R Markdown
Amy
2024-04-12
Abstract
An autotitrator diprotic acid equilibrium experiment is a basic analytical chemistry experiment that investigates the dissociation behavior of diprotic acids in solution. Diprotic acids are compounds that have the capacity to give away two protons, or H+ ions, each molecule. Oxalic acid (H2C2O4) and carbonic acid (H2CO3) are a few examples. Each proton is released successively during the dissociation of diprotic acids, which happens in steps. Acid dissociation constants (Ka values) are the equilibrium constants connected to these dissociation processes. Comprehending the diprotic acid dissociation behavior is of paramount importance in multiple branches of chemistry, such as environmental chemistry, biochemistry, and chemical engineering. High-tech lab equipment called autotitrators is used to perform automated titrations. They provide accurate control over titrant addition (strong base, for example) and real-time pH or other parameter monitoring. When an autotitrator is used instead of manual titration techniques, the titration process becomes more accurate, efficient, and repeatable. This method typically involves the presence of a neutral electrolyte with a common counterion. The pKa, an empirically determined parameter, indicates the strength of proton binding in various compounds. It signifies the strength of proton binding in a Bronsted acid; higher pKa values indicate stronger proton binding and lesser ease in proton release. A monoprotic acid, by definition, can accept only one proton. Indicators such as phenolphthalein, bromothymol blue, and bromocresol purple aid in observing the endpoint of the reaction. Phenolphthalein is colorless in acidic conditions and pink in basic conditions, while bromothymol blue turns yellow in acidic solutions and blue in basic solutions. Bromocresol purple shifts from yellow to purple under similar conditions. Utilizing potentiometric titration, MicroLab plotted volume against pH to identify equivalence points on the graphs2. The choice of appropriate electrodes and favorable equilibrium in the analytical reaction leads to a sharp voltage change at the equivalence point. This point, where the titration curve slope is maximal, indicates the highest rate of pH change with titrant addition. Graphical tools like CuritPlot help smooth raw data into titration curves, aiding in endpoint determination. In a chemistry laboratory we usually use this method to determine the reaction completion or direction. Precision, sensitivity, method stability, and tools for curve calculation are essential considerations for accurate results and ensuring consistency across samples and instruments. Potentiometric titrations offer precision and reliability, minimizing significant differences in titrated volumes and resulting pKa values. This ensures method and instrument reliability, providing similar results and values consistently.
Purpose of the experiment
Previously we did gaussian data and linear projects to create a base in basic coding that we will introduce in this project. We practiced how to get an average and plot graph using data we collected from the laboratory, we were also able to compare data from female and male and different heights in basketball. The purpose of this experiment was to identify a monoprotic acid data by a potentiometric titration and compare it to the diprotic unknown acid data by auto potentiometric titration. to find the molar mass and pKa values from the data retrieved from these titrations.
Experimental
Titration analysis (Monoprotic)
An essential method in analytical chemistry, monoprotic titration analysis is frequently used to ascertain the acid and base concentrations in a range of materials. Monoprotic acid can donate 1 proton with a standarsize solution of strong base or acid. some examples of monoprotic acid are acetic acid(CH₃COOH), nitric acid(HNO₃) and hydrochloric acid(HCL). to measure the titration curve we used the Ph of the solution and the number of titrant used. the equivalence point is the exact point where the exact amount of acid and base were added. The data collected during the experiment reflects less data shown from before and after the equivalence point meanins that there was Sodium Hydroxide was highly present in the monoptoric acid data.
