Monoprotic and Diprotic Titration Curves and Binding Curves
Valeria Sanmartin
2024-04-15
Monoprotic Titration and Binding Curves
Abstract
This program determined the concentration and Ka1(acid dissociation constant) of acetic acid by titrating it with sodium hydroxide (NaOH), using potassium hydrogen phthalate (KHP) as a standard for calibration. We performed manual titration to find out how much NaOH was needed on average across three trial and manual potentiometric titration helped us identify the precise points where the reaction completed.Using R script, we calculated the endpoints, equivalnce points, and pinpointed acetic acid’s concentration and Ka1 with high accuracy. Challenges like the excess weight of KHP affecting the reaction’s endpoint were overcome by averaging results from multiple trials.
Introduction
The goal of this experiment to obtain the concentration of acetic acid found in vinegar. The journey began with calibrating our sodium hydroxide solution against a known quantity of potassium hydrogen phthalate (KHP), a process necessary due to NaOH’s reactivity and impurities. Through manual titration of NaOH with KHP and subsequent potentiometric titration of acetic acid, we determined the concentration of acetic acid and its Ka. The chemical reaction between KHP and NaOH producing water and a salt allowed for KHP to calibrate our NaOH solution accurately. The second phase involved reacting acetic acid with NaOH. Then using the Henderson-Hasselbalch equation we were able to determine experimentally its Ka. Additionally the functionality of R script and its Non Linear Square Analysis was used to support our findings
Titration Analysis
In this phase of the experiment, we recorded the change in pH of the acetic acid solution as we added NaOH. Our aim was to draw a titration curve to visualize how close we were to neutralizing the acid with the base at different volumes of NaOH added.
Experimental Data and Titration Curve
Mydata <- read.csv("data 1.csv")
Mydata## Vol pH
## 1 0.00 3.17
## 2 1.00 3.47
## 3 3.00 3.90
## 4 4.00 4.06
## 5 5.00 4.18
## 6 6.00 4.27
## 7 7.00 4.37
## 8 8.00 4.47
## 9 8.45 4.49
## 10 9.00 4.54
## 11 9.60 4.61
## 12 10.00 4.64
## 13 11.00 4.71
## 14 12.00 4.80
## 15 13.00 4.88
## 16 14.00 4.97
## 17 14.50 5.03
## 18 14.90 5.06
## 19 15.10 5.08
## 20 15.20 5.08
## 21 15.60 5.12
## 22 16.10 5.19
## 23 16.60 5.25
## 24 17.00 5.32
## 25 17.50 5.40
## 26 18.10 5.50
## 27 18.50 5.59
## 28 19.10 5.74
## 29 19.50 5.86
## 30 20.00 6.39
## 31 21.10 9.55
## 32 21.50 10.51
## 33 22.00 10.89
## 34 25.00 11.50volume <- Mydata$Vol
pH <- Mydata$pH
volume## [1] 0.00 1.00 3.00 4.00 5.00 6.00 7.00 8.00 8.45 9.00 9.60 10.00
## [13] 11.00 12.00 13.00 14.00 14.50 14.90 15.10 15.20 15.60 16.10 16.60 17.00
## [25] 17.50 18.10 18.50 19.10 19.50 20.00 21.10 21.50 22.00 25.00pH## [1] 3.17 3.47 3.90 4.06 4.18 4.27 4.37 4.47 4.49 4.54 4.61 4.64
## [13] 4.71 4.80 4.88 4.97 5.03 5.06 5.08 5.08 5.12 5.19 5.25 5.32
## [25] 5.40 5.50 5.59 5.74 5.86 6.39 9.55 10.51 10.89 11.50plot(volume,pH,main="Volume of NaOH vs. pH of Solution",xlab="Volume (mL)",
ylab="pH",xlim=c(0,25),ylim=c(0,12))
Analysis and Discussion
We then transformed our titration data into a binding curve. This involved calculating the fraction bound of acetic acid molecules that had reacted with NaOH at different pH levels. The equation used to determine the fraction bound was FBound = 1 - ((Tbasevolume+H(Vinitial+Vend))/(Tbase*Vend) where Tbase is the concentration of the titrant (NaOH), H is 10^-ph, and Vinitial and Vend are the inital and Final volumes. This allowed us to visualize how the availability of acetic acid’s proton-binding sites decreased as the pH increased.
We analyzed our binding curve using a non-linear least squares approach to obtain Ka1, the acid dissociation constant of acetic acid. The model equation H/(1+(KD+H)) directly relates the bound fraction to the hydrogen ion concentration of H and an estimated dissociation constant, KD. This mathematical fitting functionality gave us the Ka value and adjusted a line of best fit.
