Abstract

The purpose of this experiment was to learn how to titrate a diprotic acid using an autotitrator and, based on the data, to identify the acid. The autotitrator is an automated instrument used to perform titrations with precision and efficiency equipped with several key features that improve the speed, accuracy, and reproducibility of titrations i.e high wear components, electrode holder, pH electrode technology. Compared to manual titration, the autotitrator has its own advantages where it’s faster, eliminates the handling of corrosive titrants, as well as enhanced accuracy of the titrant volume measurements. Diprotic acids are acids that contain two hydrogen atoms, each of which can be deprotonated.This experiment focused on the titration of a diprotic acid with a known strong base to determine the acid’s dissociation constants, Ka1 and Ka2 as well as its pKa values. Using an autotitrator, the base was gradually added while pH chanbges were continuously monitored, allowing for the generation of both a titration curve and a binding curve.This approach allowed for precise determination of the dissociation constants and provided a deeper understanding of the behavior of diprotic acids during titration and in aqueous solutions.

Introduction

In this experiment, we used auto-potentiometric titration with a sodium hydroxide (NaOH) titrant to identify an unknown diprotic acid. NaOH was gradually added to the acid, and pH changes were precisely measured using an autotitrator. This generated a titration curve that showed two distinct equivalence points (EQP1 and EQP2), which are characteristic of diprotic acids. These equivalence points correspond to the complete neutralization of each acidic proton. The first equivalence point (EQP1) marks the neutralization of the acid’s first proton (H₂A → HA⁻), while the second equivalence point (EQP2) indicates the neutralization of the second proton (HA⁻ → A²⁻). This data enabled us to calculate important properties of the acid, such as its molar mass, acid dissociation constants (Ka1 and Ka2), and pKa values. By comparing these values with known literature, we were able to identify the unknown acid. The Ka1 and Ka2 values provided insight into the deprotonation behavior of the acid at each equivalence point.

Titration Curve

library(readr)
mydata <- read.csv("data.csv")

VolVect <- mydata$Volume
VolVect
##  [1]  0.000  0.005  0.010  0.023  0.054  0.132  0.328  0.528  0.728  0.928
## [11]  1.128  1.328  1.528  1.728  1.928  2.128  2.328  2.528  2.728  2.928
## [21]  3.129  3.329  3.529  3.729  3.929  4.129  4.329  4.529  4.729  4.929
## [31]  5.129  5.329  5.529  5.729  5.929  6.129  6.329  6.529  6.729  6.929
## [41]  7.129  7.329  7.529  7.729  7.929  8.129  8.329  8.529  8.729  8.929
## [51]  9.129  9.329  9.529  9.730  9.930 10.130 10.330 10.530 10.730 10.930
## [61] 11.130 11.330 11.530 11.730 11.930 12.130 12.330 12.530 12.696 12.863
## [71] 13.063 13.263 13.464 13.664 13.864 14.064 14.262 14.391 14.468 14.507
## [81] 14.553 14.580 14.645 14.716 14.775 14.818 14.877 14.959 15.040 15.168
## [91] 15.338
length (VolVect)
## [1] 91
pHVect <- mydata$pH
pHVect
##  [1] 1.84 1.83 1.83 1.83 1.83 1.83 1.84 1.85 1.87 1.88 1.90 1.91 1.93 1.94 1.96
## [16] 1.99 2.01 2.03 2.06 2.08 2.11 2.14 2.16 2.20 2.22 2.27 2.29 2.34 2.39 2.44
## [31] 2.49 2.55 2.61 2.68 2.75 2.84 2.92 3.00 3.09 3.17 3.25 3.33 3.40 3.46 3.53
## [46] 3.59 3.64 3.71 3.77 3.82 3.88 3.93 3.99 4.04 4.10 4.16 4.22 4.29 4.35 4.42
## [61] 4.50 4.58 4.69 4.79 4.92 5.07 5.24 5.44 5.61 5.76 5.93 6.06 6.20 6.32 6.45
## [76] 6.63 6.86 7.07 7.29 7.42 7.63 7.73 7.93 8.15 8.36 8.51 8.67 8.87 9.03 9.21
## [91] 9.38
length (pHVect)
## [1] 91
plot(VolVect,pHVect,xlab = 'Volume (ml)',ylab = 'pH',main = 'Titration Curve')

The graph above is the data for the diprotic titration graphed.

Binding curve

As the reaction progresses, hydrogen ions (H⁺) are gradually deprotonated, leading to an increase in the concentration of H⁺ while the conjugate base concentration also rises as more protons are removed. Using this information, we can calculate the fraction of the acid that is bound as the reaction continues and volume is added. To determine the concentration of H⁺, [H+]=10^-pH can be used.

