Monoprotic & Diprotic Acid Titration
Elina Shakur
2024-04-10
#Abstract: This report compares two binding curves; a cruve from a monoprotic acid titration and a diprotic acid titration curve.
#Introduction: The purpose of this paper is to compare the curves from a monoprotic acid and a diprotic acid and identify where the equivalence point is and how it influences the curve of the graph.
Monoprotic Acid Titration Data
Data <- read.csv("Titration Lab Data 1.csv")
Data## pH Volume.Of.NaOH..mL. X X.1
## 1 3.60 0.0 NA
## 2 3.61 1.0 NA
## 3 3.70 2.0 NA
## 4 3.75 3.0 NA
## 5 3.81 4.0 NA
## 6 3.85 5.0 NA
## 7 4.00 6.0 NA
## 8 4.10 7.0 NA
## 9 4.25 8.0 NA
## 10 4.35 9.0 NA
## 11 4.40 10.0 NA 0,1
## 12 4.50 11.0 NA
## 13 4.67 12.0 NA
## 14 4.90 13.0 NA
## 15 5.10 14.0 NA
## 16 5.23 16.0 NA
## 17 5.29 17.0 NA
## 18 5.32 18.0 NA
## 19 5.38 19.0 NA
## 20 5.40 20.0 NA
## 21 5.50 21.0 NA
## 22 5.58 22.0 NA
## 23 5.74 23.0 NA
## 24 6.22 24.0 NA
## 25 7.40 25.0 NA
## 26 11.35 26.0 NA
## 27 11.59 27.0 NA
## 28 11.80 28.0 NA
## 29 11.91 29.5 NAVolume <- Data$Volume.Of.NaOH..mL.
Volume## [1] 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0
## [16] 16.0 17.0 18.0 19.0 20.0 21.0 22.0 23.0 24.0 25.0 26.0 27.0 28.0 29.5pH <-Data$pH
pH## [1] 3.60 3.61 3.70 3.75 3.81 3.85 4.00 4.10 4.25 4.35 4.40 4.50
## [13] 4.67 4.90 5.10 5.23 5.29 5.32 5.38 5.40 5.50 5.58 5.74 6.22
## [25] 7.40 11.35 11.59 11.80 11.91Monoprotic Binding Curve Information
H <- 10^-(pH)
H## [1] 2.511886e-04 2.454709e-04 1.995262e-04 1.778279e-04 1.548817e-04
## [6] 1.412538e-04 1.000000e-04 7.943282e-05 5.623413e-05 4.466836e-05
## [11] 3.981072e-05 3.162278e-05 2.137962e-05 1.258925e-05 7.943282e-06
## [16] 5.888437e-06 5.128614e-06 4.786301e-06 4.168694e-06 3.981072e-06
## [21] 3.162278e-06 2.630268e-06 1.819701e-06 6.025596e-07 3.981072e-08
## [26] 4.466836e-12 2.570396e-12 1.584893e-12 1.230269e-12plot(Volume,pH,main = "Volume of NaOH vs. pH",xlab = "Volume of NaOH (mL)",ylab = "pH")
#Analysis of Monoprotic Titration Curve: When graphing the volume and pH of the titration we noticed that it took on an “S” shape which is indicative of a monoprotic titration. Based on the graph, the equivalence point of the titration was around 8.0. This is typically seen in weak acid-strong base titrations.
Vinital<- 25.00
Vadd <- Volume
Vend <- 25.5
CB <- 0.10
FB <- 1 -(CB * Vadd + H * (Vinital + Vadd)) / (CB * Vend)
FB## [1] 0.99753737 0.95828147 0.91945600 0.88040032 0.84137586 0.80225976
## [7] 0.76349020 0.72449339 0.68554677 0.64646325 0.60729672 0.56818101
## [13] 0.52910155 0.49000847 0.45085891 0.37245434 0.33324886 0.29403694
## [19] 0.25483003 0.21561602 0.17641354 0.13720642 0.09800496 0.05881195
## [25] 0.01960706 -0.01960784 -0.05882353 -0.09803922 -0.15686275plot(pH,FB,main="Fraction Bound vs. pH",xlim = c(3,8), ylim = c(0,1), ylab="Fraction Bound")
library(nls2)## Loading required package: protofit <- nls2(FB ~ H/(KD+H), start=c(KD=0.001))
summary(fit)##
## Formula: FB ~ H/(KD + H)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## KD 1.695e-05 1.655e-06 10.24 5.68e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07523 on 28 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 2.534e-06lines(pH,predict(fit),col="red")
#Transforming Monoprotic Acid Data into Binding Curve: To transform our titration in a binding curve, we first establish some paramenters. Our inital volume of the acid was 25 mL, the volume added was the NaOH that was intermentally added, the end volume was the volume of NaOH we ended with when the titration come to completion. We then placed there parameters into our equation: \(F = \frac {H}{H+KD}\).
