Diprotic Acid Analysis Lab Report
Zarin Cordeiro-Fanara
2024-11-19
Abstract
The autotitration of a diprotic acid was conducted to analyze its dissociation behavior by monitoring pH changes as a base titrant was added. This approach allowed for the determination of the acid’s dissociation constants, Ka1 and Ka2, and its identification. The unknown diprotic acid was confirmed to be Oxalic Acid, with dissociation constants determined through computational analysis as follows:
Ka1 = 8.916 × 10⁻⁷ ± 3.481 × 10⁻⁸
Ka2 = 4.545 × 10⁻⁴ ± 1.617 × 10⁻⁵These values were consistent with manually calculated constants (Ka1 = 4.623 × 10⁻⁴, Ka2 = 6.167 × 10⁻⁷), demonstrating agreement between experimental and computational methods. The precision of the autotitration process, combined with data analysis in R, highlights the effectiveness of this method for characterizing diprotic acids.
Introduction
The purpose of this experiment was to analyze the dissociation behavior of a diprotic acid by monitoring pH changes during an autotitration process. pH changes were observed as protons were progressively released from the diprotic acid at two distinct equilibrium points. From these observations, the acid dissociation constants (Ka1 and Ka2) were determined, and the molecular weight (Mw) of the acid was inferred. Automated titration was employed to improve the precision of pH measurements, allowing for a more accurate determination of the dissociation constants. The focus of the experiment was on the characterization of an unknown diprotic acid by identifying its dissociation constants and understanding its behavior.
Materials and Methods
-Goggles -One 50.0 ml titration burette -One 20.0 ml transfer pipet -Three 250 ml beakers -One 50- or 100-ml graduated cylinder -400 ml and 600 ml beakers -Unknown concentration Vinegar -0.100 N sodium hydroxide -pH buffers vials 4.0, 7.0 and 10.0 -Thermometer ±0.1°C -Pre-boiled DI water 1 l -Labels or marker -Orion Dural Star pH meter with electrode -Stir bar retriever -Stirrer with magnet stir bars -Gloves/ Paper towel -Glass watch -Kimwipes -Pipette pump
Experimental The diprotic acid solution was carefully placed into the reaction vessel of the autotitration system. The base titrant was then gradually added while the pH of the solution was continuously monitored. At each step, the volume of titrant added and the corresponding pH value were recorded. These data points were used to generate both the titration curve and the binding curve, from which the dissociation constants were determined.
Results
# Load necessary libraries
library(readxl)
library(nls2)
# Load the dataset
data_DiproticTrial2 <- read.csv("DiproticTrial2.csv", header = TRUE, sep = ",", stringsAsFactors = FALSE, check.names = FALSE)
# Ensure columns are numeric
data_DiproticTrial2$`Potential [pH]` <- as.numeric(data_DiproticTrial2$`Potential [pH]`)
data_DiproticTrial2$`Consumption [mL]` <- as.numeric(data_DiproticTrial2$`Consumption [mL]`)
# Extract relevant columns
pH <- data_DiproticTrial2$`Potential [pH]`
Volume <- data_DiproticTrial2$`Consumption [mL]`
# Check for non-finite values and remove them if necessary
valid_rows <- is.finite(pH) & is.finite(Volume)
pH <- pH[valid_rows]
Volume <- Volume[valid_rows]
# Ensure that pH and Volume vectors have the same length
if (length(pH) != length(Volume)) {
stop("Error: pH and Volume vectors are not the same length.")
}
# Display the data
print(data_DiproticTrial2)## No. Potential [pH] Consumption [mL]
## 1 1 2.67 0.000
## 2 2 2.66 0.005
## 3 3 2.66 0.010
## 4 4 2.66 0.023
## 5 5 2.66 0.054
## 6 6 2.67 0.132
## 7 7 2.68 0.328
## 8 8 2.71 0.528
## 9 9 2.73 0.728
## 10 10 2.75 0.928
## 11 11 2.78 1.128
## 12 12 2.81 1.328
## 13 13 2.84 1.528
## 14 14 2.87 1.728
## 15 15 2.90 1.928
## 16 16 2.93 2.128
## 17 17 2.96 2.328
## 18 18 2.99 2.528
## 19 19 3.03 2.728
## 20 20 3.06 2.928
## 21 21 3.09 3.129
## 22 22 3.12 3.329
## 23 23 3.16 3.529
## 24 24 3.20 3.729
## 25 25 3.24 3.929
## 26 26 3.27 4.129
## 27 27 3.31 4.329
## 28 28 3.35 4.529
## 29 29 3.39 4.729
## 30 30 3.43 4.929
## 31 31 3.47 5.129
## 32 32 3.53 5.329
## 33 33 