Abstract

Titration is a method that can be used to discover the concentration of a solution in which acid-base titration alongside neutralization proves to be highly useful in determining this concentration. Titration curve analysis therefore allows us to view the changes in pH of an acid after being titrated by a base. There are different forms of titration that can be performed. There is manual titration in which the end point (the point in which the reaction between the titrant and the analyte is complete) is obtained through observation of color change, and there is potentiometric titration, which involves a more intricate approach in determining the endpoint as well as the equivalence point. The neutralization of the acid with the use of the base is what helps produce the titration curve in which the amount of titrant that is added to the acid to neutralize it (indicated by color change) can be ploted against the pH change as the titrant is being added. The titration curve can thus allow us to analyze the equivalence point alongside the pKa values of the acids.

The binding curve is focused on the ability of a ligand binding to a target molecule. What is meant by this action is that depending on the amount of ligand that binds to the target molecule, the binding affinity can be concluded. This relates to acid-base titration since the affinity of an acid can determine the capability of it being able to donate a proton. This is curve can be produced from a titration curve with the usage of the Kd value (dissociation constant). Through doing the binding curve analysis the Ka values were determined for both the monoprotic and diprotic acids in which the Ka for monoprotic was 4.629e-06 while for the diprotic the Ka1=6.710e-02 and Ka2=5.16e-05.

Introduction

Titration is utilized to determine the concentration of solution to which there are different forms of titration. There is manual titration in which the end point (the point in which the reaction between the titrant and the analyte is complete) is obtained through observation of color change, and there is potentiometric titration, which involves a more intricate approach in determining the endpoint as well as the equivalence point. With titration, determination of acids can be done whether it is a monoprotic acid or diprotic acid. In this lab we we will be using both manula and potentiometric titration to classify an unknown diprotic and monoprotic compounds by determining the equivalence points and the Ka values from the titration curve.

The purpose of this report is to transform the titration curves of the monoprotic and diprotic acids into binding curves using Rcode. We can use the binding curve to determine the Ka values and compare them to the experimental method done in the laboratory.

Monoprotic Titration Analysis

A monoprotic acid is an acid that is capable of donating one proton, which is otherwise known as the the Hydrogen atom. When a base is added to a monoprotic acid solution, deprotanation occurs for the acid molecules which can cause a change in pH in the solution. The pH of the the solution can help us determine the pKa value of the acid in which the pH where half of the acid molecules are deprotanated gives us said value. The equivalence point, also known as the endpoint, is the point at which all the acid molecules have been deprotanated. The equivalence point can be obtained due to it being the point at which the pH increase is the sharpest. The equivalence point can then be used to determine the concentration of the solution since at that point is where the mole of the added base is equal to the moles of the acid therefore it can be used in the equation of \(concentration= \frac{mole}{volume}\) to determine the concentration of the unknown solution. The pKa value can also be obtained through the equivalence point since dividing the base required to reach the equivalence point by 2 and determining the pH of the equivalence point can give us the pKa value.

The titration curve is graphed below in which it mainly focuses on the data closest to the equivalence point.

mydata<- read.csv("Book1.csv")

volume <- mydata$Vol

pH<-mydata$pH

volume
##  [1]  0.0  1.0  2.0  3.0  4.0  5.0  6.0  7.0  7.2  7.4  7.6  7.8  8.0  8.2  8.5
## [16]  9.0  9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0
## [31] 16.5 17.0 17.5 18.0 18.5 19.0 19.5 19.6 19.7 19.8 19.9 20.0 20.1 20.2 20.3
## [46] 20.4 20.5 20.6 20.7 20.8 20.9 21.0 21.1 21.2 21.3 21.4 21.5 21.6 22.6 23.6
pH
##  [1]  3.788  3.955  4.367  4.544  4.685  4.860  4.940  4.940  5.040  5.047
## [11]  5.117  5.128  5.153  5.170  5.201  5.234  5.285  5.326  5.370  5.404
## [21]  5.457  5.519  5.572  5.625  5.700  5.740  5.808  5.878  5.984  6.047
## [31]  6.162  6.275  6.445  6.703  7.132  7.623 11.132 11.253 11.319 11.374
## [41] 11.459 11.532 11.557 11.598 11.691 11.719 11.755 11.776 11.812 11.851
## [51] 11.873 11.894 11.903 11.939 11.957 11.976 11.991 12.000 12.132 12.228
write(volume,file="newfile")

plot(volume,pH, main="Titration Curve for Monoprotic Acid", xlab="Volume of NaOH", ylab="pH")

Binding Curve Transformation of Monoprotic data set

Below is the binding curve of the monoprotic data set in which it illustrates the binding affinity of the acid. The graph shows that as the pH increases the fraction binding of the acid decreases.

The equation used to produce the binding curve is as follows:

\(fraction bound= 1-\frac{(CB * Vadd) + H * (Vini + Vadd)}{CB * Vend}\)

The Ka value was obtained through the the nls2 function which gave an estimate of the value based on the data given. The Ka value found was Ka=4.629e-06.In the lab report, we calculated the Ka=4.846e-06 through a series of calculations.

