Lab Report Data

The data from this experiment was obtained by Auto-Potentiometric titration. An unknown diprotic acid sample was titrated with NaOH solution. After analyzing the data using the equivalence points, molar mass, and acid dissociation constants, the unknown acid is identified. Afterwards, a deeper understanding of both manual and potentiometric titrations is gained.

mydata <- read.csv("data2.csv")

volvect <- mydata$Volume

pHvect <- mydata$pH

plot(volvect, pHvect,
     xlab= "Volume (mL)", ylab= "pH", main= "Titration Curve")

Transforming Diprotic Data

The fraction bound equation below was used to transform the data.

\[ f = 2- \frac {( VA \cdot CB ) + (H^+ \cdot (VI+VA))}{(VI \cdot CB)} \] where:

Since a diprotic acid is being used, the full binding is equal to 2. The reduction in binding is caused by the addition of the base and the dissociation of HA. This is subtracted from the full binding value to get the fraction bound. This only applies up until the endpoint volume is reached. It does not go further.

# Concentration of H+
H <- 10^-(pHvect)

VE= 7.4
VI= 25

# Concentration of NaOH
CB= 0.1

VA <- volvect

FB <- (2-(((VA*CB)+((H)*(VI+VA)))/(VE*CB)))

plot(pHvect, FB,
     xlab= "pH", ylab= "Fraction Bound", main= "Binding Curve")

NLS2 Analysis

The theoretical equation below was used to determine Ka1 and Ka2 values.

\[ f = \frac {\frac {H}{Ka1}+ \frac {2H^2}{Ka1 \cdot Ka2}}{1+\frac{H}{Ka1}+\frac{H^2}{Ka1 \cdot Ka2}} \]

library(nls2)
## Loading required package: proto
tryfit <- nls2(FB ~ (H/KA1 + 2*H^2/(KA1*KA2))/(1+H/KA1 + H^2/(KA1*KA2)),
               start = c(KA1 = 0.0001, KA2 = 0.01))
tryfit
## Nonlinear regression model
##   model: FB ~ (H/KA1 + 2 * H^2/(KA1 * KA2))/(1 + H/KA1 + H^2/(KA1 * KA2))
##    data: parent.frame()
##       KA1       KA2 
## 2.963e-05 1.743e-02 
##  residual sum-of-squares: 0.4385
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 9.325e-06
plot(pHvect, FB,
     xlab = "pH", ylab = "Fractional Binding", main = "Acid/Base Binding")

lines(pHvect,predict(tryfit), col = "blue")

Obtained from nls2:

Ka1 = 2.963e-05
Ka2 = 1.743e-02

Obtained from lab report:

Ka1 = 8.71e-03
Ka2 = 3.80e-05

The Ka values obtained from the nls2 analysis and from the lab report calculations are different. The lab report value for Ka1 is greater than the nls2 analysis value while the lab Ka2 value is less than the nls2 value. Based on the molar mass and Ka values from the lab report, the unknown acid was identified as malonic acid. Its Ka1 value is 1.42e-03 and its Ka2 value is 2.01e-06.

Thoughts/Questions: The titration curve was a little off for the first equivalence point. The slope is not as sharp as it is for the second EQ point. For the binding curve with the tryfit line, instead of dipping down, some of the points lie above the line. I wonder if this means there was something wrong with the data collection. Possibly the autotitrator not calibrating properly. The software for the autotitrator already caused problems during the lab. The data was unable to be exported.