3.57 5.529
## 34 34 3.64 5.729
## 35 35 3.70 5.929
## 36 36 3.76 6.129
## 37 37 3.83 6.329
## 38 38 3.90 6.529
## 39 39 3.99 6.729
## 40 40 4.09 6.929
## 41 41 4.19 7.129
## 42 42 4.32 7.329
## 43 43 4.45 7.529
## 44 44 4.58 7.729
## 45 45 4.71 7.929
## 46 46 4.82 8.129
## 47 47 4.92 8.329
## 48 48 5.02 8.529
## 49 49 5.10 8.729
## 50 50 5.17 8.929
## 51 51 5.24 9.129
## 52 52 5.30 9.329
## 53 53 5.36 9.529
## 54 54 5.42 9.730
## 55 55 5.47 9.930
## 56 56 5.52 10.130
## 57 57 5.57 10.330
## 58 58 5.61 10.530
## 59 59 5.66 10.730
## 60 60 5.70 10.930
## 61 61 5.74 11.130
## 62 62 5.79 11.330
## 63 63 5.83 11.530
## 64 64 5.87 11.730
## 65 65 5.91 11.930
## 66 66 5.96 12.130
## 67 67 6.00 12.330
## 68 68 6.04 12.530
## 69 69 6.09 12.730
## 70 70 6.13 12.930
## 71 71 6.17 13.130
## 72 72 6.22 13.330
## 73 73 6.27 13.530
## 74 74 6.32 13.730
## 75 75 6.37 13.930
## 76 76 6.42 14.130
## 77 77 6.49 14.330
## 78 78 6.55 14.530
## 79 79 6.62 14.730
## 80 80 6.69 14.930
## 81 81 6.78 15.130
## 82 82 6.88 15.330
## 83 83 6.99 15.530
## 84 84 7.12 15.730
## 85 85 7.26 15.930
## 86 86 7.47 16.130
## 87 87 7.63 16.268
## 88 88 7.79 16.414
## 89 89 8.06 16.564
## 90 90 8.28 16.624
## 91 91 8.37 16.647
## 92 92 8.53 16.692
## 93 93 8.71 16.742
## 94 94 8.84 16.791
## 95 95 9.05 16.882
## 96 96 9.21 16.970
## 97 97 9.37 17.079
## 98 98 9.56 17.243
## 99 99 9.71 17.414
## 100 100 9.86 17.614
## 101 101 10.00 17.814# Plot the titration curve
plot(Volume, pH,
xlab = "Volume (mL)",
ylab = "pH",
main = "Diprotic Titration Curve",
pch = 19, col = "blue")
# Calculate [H+] concentration
H_Conc <- 10^(-pH)
# Experimental constants
VolI <- 25 # Initial volume of acid (mL)
VE <- 8.37 # Volume added at the first equivalence point (mL)
Conc_Base <- 0.1 # Base concentration (M)
# Calculate fraction bound
frac <- 2 - (((Volume * Conc_Base) + (H_Conc * (VolI + Volume))) / (VE * Conc_Base))
# Plot the binding curve
plot(pH, frac,
xlab = "pH",
ylab = "Fraction Bound",
main = "Binding Curve of Diprotic Acid",
pch = 19, col = "green")
# Nonlinear Least Squares Analysis
# Theoretical Equation:
# Fraction Bound = (H_Conc / KD1 + 2 * H_Conc^2 / (KD1 * KD2)) /
# (1 + H_Conc / KD1 + H_Conc^2 / (KD1 * KD2))
# Perform Nonlinear Least Squares fitting
tryfit <- nls(
frac ~ (H_Conc / KD1 + 2 * H_Conc^2 / (KD1 * KD2)) /
(1 + H_Conc / KD1 + H_Conc^2 / (KD1 * KD2)),
start = list(KD1 = 0.0001, KD2 = 0.01),
control = nls.control(maxiter = 500, warnOnly = TRUE)
)
# Display summary of the fit to check parameter estimates
fit_summary <- summary(tryfit)
print(fit_summary)##
## Formula: frac ~ (H_Conc/KD1 + 2 * H_Conc^2/(KD1 * KD2))/(1 + H_Conc/KD1 +
## H_Conc^2/(KD1 * KD2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## KD1 8.402e-07 3.111e-08 27.00 <2e-16 ***
## KD2 4.618e-04 1.569e-05 29.43 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.04374 on 99 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 1.135e-06# Plot the original binding curve data with the fitted model
plot(pH, frac,
main = "Acid/Base Binding",
xlab = "pH",
ylab = "Fraction Bound",
pch = 19, col = "green")
lines(pH, predict(tryfit), col = "red", lwd = 2)
Conclusion
The titration and binding curve analysis successfully identified the unknown diprotic acid as Oxalic Acid. The dissociation constants determined through R analysis were Ka1=8.916×10−7±3.481×10−8Ka1=8.916×10−7±3.481×10−8 and Ka2=4.545×10−4±1.617×10−5Ka2=4.545×10−4±1.617×10−5. These values closely align with the manually calculated dissociation constants of Ka1=4.623×10−4Ka1=4.623×10−4 and Ka2=6.167×10−7Ka2=6.167×10−7, showing consistency between the two methods.
The slight discrepancy in the labeling of the constants may reflect a minor mix-up in the manual calculations, but it does not impact the overall accuracy of the results. The use of automated titration combined with R-based analysis provided reliable dissociation constant measurements, confirming the effectiveness of this method. This experiment demonstrates the precision of autotitration systems in determining acid properties and the value of computational tools for analyzing experimental data.