#Proton Concentration

H <- 10^-(pH)

#Base concentration

CB <- 0.01 

#Amount of Volume Added

Vadd <- volume

#initial acid Volume

Vini <- 25 

#Estimated Volume of Base Needed to reach Endpoint

Vend <- 20 

#Fraction Bound

FB <- 1 - ((CB * Vadd) + H  * (Vini + Vadd)) / (CB * Vend)

FB
##  [1]  9.796338e-01  9.355807e-01  8.942013e-01  8.459994e-01  7.970052e-01
##  [6]  7.479294e-01  6.982204e-01  6.481630e-01  6.385317e-01  6.285462e-01
## [11]  6.187549e-01  6.087786e-01  5.988399e-01  5.888777e-01  5.739456e-01
## [16]  5.490081e-01  5.241051e-01  4.991739e-01  4.742428e-01  4.492900e-01
## [21]  4.243628e-01  3.994400e-01  3.744977e-01  3.495494e-01  3.246159e-01
## [26]  2.996452e-01  2.746927e-01  2.497351e-01  2.247899e-01  1.998160e-01
## [31]  1.748571e-01  1.498885e-01  1.249237e-01  9.995740e-02  7.498395e-02
## [36]  4.999476e-02  2.500000e-02  2.000000e-02  1.500000e-02  9.999999e-03
## [41]  4.999999e-03 -6.609711e-10 -5.000001e-03 -1.000000e-02 -1.500000e-02
## [46] -2.000000e-02 -2.500000e-02 -3.000000e-02 -3.500000e-02 -4.000000e-02
## [51] -4.500000e-02 -5.000000e-02 -5.500000e-02 -6.000000e-02 -6.500000e-02
## [56] -7.000000e-02 -7.500000e-02 -8.000000e-02 -1.300000e-01 -1.800000e-01
plot(pH,FB, main = "Monoprotic acid Binding Curve",xlab = "pH",ylab = "Fraction Bound",pch=20,col="green")

library(nls2)
## Loading required package: proto
fit <- nls2(FB ~ H/(Ka+H), start=c(Ka=0.000004629))

summary(fit)
## 
## Formula: FB ~ H/(Ka + H)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## Ka 4.629e-06  1.809e-07   25.59   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04459 on 59 degrees of freedom
## 
## Number of iterations to convergence: 1 
## Achieved convergence tolerance: 5.649e-06
lines(pH,predict(fit),col="blue")

Comparing Tradition Titration to Binding curve

Titration analysis and Binding curve analysis both have their strengths and weaknesses when it comes to retrieving conclusions regarding the acids being investigated. Some benefits of titration analysis involves the ability to measure the concentrations of the acids and bases used directly from the titration process. Another benefit comes from the simplicity of performing a titration in which it can be performed with ease, however, this can pose for some errors unfortunately. There are limits to how much information titration curves can provide in which this is mostly restricted to the usage of acids and bases. Binding curves on the other hand are capable of providing information of compounds that aren’t just acids and bases. Binding curves are also capable of providing information regarding the affinities of the compounds being investigated. All in all, it is clear that both analysis have their strengths and weaknesses which each one being utilized to retrieve certain information.

Diprotic acid analysis

Monoprotic acids and diprotic acids behave similarly with one exception which is that monoprotic acids donate one proton while diprotic acids can donate two. Because the number of protons donated differs between monoprotic and diprotic acids, their titration curves also present differences. Since diprotic acids donate two protons, two equivalence points appear on the titration curve due to the donation occurring in two separate steps rather than simultaneously.

Below is the titration curve of the diprotic acid titration with it focused mainly on the data points surrounding the equivalence points.

Titration_Data <- read.csv("diprotic.csv")


Volume <- Titration_Data$Volume

pH <- Titration_Data$pH

pH
##  [1] 1.80 1.82 1.83 1.86 1.87 1.90 1.92 1.93 1.97 1.99 2.02 2.06 2.09 2.12 2.17
## [16] 2.21 2.26 2.31 2.37 2.43 2.50 2.58 2.67 2.76 2.86 2.96 3.06 3.16 3.25 3.34
## [31] 3.42 3.48 3.56 3.63 3.69 3.75 3.81 3.87 3.93 3.99 4.05 4.10 4.15 4.20 4.24
## [46] 4.28 4.33 4.38 4.44 4.50 4.57 4.64 4.72 4.80 4.90 4.98 5.09 5.20 5.33 5.52
## [61] 5.72 5.98 6.13 6.63 6.92 7.22 7.42 7.67 7.82 8.02 8.20 8.36 8.51 8.65 8.78
## [76] 8.90
plot(Volume, pH, main = "Diprotic Acid Titration Curve", xlab = "Volume of NaOH (mL)", ylab = "pH",pch = 20, col = "turquoise")

Binding Curve Transformation for Diprotic acid

-Below is the binding curve of the diprotic acid data set in which it illustrates the binding affinity of the acid. The graph shows that as the pH increases the fraction binding of the acid decreases.