Hc <- 10^(-pHVect)
Hc
##  [1] 1.445440e-02 1.479108e-02 1.479108e-02 1.479108e-02 1.479108e-02
##  [6] 1.479108e-02 1.445440e-02 1.412538e-02 1.348963e-02 1.318257e-02
## [11] 1.258925e-02 1.230269e-02 1.174898e-02 1.148154e-02 1.096478e-02
## [16] 1.023293e-02 9.772372e-03 9.332543e-03 8.709636e-03 8.317638e-03
## [21] 7.762471e-03 7.244360e-03 6.918310e-03 6.309573e-03 6.025596e-03
## [26] 5.370318e-03 5.128614e-03 4.570882e-03 4.073803e-03 3.630781e-03
## [31] 3.235937e-03 2.818383e-03 2.454709e-03 2.089296e-03 1.778279e-03
## [36] 1.445440e-03 1.202264e-03 1.000000e-03 8.128305e-04 6.760830e-04
## [41] 5.623413e-04 4.677351e-04 3.981072e-04 3.467369e-04 2.951209e-04
## [46] 2.570396e-04 2.290868e-04 1.949845e-04 1.698244e-04 1.513561e-04
## [51] 1.318257e-04 1.174898e-04 1.023293e-04 9.120108e-05 7.943282e-05
## [56] 6.918310e-05 6.025596e-05 5.128614e-05 4.466836e-05 3.801894e-05
## [61] 3.162278e-05 2.630268e-05 2.041738e-05 1.621810e-05 1.202264e-05
## [66] 8.511380e-06 5.754399e-06 3.630781e-06 2.454709e-06 1.737801e-06
## [71] 1.174898e-06 8.709636e-07 6.309573e-07 4.786301e-07 3.548134e-07
## [76] 2.344229e-07 1.380384e-07 8.511380e-08 5.128614e-08 3.801894e-08
## [81] 2.344229e-08 1.862087e-08 1.174898e-08 7.079458e-09 4.365158e-09
## [86] 3.090295e-09 2.137962e-09 1.348963e-09 9.332543e-10 6.165950e-10
## [91] 4.168694e-10

Fraction bound curve

#[H+]

Hc <- 10^-(pHVect)
Hc
##  [1] 1.445440e-02 1.479108e-02 1.479108e-02 1.479108e-02 1.479108e-02
##  [6] 1.479108e-02 1.445440e-02 1.412538e-02 1.348963e-02 1.318257e-02
## [11] 1.258925e-02 1.230269e-02 1.174898e-02 1.148154e-02 1.096478e-02
## [16] 1.023293e-02 9.772372e-03 9.332543e-03 8.709636e-03 8.317638e-03
## [21] 7.762471e-03 7.244360e-03 6.918310e-03 6.309573e-03 6.025596e-03
## [26] 5.370318e-03 5.128614e-03 4.570882e-03 4.073803e-03 3.630781e-03
## [31] 3.235937e-03 2.818383e-03 2.454709e-03 2.089296e-03 1.778279e-03
## [36] 1.445440e-03 1.202264e-03 1.000000e-03 8.128305e-04 6.760830e-04
## [41] 5.623413e-04 4.677351e-04 3.981072e-04 3.467369e-04 2.951209e-04
## [46] 2.570396e-04 2.290868e-04 1.949845e-04 1.698244e-04 1.513561e-04
## [51] 1.318257e-04 1.174898e-04 1.023293e-04 9.120108e-05 7.943282e-05
## [56] 6.918310e-05 6.025596e-05 5.128614e-05 4.466836e-05 3.801894e-05
## [61] 3.162278e-05 2.630268e-05 2.041738e-05 1.621810e-05 1.202264e-05
## [66] 8.511380e-06 5.754399e-06 3.630781e-06 2.454709e-06 1.737801e-06
## [71] 1.174898e-06 8.709636e-07 6.309573e-07 4.786301e-07 3.548134e-07
## [76] 2.344229e-07 1.380384e-07 8.511380e-08 5.128614e-08 3.801894e-08
## [81] 2.344229e-08 1.862087e-08 1.174898e-08 7.079458e-09 4.365158e-09
## [86] 3.090295e-09 2.137962e-09 1.348963e-09 9.332543e-10 6.165950e-10
## [91] 4.168694e-10
#Volume added at 1st endpoint
VE <- 6.729

