and the observed values given the nls fit. One possible reason was that nls function failed to accurate fit the data. Althought I think that this is unlikely given the results are so close to the turning points of the binding the binding curve and only the ends deviate slightly. Another potential reason is perhaps an technical failure. Perhaps after repeated use our autotitrator failed to perform its self calibration correctly and introduced some slight error into our data. Another possible cause could be the age of our sample. Or human error could have played a role in introducing some errors and perhaps redoing the experminent under tighter controls will bring the result to within the reported values.

Refrerences

  1. Gosser, David. Quantitive Anylsis Book. Decemeber 2022
  2. Teresa J. Bandosz, Christina I. Veresmoretean Quantitative Analysis Laboratory
  3. https://en.wikipedia.org/wiki/Oxalic_acid