-The equation used to produce the binding curve is as follows:

\(fraction bound= \frac{(\frac{H}{Ka2}+\frac{(2*H^2)}{(Ka1*Ka2)})}{(\frac{1+H}{Ka2}+\frac{H^2}{(Ka1*Ka2)})}\)

This equation is much more complex than the monoprotic fraction bound equation due to there being more Ka values being produced since there diprotic acid is capable of donating more than one proton.

The Ka1 and Ka2 values were obtained through the nls2 function in which Ka1=6.710e-02 and Ka2=5.16e-05.In the lab report, we determined through a series of equations that Ka1=0.00871 whereas Ka2=5.49e-05 which is approximate to what the nls2 function provided.

#Proton Concentration

H <- 10^(-pH) 

#Base Concentration

BC <- 0.1

#Initial Acid Volume

Vini <- 25

#Estimated Volume of Base Needed to reach Endpoint 

Vend <- 13.5/2     

#Amount of Volume Added

Vadd <- Volume

Vadd
##  [1]  1.328  1.528  1.728  1.928  2.128  2.328  2.528  2.728  2.928  3.129
## [11]  3.329  3.529  3.729  3.929  4.129  4.329  4.529  4.729  4.929  5.129
## [21]  5.329  5.529  5.729  5.929  6.129  6.329  6.529  6.729  6.929  7.129
## [31]  7.329  7.529  7.729  7.929  8.129  8.329  8.529  8.729  8.929  9.129
## [41]  9.329  9.529  9.730  9.930 10.130 10.330 10.530 10.730 10.930 11.130
## [51] 11.330 11.530 11.730 11.930 12.103 12.232 12.345 12.479 12.627 12.827
## [61] 12.979 13.108 13.162 13.297 13.317 13.322 13.331 13.352 13.362 13.387
## [71] 13.392 13.405 13.436 13.442 13.454 13.485
#Fraction Bound
FB <- 2 - ((BC * Vadd) + H  * (Vini + Vadd)) / (BC * Vend)

FB
##  [1] 1.185080475 1.178788847 1.158316904 1.163689074 1.142597554 1.145423501
##  [7] 1.135171328 1.113221342 1.122883094 1.110011725 1.106015037 1.109070811
## [13] 1.101602846 1.092816435 1.096538948 1.090753855 1.088631223 1.083694303
## [19] 1.080635579 1.074311335 1.068431527 1.061926738 1.053929723 1.042002308
## [25] 1.028340768 1.011479162 0.992058354 0.970590956 0.946881487 0.922095131
## [31] 0.896013121 0.868635016 0.841608422 0.813897317 0.785682854 0.757293589
## [37] 0.728751071 0.700074197 0.671279541 0.642381635 0.613393222 0.584232984
## [43] 0.554876006 0.525623801 0.496264414 0.466882749 0.437537981 0.408163742
## [49] 0.378808090 0.349418473 0.320032838 0.290612068 0.261185369 0.231725480
## [55] 0.206270964 0.187274271 0.170661405 0.150908924 0.129072600 0.099534466
## [61] 0.077077974 0.058014957 0.050032163 0.030060774 0.027104286 0.026366949
## [67] 0.025034878 0.021924711 0.020443584 0.016740198 0.015999641 0.014073826
## [73] 0.009481306 0.008592465 0.006814720 0.002222150
plot(pH,FB, main = "Diprotic Acid Binding Curve",xlab = "pH",ylab = "Fraction Bound",pch=20,col="green")

library(nls2) 

fit <- nls2(FB ~ (H/Ka2+(2*H^2)/(Ka1*Ka2))/(1+H/Ka2+H^2/(Ka1*Ka2)), 
                  start=c(Ka1=0.06710,Ka2=0.00005516))
summary(fit)
## 
## Formula: FB ~ (H/Ka2 + (2 * H^2)/(Ka1 * Ka2))/(1 + H/Ka2 + H^2/(Ka1 * 
##     Ka2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## Ka1 6.710e-02  3.280e-03   20.46   <2e-16 ***
## Ka2 5.516e-05  1.271e-06   43.38   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.02486 on 74 degrees of freedom
## 
## Number of iterations to convergence: 1 
## Achieved convergence tolerance: 1.386e-06
lines(pH,predict(fit),col="blue")

Further thoughts

After performing this experiment and comparing the results of the Ka values obtained through rcode with the Ka values obtained through the experimental method done in the lab report, it can be seen that the values were extremely close to each other indicating small error in the experiment. Some errors that have been produced can be stemmed from the nls2 coding in which when obtaining the Ka1 and Ka2 values, the original equation \(fraction bound= \frac{(\frac{H}{Ka1}+\frac{(2*H^2)}{(Ka1*Ka2)})}{(\frac{1+H}{Ka1}+\frac{H^2}{(Ka1*Ka2)})}\) would have given us values that would not have made sense. The reason being is that the Ka1 value should be greater than the Ka2 value since the first Ka1 value is when the deprotanation is easiest, however, with this equation it would have made the Ka1 value much smaller than the Ka2. With this in mind, I changed the fraction son that the H and 1+H values were divided by Ka2 rather than Ka1. For future experiments, it would be interesting to use this coding program to analyze the binding curves of proteins or anything other than acids and bases.