Diprotic Acid Titration Data
Data <- read.csv("Diprotic Acid Data.csv")
Data## Volume.of.NaOH.mL. pH
## 1 0.000 2.14
## 2 0.005 2.14
## 3 0.010 2.14
## 4 0.023 2.14
## 5 0.054 2.15
## 6 0.132 2.15
## 7 0.328 2.17
## 8 0.528 2.19
## 9 0.728 2.22
## 10 0.928 2.26
## 11 1.128 2.28
## 12 1.328 2.30
## 13 1.528 2.34
## 14 1.728 2.38
## 15 1.928 2.42
## 16 2.128 2.46
## 17 2.328 2.50
## 18 2.528 2.53
## 19 2.728 2.57
## 20 2.928 2.60
## 21 3.129 2.64
## 22 3.329 2.68
## 23 3.529 2.71
## 24 3.729 2.75
## 25 3.929 2.80
## 26 4.129 2.85
## 27 4.329 2.91
## 28 4.529 2.92
## 29 4.729 2.97
## 30 4.929 3.03
## 31 5.129 3.10
## 32 5.329 3.15
## 33 5.529 3.25
## 34 5.729 3.25
## 35 5.929 3.35
## 36 6.129 3.43
## 37 6.329 3.55
## 38 6.529 3.63
## 39 6.729 3.67
## 40 6.929 3.74
## 41 7.129 3.95
## 42 7.288 4.06
## 43 7.488 4.18
## 44 7.689 4.29
## 45 7.889 4.41
## 46 8.089 4.54
## 47 8.289 4.64
## 48 8.489 4.72
## 49 8.689 4.86
## 50 8.889 4.90
## 51 9.089 4.96
## 52 9.289 5.03
## 53 9.489 5.09
## 54 9.689 5.15
## 55 9.889 5.21
## 56 10.089 5.29
## 57 10.289 5.32
## 58 10.489 5.36
## 59 10.689 5.40
## 60 10.889 5.47
## 61 11.089 5.51
## 62 11.289 5.52
## 63 11.489 5.59
## 64 11.689 5.65
## 65 11.889 5.71
## 66 12.089 5.71
## 67 12.289 5.78
## 68 12.489 5.85
## 69 12.689 5.88
## 70 12.889 5.95
## 71 13.089 5.99
## 72 13.289 6.08
## 73 13.489 6.06
## 74 13.689 6.18
## 75 13.889 6.17
## 76 14.089 6.29
## 77 14.289 6.34
## 78 14.490 6.51
## 79 14.690 6.52
## 80 14.890 6.79
## 81 14.978 6.71
## 82 15.178 6.95
## 83 15.300 7.08
## 84 15.491 7.25
## 85 15.691 7.77
## 86 15.716 7.82
## 87 15.777 7.80
## 88 15.931 8.41
## 89 15.942 8.43
## 90 15.968 8.46
## 91 16.032 8.60
## 92 16.067 8.62
## 93 16.155 9.02
## 94 16.163 9.03
## 95 16.184 9.05
## 96 16.235 9.20
## 97 16.254 9.27
## 98 16.302 9.33
## 99 16.421 9.56
## 100 16.489 9.68
## 101 16.595 9.83
## 102 16.758 9.96
## 103 16.958 10.15Volume <-Data$Volume.of.NaOH.mL.
Volume## [1] 0.000 0.005 0.010 0.023 0.054 0.132 0.328 0.528 0.728 0.928
## [11] 1.128 1.328 1.528 1.728 1.928 2.128 2.328 2.528 2.728 2.928
## [21] 3.129 3.329 3.529 3.729 3.929 4.129 4.329 4.529 4.729 4.929
## [31] 5.129 5.329 5.529 5.729 5.929 6.129 6.329 6.529 6.729 6.929
## [41] 7.129 7.288 7.488 7.689 7.889 8.089 8.289 8.489 8.689 8.889
## [51] 9.089 9.289 9.489 9.689 9.889 10.089 10.289 10.489 10.689 10.889
## [61] 11.089 11.289 11.489 11.689 11.889 12.089 12.289 12.489 12.689 12.889
## [71] 13.089 13.289 13.489 13.689 13.889 14.089 14.289 14.490 14.690 14.890
## [81] 14.978 15.178 15.300 15.491 15.691 15.716 15.777 15.931 15.942 15.968
## [91] 16.032 16.067 16.155 16.163 16.184 16.235 16.254 16.302 16.421 16.489
## [101] 16.595 16.758 16.958pH <- Data$pH
pH## [1] 2.14 2.14 2.14 2.14 2.15 2.15 2.17 2.19 2.22 2.26 2.28 2.30
