Diprotic Acid
Valeria Sanmartin
2024-04-15
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)## Loading required package: protofit <- 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.