mydata <- read.csv("Titration.csv")
mydata## X.mL. pH
## 1 3 3.79
## 2 4 3.95
## 3 5 4.05
## 4 6 4.17
## 5 7 4.26
## 6 8 4.38
## 7 9 4.45
## 8 10 4.54
## 9 11 4.63
## 10 12 4.72
## 11 13 4.83
## 12 14 4.93
## 13 15 5.04
## 14 16 5.18
## 15 17 5.40
## 16 18 5.61
## 17 19 6.18pH <- mydata$pH
volume <- mydata$X.mL
volume## [1] 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19pH## [1] 3.79 3.95 4.05 4.17 4.26 4.38 4.45 4.54 4.63 4.72 4.83 4.93 5.04 5.18 5.40
## [16] 5.61 6.18plot(volume, pH, main = "monoprotic curve", xlab = "volume" , ylab ="pH")
#binding curve for titration data
H <- 10^-(pH)
CB <- 0.01
Vadd <- volume
Vini <- 25 #initial volume of acid
Vend <- 19.5 #volume added binding curve trasnformation
\(Fb = \frac {H}{H+KD}\),This is the basic fraction bound equation, where KD is the dissociation constant and H is the number of protons. KD, or the acidic dissociation constant, can also be referred to as KA in this context. These are interchangeable terms. The binding curve is constructed using this equation and the parameters Fb (Fraction Bound) vs. pH. Throughout the experiment, pH measurements were collected and calculated. In this experiment, Ka is needed to check whether the titration is being done appropriately. \(Ka = \exp {10}{-pKa}\) is the equation that can be used to find Ka.It is evident that Ka and pKa have an inverse relationship, which makes it possible to make links between the two and determine the acid’s Ka or pKa.
We were able to measure that by the potentiometric titration of the unknown acid with NaOH. The moles of the unknown were found by titrating the sample and using the volume needed to reach the endpoint and with the Molarity of NaOH, and then applying stoichiometry to find the moles of the unknown acid. The moles and mass of the unknown acid was then used to find the molar mass of the unknown. The results showed the standard deviation of the unknown was then found to be 0.005775 g/mol. The percent relative standard deviation and confidence level at 95% were also found to be 1.1254%. Then the pKa of each of the three titrations was calculated by using the half- equivalence point and pH in the titration curve. The average pKa of the unknown acid was found to be 4.515.
#Equation
fb <- 1 - (CB * Vadd + H * (Vini + Vadd)) / (CB * Vend)
fb## [1] 0.82286632 0.77818537 0.72987819 0.68155971 0.63200753 0.58268888
## [7] 0.53227505 0.48200302 0.43156963 0.38099990 0.33045097 0.27970149
## [13] 0.22889844 0.17809803 0.12734767 0.07638178 0.02549195plot(pH,fb, main= "Binding analysis of monoprotic titration")
library(nls2)## Loading required package: protofit <- nls2((fb ~ H/(KD+H)), start = c(KD=0.0003))
summary(fit)##
## Formula: fb ~ H/(KD + H)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## KD 3.105e-05 2.930e-07 105.9 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.007537 on 16 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 3.612e-06lines(pH,predict(fit), col="red")
##Pros and Cons of traditional titration analysis and binding analysis #pros of titration analysis titration analysis we can quantify the information about the concentration in a soluiton and for this analysis the equipments and very simple and low cost comparing to others. #pros of binding analysis bindng analysis is also quantitative and qualitative giving enough information about the nature interaction. is also sensitive allowing the detection of low concentration and that is has versatile techniques such as chromatography andd spectroscopy. #cons of titration analysis some cons of titration analysis is the endpoint determination for some reactions can be affected by small mistakes and that is time consuming meanins that it could be very time demanding for multiple titration. #cons of binding analysis the cost of binding analysis are high base on the equipment that are request for it and the complexity of the technique to analyze results. another one could be the interference to similar titration analysis can affect the accuracy of the results in complex samples.
Diprotic Acid data
the diprotic acid donate 2 protons, during the titration the acid is titrated by a base creating a curve. in the graph we will be able to look at 2 peaks in pH from the 2 protons to donate. the formula used to produce the titration curve for this acid is reflected bellow using similar base as de monoprotic acid formula.