H <- 10^(-pH)
tbase <- 0.10
Vini <- 25
Vend <- 21.5
fbound <- 1-(tbase*volume + H*(Vini+Vend))/(tbase*Vend)
fbound## [1] 9.853777e-01 9.461599e-01 8.577423e-01 8.120698e-01 7.660129e-01
## [6] 7.197687e-01 6.734960e-01 6.271741e-01 6.062769e-01 5.807716e-01
## [11] 5.529575e-01 5.343883e-01 4.879504e-01 4.415177e-01 3.950637e-01
## [16] 3.486055e-01 3.253796e-01 3.067884e-01 2.974945e-01 2.928434e-01
## [21] 2.742545e-01 2.510231e-01 2.277854e-01 2.091988e-01 1.859604e-01
## [26] 1.580711e-01 1.394793e-01 1.115886e-01 9.299340e-02 6.975863e-02
## [31] 1.860465e-02 -6.683663e-10 -2.325581e-02 -1.627907e-01plot(pH,fbound,xlim=c(0,11.59),main="Binding Analysis of Monoprotic Titration")
library(nls2)## Loading required package: protofit <- nls2(fbound ~ H/(KD+H), start=c(KD=0.0001))
summary(fit) ##
## Formula: fbound ~ H/(KD + H)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## KD 1.981e-05 6.227e-07 31.82 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0321 on 33 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.253e-06lines(pH,predict(fit), col="red")
summary(cars)## speed dist
## Min. : 4.0 Min. : 2.00
## 1st Qu.:12.0 1st Qu.: 26.00
## Median :15.0 Median : 36.00
## Mean :15.4 Mean : 42.98
## 3rd Qu.:19.0 3rd Qu.: 56.00
## Max. :25.0 Max. :120.00Conclusion
Our experiment revealed that traditional titration offers a straightforward way to estimate an acid’s concentration, but it may fall short in precision when compared to the binding curve method using R scropt. R script uses detailed mathematical modeling that readily provides in depth information of the acid’s dissociation at various pH levels in such short time.
Titration and Binding Curve for Diprotic Acid
Abstract
This paper presents an in-depth analysis of an unknown diprotic acid via the use of an auto titrator, generating a titration curve and coverting it into a binding curve analysis. By combiningthese techniques we were able to determine the acid’s dissociation constants with greater precision than manual calculation.This gives us a Ka1=1.608e^-6 and a Ka2=1.809e^-3. This experiment highlights how r script can be used to thorughly analyze an acid-base behavior of the compound in question in a fraction of the time.
Introduction
In a diprotic acid, there will be two protons that will be dissociate and when titrated there will be two equivalent points as a result of being titrated with a strong base; sodium hydroxide. The unknown acid undergoes deprotonation twice and demonstrates two stages of dissociation. The goal of this experiment is to identify the unknown diprotic acid by calculating the molecular mass and using titration data to determine pKa and then convert this to Ka manually. Additionally, using the NLS2 function within r script to support our findings. This will be achieved through the application of specific equations that relate the mole of the acid to its mass and the molar mass, incorporating the concentration (CNaOH) and volume (VNaOH) of sodium hydroxide used in the titration process. Moreover, the determination of the acid’s dissociation constants (pKa1 and pKa2) will be conducted by analyzing the titration curve to identify the pH values at half-equivalence points. This process will be aided by visual cues from the Bromocresol Green indicator, which exhibits a distinct color change across different pH ranges, facilitating the identification of equivalence points. Then NLS2 functionality of the R language programing was used to support our findings.
Dripotic Acid Analysis
Mydata <- read.csv("diprotic1.csv")
Mydata## pH Vol
## 1 2.10 0.000
## 2 2.10 0.005
## 3 2.10 0.010
## 4 2.10 0.023
## 5 2.10 0.054
## 6 2.11 0.132
## 7 2.11 0.328
## 8 2.12 0.528
## 9 2.20 0.728
## 10 2.20 0.928
## 11 2.26 1.128
## 12 2.26 1.328
## 13 2.32 1.528
## 14 2.32 1.728
## 15 2.34 1.928
## 16 2.41 2.128
## 17 2.42 2.328
## 18 2.48 2.528
## 19 2.49 2.728
## 20 2.55 2.928
## 21 2.56 3.129
## 22 2.61 3.329
## 23 2.62 3.529
## 24 2.68 3.729
## 25 2.69 3.929
## 26 2.76 4.129
## 27 2.76 4.329
## 28 2.83 4.529
## 29 2.84 4.729
## 30 2.91 4.929
## 31 2.91 5.129
## 32 2.99 5.329
## 33 3.00 5.529
## 34 3.08 5.729
## 35 3.09 5.929
## 36 3.19 6.129
## 37 3.20 6.329
## 38 3.31 6.529
## 39 3.31 6.729
## 40 3.44 6.929
## 41 3.45 7.129
## 