## [13] 2.34 2.38 2.42 2.46 2.50 2.53 2.57 2.60 2.64 2.68 2.71 2.75
## [25] 2.80 2.85 2.91 2.92 2.97 3.03 3.10 3.15 3.25 3.25 3.35 3.43
## [37] 3.55 3.63 3.67 3.74 3.95 4.06 4.18 4.29 4.41 4.54 4.64 4.72
## [49] 4.86 4.90 4.96 5.03 5.09 5.15 5.21 5.29 5.32 5.36 5.40 5.47
## [61] 5.51 5.52 5.59 5.65 5.71 5.71 5.78 5.85 5.88 5.95 5.99 6.08
## [73] 6.06 6.18 6.17 6.29 6.34 6.51 6.52 6.79 6.71 6.95 7.08 7.25
## [85] 7.77 7.82 7.80 8.41 8.43 8.46 8.60 8.62 9.02 9.03 9.05 9.20
## [97] 9.27 9.33 9.56 9.68 9.83 9.96 10.15H <- 10^(-pH)
H## [1] 7.244360e-03 7.244360e-03 7.244360e-03 7.244360e-03 7.079458e-03
## [6] 7.079458e-03 6.760830e-03 6.456542e-03 6.025596e-03 5.495409e-03
## [11] 5.248075e-03 5.011872e-03 4.570882e-03 4.168694e-03 3.801894e-03
## [16] 3.467369e-03 3.162278e-03 2.951209e-03 2.691535e-03 2.511886e-03
## [21] 2.290868e-03 2.089296e-03 1.949845e-03 1.778279e-03 1.584893e-03
## [26] 1.412538e-03 1.230269e-03 1.202264e-03 1.071519e-03 9.332543e-04
## [31] 7.943282e-04 7.079458e-04 5.623413e-04 5.623413e-04 4.466836e-04
## [36] 3.715352e-04 2.818383e-04 2.344229e-04 2.137962e-04 1.819701e-04
## [41] 1.122018e-04 8.709636e-05 6.606934e-05 5.128614e-05 3.890451e-05
## [46] 2.884032e-05 2.290868e-05 1.905461e-05 1.380384e-05 1.258925e-05
## [51] 1.096478e-05 9.332543e-06 8.128305e-06 7.079458e-06 6.165950e-06
## [56] 5.128614e-06 4.786301e-06 4.365158e-06 3.981072e-06 3.388442e-06
## [61] 3.090295e-06 3.019952e-06 2.570396e-06 2.238721e-06 1.949845e-06
## [66] 1.949845e-06 1.659587e-06 1.412538e-06 1.318257e-06 1.122018e-06
## [71] 1.023293e-06 8.317638e-07 8.709636e-07 6.606934e-07 6.760830e-07
## [76] 5.128614e-07 4.570882e-07 3.090295e-07 3.019952e-07 1.621810e-07
## [81] 1.949845e-07 1.122018e-07 8.317638e-08 5.623413e-08 1.698244e-08
## [86] 1.513561e-08 1.584893e-08 3.890451e-09 3.715352e-09 3.467369e-09
## [91] 2.511886e-09 2.398833e-09 9.549926e-10 9.332543e-10 8.912509e-10
## [96] 6.309573e-10 5.370318e-10 4.677351e-10 2.754229e-10 2.089296e-10
## [101] 1.479108e-10 1.096478e-10 7.079458e-11plot(Volume,pH,main="Volume of NaOH vs. pH In Diprotic Titration",xlab = "Volume of NaOH (mL)",ylab="pH")
#Analysis of Diprotic Acid Titration Curve: When looking at the curve we see a much steeper curve than the monoprotic acid. We see that there are two equivalence points in the diprotic titration. This indicats that there was two hydrogens that were ionized. The first equivalence point is near 4 while the second equivalence point is at around 8.