#Initial volume of unknown acid
VI <- 25

#[base] [NaOH]
Bc <- 0.1

#FB Equation
F <- (2-((VolVect*Bc)+ (Hc)*(VI+VolVect))/(VE*Bc))
F
##  [1]  1.4629812116  1.4496194792  1.4487665212  1.4465488305  1.4412604911
##  [6]  1.4279543467  1.4071912838  1.3856552469  1.3760422493  1.3541423582
## [11]  1.3435398550  1.3212882122  1.3097387080  1.2871474217  1.2746921554
## [16]  1.2712157483  1.2571565051  1.2425230437  1.2356950747  1.2196537584
## [21]  1.2105059423  1.2002891022  1.1822373938  1.1764486023  1.1570597969
## [26]  1.1539129262  1.1331295656  1.1263581936  1.1172386940  1.1060103566
## [31]  1.0928881960  1.0810243187  1.0669641723  1.0531996124  1.0371520228
## [36]  1.0222988637  1.0034689516  0.9828666964  0.9616729091  0.9381978699
## [41]  0.9137056555  0.8883617040  0.8618665059  0.8345246688  0.8072253873
## [46]  0.7792904381  0.7508764559  0.7227855046  0.6942665983  0.6654252311
## [51]  0.6366487169  0.6076188054  0.5786397260  0.5493128048  0.5201744858
## [56]  0.4909638844  0.4616899346  0.4324235451  0.4030375977  0.3736572737
## [61]  0.3442673043  0.3148230400  0.2854126217  0.2559136709  0.2264170066
## [66]  0.1968850831  0.1673134021  0.1377080351  0.1131036815  0.0883254594
## [71]  0.0586346855  0.0289295205 -0.0009277294 -0.0306412628 -0.0603563523
## [76] -0.0900715671 -0.1194908897 -0.1386585714 -0.1500996049 -0.1558946382
## [81] -0.1627298666 -0.1667420672 -0.1764013461 -0.1869524167 -0.1957202759
## [86] -0.2021104518 -0.2108784147 -0.2230644284 -0.2351018537 -0.2541239780
## [91] -0.2793877498

A graph of the results is shown below, plotting Fraction Bound vs. pH:

#Graphing the Fraction Bound Curve
plot(pHVect,F, xlab = 'pH',ylab = 'Fraction Bound', main = "Fraction Bound Curve")

## Fitline for nonlinear model To perform non-linear least squares regression, which is useful for fitting complex non-linear models, the ‘nls2’ package in R Markdown was used. This method was applied to the data points on the Fraction Bound curve, enabling the fitting of a non-linear model to the titration data. By doing so, we were able to extract key information regarding the acid’s dissociation constants,Ka1 and Ka2 The model used to represent the fraction bound curve is based on the following equation: \[F = \frac{{Hc/Ka_1 + 2 \times Hc^2/(Ka_1 \times Ka_2))}}{{1 + Hc/Ka_1 + Hc^2/(Ka_1 \times Ka_2)}} \]

Where:
\(F\) is the Fraction bound
\(Hc\) is the concentration of protons or H+ ions in the solution
\(Ka_1\) and \(Ka_2\) are the acid dissociation constants of each proton 
#A fitline for a non-linear model

library (nls2)
## Loading required package: proto
fitline <- nls(F ~ (Hc/Ka1+2*Hc^2/(Ka1*Ka2))/(1+Hc/Ka1+Hc^2/(Ka1*Ka2)),
                start = c(Ka1 = 0.0001,Ka2=0.01))

summary (fitline)
## 
## Formula: F ~ (Hc/Ka1 + 2 * Hc^2/(Ka1 * Ka2))/(1 + Hc/Ka1 + Hc^2/(Ka1 * 
##     Ka2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## Ka1 6.818e-05  5.867e-06   11.62   <2e-16 ***
## Ka2 2.335e-02  1.796e-03   13.00   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.08799 on 89 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.023e-06
plot(pHVect,F, xlab = 'pH',ylab = 'Fraction Bound', 
     main = "Fraction Bound vs pH")

lines (pHVect, predict (fitline), col = "orange")

A fit line was made and Ka values were given by R. Ka1 was 6.818e-05 and Ka2 was 2.335e-02.

Conclusions

From R, Ka1 was 6.818e-05 and Ka2 was 2.335e-02 and from the lab report, Ka1 was 6.91e-06 and Ka2 was 2e-02 (which was similar to what we had). The error percentage for Ka1 was 986% which is a tremendously large percentage error. The error percentage for Ka2 was 116% which was relatively still large. There are a lot of reasons that can contribute to this large amount of error. Discrepancies in an autotitrator can result from issues like improper calibration, faulty electrodes, equipment malfunctions, sample contamination, air bubbles, incorrect settings, side reactions, or software errors. There is a possibility that we might get a different results if we were to use our results from the manual titration. Overall, the Ka values were the only result that were not satisfactory. Graphs and the curve obtained in R were all rather similiar to each other and seem to be consistent. It’s most likely the error in techniques and small experimental errors that caused a large error percentage.