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 11.50
volume <- 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 25.00
pH
##  [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 11.50
plot(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-01
plot(pH,fbound,xlim=c(0,11.59),main="Binding Analysis of Monoprotic Titration")

library(nls2)
## Loading required package: proto
fit <- 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-06
lines(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.   :120.00

Conclusion

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.