library(readxl)
mydata <- read.csv("Diprotic.csv")
mydata## Volume.mL. pH
## 1 2.128 1.90
## 2 2.328 1.92
## 3 2.528 1.94
## 4 2.728 1.96
## 5 2.928 1.99
## 6 3.129 2.01
## 7 3.329 2.03
## 8 3.529 2.06
## 9 3.729 2.09
## 10 3.929 2.12
## 11 4.129 2.15
## 12 4.329 2.19
## 13 4.529 2.23
## 14 4.729 2.28
## 15 4.929 2.33
## 16 5.129 2.39
## 17 5.329 2.45
## 18 5.529 2.52
## 19 5.729 2.60
## 20 5.929 2.67
## 21 6.129 2.77
## 22 6.329 2.85
## 23 6.529 2.97
## 24 6.729 3.07
## 25 6.929 3.15
## 26 7.129 3.25
## 27 7.329 3.33
## 28 7.529 3.39
## 29 7.729 3.48
## 30 7.929 3.54
## 31 8.129 3.61
## 32 8.329 3.67
## 33 8.529 3.73
## 34 8.729 3.79
## 35 8.929 3.85
## 36 9.129 3.91
## 37 9.329 3.96
## 38 9.529 4.02
## 39 9.730 4.07
## 40 9.930 4.14
## 41 10.130 4.19
## 42 10.330 4.26
## 43 10.530 4.32
## 44 10.730 4.39
## 45 10.930 4.46
## 46 11.130 4.54
## 47 11.330 4.62
## 48 11.530 4.72
## 49 11.730 4.83
## 50 11.930 4.96
## 51 12.130 5.12
## 52 12.330 5.30
## 53 12.521 5.53
## 54 12.638 5.67
## 55 12.788 5.81
## 56 12.988 5.93
## 57 13.188 6.05
## 58 13.388 6.22
## 59 13.588 6.49
## 60 13.677 6.69
## 61 13.728 6.90
## 62 13.751 7.01
## 63 13.783 7.06
## 64 13.864 7.34
## 65 13.890 7.54
## 66 13.901 7.57
## 67 13.929 7.73
## 68 13.943 7.84
## 69 13.962 7.96
## 70 13.998 8.09
## 71 14.084 8.38
## 72 14.139 8.65
## 73 14.166 8.83
## 74 14.184 8.86
## 75 14.230 8.98
## 76 14.278 9.08Volume <- mydata$Volume.mL
Volume## [1] 2.128 2.328 2.528 2.728 2.928 3.129 3.329 3.529 3.729 3.929
## [11] 4.129 4.329 4.529 4.729 4.929 5.129 5.329 5.529 5.729 5.929
## [21] 6.129 6.329 6.529 6.729 6.929 7.129 7.329 7.529 7.729 7.929
## [31] 8.129 8.329 8.529 8.729 8.929 9.129 9.329 9.529 9.730 9.930
## [41] 10.130 10.330 10.530 10.730 10.930 11.130 11.330 11.530 11.730 11.930
## [51] 12.130 12.330 12.521 12.638 12.788 12.988 13.188 13.388 13.588 13.677
## [61] 13.728 13.751 13.783 13.864 13.890 13.901 13.929 13.943 13.962 13.998
## [71] 14.084 14.139 14.166 14.184 14.230 14.278pH <- mydata$pH
pH## [1] 1.90 1.92 1.94 1.96 1.99 2.01 2.03 2.06 2.09 2.12 2.15 2.19 2.23 2.28 2.33
## [16] 2.39 2.45 2.52 2.60 2.67 2.77 2.85 2.97 3.07 3.15 3.25 3.33 3.39 3.48 3.54
## [31] 3.61 3.67 3.73 3.79 3.85 3.91 3.96 4.02 4.07 4.14 4.19 4.26 4.32 4.39 4.46
## [46] 4.54 4.62 4.72 4.83 4.96 5.12 5.30 5.53 5.67 5.81 5.93 6.05 6.22 6.49 6.69
## [61] 6.90 7.01 7.06 7.34 7.54 7.57 7.73 7.84 7.96 8.09 8.38 8.65 8.83 8.86 8.98
## [76] 9.08length(Volume)## [1] 76length(pH)## [1] 76H <- 10^(-pH)
H## [1] 1.258925e-02 1.202264e-02 1.148154e-02 1.096478e-02 1.023293e-02
## [6] 9.772372e-03 9.332543e-03 8.709636e-03 8.128305e-03 7.585776e-03
## [11] 7.079458e-03 6.456542e-03 5.888437e-03 5.248075e-03 4.677351e-03
## [16] 4.073803e-03 3.548134e-03 3.019952e-03 2.511886e-03 2.137962e-03
## [21] 1.698244e-03 1.412538e-03 1.071519e-03 8.511380e-04 7.079458e-04
## [26] 5.623413e-04 4.677351e-04 4.073803e-04 3.311311e-04 2.884032e-04
## [31] 2.454709e-04 2.137962e-04 1.862087e-04 1.621810e-04 1.412538e-04
## [36] 1.230269e-04 1.096478e-04 9.549926e-05 8.511380e-05 