Diprotic Acid Binding Curve Information
Vinital <- 25.00
Vadd <- Volume
Vend <- 15.8/2
CB <- 0.100
FB <- 2 -(CB * Vadd + H * (Vinital + Vadd)) / (CB * Vend)
FB## [1] 1.770748114 1.770069352 1.769390590 1.767625810 1.768647169
## [6] 1.758074766 1.741723676 1.724528340 1.711611987 1.702170940
## [11] 1.683643426 1.664870158 1.653093222 1.640226774 1.626357721
## [16] 1.611566110 1.595925666 1.577163433 1.560214080 1.540567134
## [21] 1.522354663 1.503686494 1.482877068 1.463306090 1.444621044
## [26] 1.425258473 1.406351199 1.381770042 1.361069370 1.340719787
## [31] 1.320465424 1.298264193 1.278395293 1.252936473 1.232005726
## [36] 1.209537316 1.187683909 1.164188457 1.139641089 1.115556806
## [41] 1.093031730 1.073908649 1.049434860 1.024586718 0.999772746
## [46] 0.974867978 0.949794168 0.924635291 0.899537927 0.874270079
## [51] 0.849020534 0.823772147 0.798505902 0.773233444 0.747955539
## [56] 0.722683598 0.697381134 0.672082386 0.646782177 0.621491636
## [61] 0.596187942 0.570873935 0.545577480 0.520275777 0.494972243
## [66] 0.469655294 0.444352045 0.419046893 0.393734577 0.368427200
## [71] 0.343115220 0.317807788 0.292489212 0.267182833 0.241865453
## [76] 0.216556902 0.191243090 0.165807337 0.140491157 0.115181684
## [81] 0.104040766 0.078728471 0.063286896 0.039111042 0.013796594
## [86] 0.010632131 0.002910574 -0.016582480 -0.017974876 -0.021266003
## [91] -0.029367219 -0.033797593 -0.044936759 -0.045949416 -0.048607641
## [96] -0.055063324 -0.057468382 -0.063544328 -0.078607609 -0.087215201
## [101] -0.100632919 -0.121265829 -0.146582282plot(pH,FB,main ="Fraction Bound vs. pH of Diprotic Acid",xlim = c(2,8),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 2.010e-06 6.747e-08 29.79 <2e-16 ***
## KD2 2.016e-03 6.065e-05 33.23 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03835 on 101 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 1.456e-06lines(pH,predict(fit),col="blue")
#Tranforming Diprotic Acid Data into Binding Curve: To transform the data into a binding curve, we first established some parameters. The inital volume ofthe acid was 25 mL, the volume added was the increments of NaOH added into the acid, the end volume was the volume of NaOH needed to complete the titration and was divided by two to show the volume for the frist and second ionization. Once those were established, we used the equation: F = {H}/KD1+{2H^2}/{KD1KD2}}/{1+H/KD1+H^2/{KD1*KD2}}.
#Comparing Traditional Titration Analysis to Binding Curves: Tradiditonal titration analysis allowed up to look at the point individally and find the amount of NaOH it took to get to a specific pH. However, it may be difficult to analyze if your volume was added in very small increments, resulting in many data points you would have to sift through. Binding curves may not let you analyze the exact volume it took to get a certain pH, but it can show you clearly where the equivalence point is even if you have many data points.
#Further Thoughts: I would compare the traditional titration and the binding curve with polyprotic acids, and see which one is overall better for titration analysis. Since polyprotic acid have many ionizable hydrogens, there will be many equivalence points to look for. The comparison between the binding curve and tradtional analysis would show us which one is better fit.