42 3.62 7.329
## 43 3.62 7.529
## 44 3.82 7.729
## 45 3.83 7.877
## 46 4.04 8.078
## 47 4.04 8.222
## 48 4.25 8.422
## 49 4.25 8.568
## 50 4.43 8.768
## 51 4.52 8.968
## 52 4.53 9.168
## 53 4.68 9.368
## 54 4.70 9.568
## 55 4.81 9.768
## 56 4.83 9.968
## 57 4.92 10.168
## 58 4.98 10.369
## 59 4.98 10.569
## 60 5.07 10.769
## 61 5.08 10.969
## 62 5.16 11.169
## 63 5.17 11.369
## 64 5.25 11.569
## 65 5.26 11.769
## 66 5.27 11.969
## 67 5.37 12.169
## 68 5.38 12.369
## 69 5.46 12.569
## 70 5.47 12.769
## 71 5.53 12.969
## 72 5.55 13.169
## 73 5.63 13.369
## 74 5.64 13.569
## 75 5.71 13.769
## 76 5.72 13.969
## 77 5.74 14.169
## 78 5.87 14.369
## 79 5.87 14.569
## 80 5.97 14.769
## 81 5.99 14.969
## 82 6.09 15.169
## 83 6.10 15.369
## 84 6.23 15.569
## 85 6.31 15.769
## 86 6.32 15.969
## 87 6.51 16.169
## 88 6.52 16.346
## 89 6.76 16.546
## 90 6.77 16.656
## 91 7.07 16.856
## 92 7.08 16.928
## 93 7.39 17.110
## 94 7.42 17.164
## 95 7.60 17.300
## 96 7.61 17.390
## 97 8.30 17.590volume <- Mydata$Vol ## Volume vector
pH <- Mydata$pH ## pH vector
plot(volume,pH,main="Volume of NaOH vs. pH of Solution",xlab="Volume (mL)",
ylab="pH")
H <- 10^-(pH) ## H+ from pH
Vini <- 25 ## Initial Volume
Vend <- 9.3025 ## Volume added in endpoint
tbase <- 0.10 ## [Base]Binding Curve Analysis
The transformation of titration data into binding curves was accomplished by calculating the hydrogen ion concentration from the measured pH values and subsequently determining the fraction of binding sites occupied by hydrogen ions. The equation used for this transformation considers the initial concentration of the acid, the volume of titrant added, and the effective volume of the solution to account for dilution effects. This process yields a binding curve that reflects the fraction of acid molecules that have bound hydrogen ions as a function of pH, providing a detailed view of the acid’s protonation states across the pH spectrum
The binding curves were analyzed using a non-linear least squares (NLS) method to precisely determine the acid’s dissociation constants, Ka1 and Ka2. The formula used is (fb ~ (h / KD1 + (2 * h^2) / (KD1 * KD2)) / (1 + h / KD1 + h^2 / (KD1 * KD2)). This equation models the relationship between the fraction of bound sites and the hydrogen ion concentration, incorporating both dissociation constants as parameters. The NLS method also add ands adjusts a line of best fit to minimize the difference between the observed binding data and the model, resulting in accurate estimates of Ka1 and Ka2 in the summary poseted. This gives us a Ka1=1.608e^-6 and a Ka2=1.809e^-3.
Fb <- (2-(((volume*tbase)+((H)*(Vini+volume)))/(Vend*tbase)))
library(nls2)
fit <- nls2(Fb~(H/KD1+2*H^2/(KD1*KD2))/(1+H/KD1+H^2/(KD1*KD2))
,start = c(KD1=0.001,KD2=0.000001))
summary(fit)##
## Formula: Fb ~ (H/KD1 + 2 * H^2/(KD1 * KD2))/(1 + H/KD1 + H^2/(KD1 * KD2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## KD1 1.608e-06 8.373e-08 19.21 <2e-16 ***
## KD2 1.809e-03 8.166e-05 22.16 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.05993 on 95 degrees of freedom
##
## Number of iterations to convergence: 16
## Achieved convergence tolerance: 2.495e-06plot(pH,Fb)
lines(pH,Fb,col="royalblue1")
Comparison and conclusion
Auto titration analysis and binding curve techniques offer complementary perspectives on the behavior of diprotic acids. While titration provides a straightforward, visually intuitive means of estimating dissociation constants, it may lack the precision obtainable through binding curve analysis, which leverages mathematical modeling to refine these estimates. However, binding curve analysis requires more complex data processing and a deeper understanding of the underlying chemical equilibria. Additionally NLS and r script programming provides further information on the analysis as it automaticall runs reltive accuracy percentage, standard deviation. Each method has its advantages and limitations, underscoring the importance of employing both to achieve a comprehensive analysis of diprotic acids.
The combined use of traditional titration and binding curve analysis methodologies has yielded detailed insights into the dissociation characteristics of an unknown diprotic acid, demonstrating the strengths of each approach.