7.244360e-05
## [41] 6.456542e-05 5.495409e-05 4.786301e-05 4.073803e-05 3.467369e-05
## [46] 2.884032e-05 2.398833e-05 1.905461e-05 1.479108e-05 1.096478e-05
## [51] 7.585776e-06 5.011872e-06 2.951209e-06 2.137962e-06 1.548817e-06
## [56] 1.174898e-06 8.912509e-07 6.025596e-07 3.235937e-07 2.041738e-07
## [61] 1.258925e-07 9.772372e-08 8.709636e-08 4.570882e-08 2.884032e-08
## [66] 2.691535e-08 1.862087e-08 1.445440e-08 1.096478e-08 8.128305e-09
## [71] 4.168694e-09 2.238721e-09 1.479108e-09 1.380384e-09 1.047129e-09
## [76] 8.317638e-10plot(Volume, pH, main = "Diprotic", xlab = "Volume" , ylab ="pH of Diprotic acid")
Binding curve data for Diprotic analysis
Diprotic formula refers to 2 protons that can be donate per molecule in acid reaction, this formula is similar to the monoprotic formula. in the diprotic formula we have the Vend divide by 2 or use half of the data points; there are also 2 Kd values used in the line. for the diprotic data we had the same initial volume as monoprotic but it has a lower ending volume comparing to the other data.
Vinital <- 25.00
Vadd <- Volume
Vend <- 14.278/2
CB <- 0.100
FB <- 2 - ((CB * Vadd) + H * (Vinital + Vadd)) / (CB * Vend)
FB## [1] 1.223531e+00 1.213679e+00 1.203160e+00 1.192000e+00 1.189543e+00
## [6] 1.176654e+00 1.163354e+00 1.157617e+00 1.150556e+00 1.142248e+00
## [11] 1.132767e+00 1.128360e+00 1.122034e+00 1.119036e+00 1.113477e+00
## [16] 1.109624e+00 1.102800e+00 1.096377e+00 1.089385e+00 1.076866e+00
## [21] 1.067426e+00 1.051473e+00 1.038123e+00 1.019603e+00 9.977532e-01
## [26] 9.760926e-01 9.522042e-01 9.268081e-01 9.021745e-01 8.760375e-01
## [31] 8.499339e-01 8.233287e-01 7.965494e-01 7.696173e-01 7.425513e-01
## [36] 7.153680e-01 6.879618e-01 6.606002e-01 6.329234e-01 6.055043e-01
## [41] 5.778566e-01 5.502990e-01 5.226214e-01 4.949495e-01 4.672281e-01
## [46] 4.394985e-01 4.117222e-01 3.839528e-01 3.561517e-01 3.283304e-01
## [51] 3.004879e-01 2.726053e-01 2.459578e-01 2.296113e-01 2.086307e-01
## [56] 1.806351e-01 1.526348e-01 1.246349e-01 9.663470e-02 8.417440e-02
## [61] 7.703477e-02 7.381456e-02 6.933271e-02 5.798883e-02 5.434778e-02
## [66] 5.280705e-02 4.888538e-02 4.692455e-02 4.426330e-02 3.922074e-02
## [71] 2.717445e-02 1.947039e-02 1.568839e-02 1.316703e-02 6.723573e-03
## [76] -4.576274e-08plot(pH,FB,main ="Fraction Bound vs. pH of Diprotic Acid ",xlim = c(1,9),ylim = c(0.0,2.0) )
library(nls2)
fit <- nls2(FB ~ (H/KD1+(2*H^2)/(KD1*KD2))/(1+H/KD1+H^2/(KD1*KD2)), start=c(KD1=0.000001,KD2=0.0001))
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 3.744e-05 2.486e-06 15.06 < 2e-16 ***
## KD2 4.099e-02 4.505e-03 9.10 1.08e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0637 on 74 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 9.338e-06lines(pH,predict(fit),col="purple")
Further thoughts for future studies
for the future i will wonder what other kind of chemistry analysis we can do using R code. and if is possible use the help from other reports measuring the basicity of compounds using monoprotic and diporotic analysis.