Tritration of A Monoprotic Acid

The potentiometric titration of an unknown vinegar solution (acetic acid) data points were recorded and formatted into graph in order to analyze the data. The unknown vinegar solution is a monoprotic acid that was titrated with a sodium hydroxide (NaOH) 0.1 M solution.

The data obtained from the titration of the unknown vinegar solution. Vinergar contains acetic acid which is the acid that will be titrated with NaOH. Acetic acid is a monoprotic acid meaning that it can only be deprotonated once by a strong base. Therefore, due to only having one proton available to donate, the titration curve of acetic acid/ unknown vinegar solution will have a single equivalence point. This is shown in the Titration Curve (Trial 2) of Acetic Acid graph.

The fractional bound of the solution was also determined using the equation and data given. By determining the fractional bound, a graph of the binding analysis of this monoprotic titration can be determined which is shown in Binding Curve (Trial 2) graph. The fit of the binding curve as the titration went one determined by using the tryfit command on R programming. The Acid/Base Binding graph shows the tryfit curve obtained with the data and there appears to be a strong correlation between the fractional amount of acid left compared to the pH of the solution.

#monoprotic trial 2
Trial2 <- read.csv ("Trial 2- titration of vinegar.csv")
Trial2 
##     NaOH    pH
## 1   0.00  3.89
## 2   5.00  5.05
## 3  10.00  5.50
## 4  15.00  5.98
## 5  16.00  6.13
## 6  17.00  6.30
## 7  18.00  6.55
## 8  19.00  6.96
## 9  19.50  7.61
## 10 19.75  8.27
## 11 20.00 10.72
## 12 21.00 11.91
## 13 22.00 12.24
volume <- Trial2$NaOH
pH <- Trial2$pH
volume
##  [1]  0.00  5.00 10.00 15.00 16.00 17.00 18.00 19.00 19.50 19.75 20.00 21.00
## [13] 22.00
pH
##  [1]  3.89  5.05  5.50  5.98  6.13  6.30  6.55  6.96  7.61  8.27 10.72 11.91
## [13] 12.24
plot (volume, pH, main = "Titration Curve (T2) of Acetic Acid", xlab = "Volume of NaOH Added (mL)", ylab = "pH")

H <- 10^-pH
#H+
CB <- 0.1
#Base concentration
IV <- 25 
#inital volume
VE <- 20 
#volume of endpoint
fB = 1 - (CB*volume + H*(IV+volume))/(CB*VE)
fB
##  [1]  9.983897e-01  7.498663e-01  4.999447e-01  2.499791e-01  1.999848e-01
##  [6]  1.499895e-01  9.999394e-02  4.999759e-02  2.499945e-02  1.249988e-02
## [11] -4.287286e-10 -5.000000e-02 -1.000000e-01
plot (pH, fB, main = "Binding Curve (T2)")

tryfit <- nls(fB ~ H/ (KD+H), 
              start = c(KD = 0.0001))
summary(tryfit)
## 
## Formula: fB ~ H/(KD + H)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## KD 3.022e-06  2.421e-07   12.48 3.12e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.03423 on 12 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.619e-06
plot (pH,fB, main = "Acid/Base Binding", xlab = "pH",
      ylab = "Fractional Binding")
lines(pH,predict(tryfit), col = "blue")

Titration of Diprotic Acid

The titration of an unknown diprotic acid is done using a strong base, sodium hydroxide. Diprotic acids have 2 protons that can be released when in a solution basic enough to do so. This means that there will be two equivalence points on the titration curve graph. Therefore, there will two Ka values at two different volume on the titration curve as well. The titration curve of the diprotic acid is shown in Titration Curve (Trial 1).

The fraction bound of the titration of the diprotic acid was also found and shown in Binding Curve (Trial 1) graph compared to pH. By using the tryfit function, the fraction bound of the diprotic acid vs. pH the fraction bound displayed a good fit when compared to pH increase of the solution. Viewing these graphs, the two equivalence points can be seen meaning that there was a titration of a diprotic acid. The frist titration of the first proton of the diprotic acid is seen around a pH of 4 where the decrease in the acid in the solution slows down. The second titration of the second proton is at the pH of 8 where another decrease in acid slows down again.

#diprotic trial 1
Trial1 <- read.csv ("Trial 1 Data Points Diprotic.csv")
Trial1 
##       pH    vol
## 1   1.51  0.000
## 2   1.51  0.005
## 3   1.51  0.010
## 4   1.51  0.023
## 5   1.51  0.054
## 6   1.51  0.132
## 7   1.52  0.328
## 8   1.55  0.528
## 9   1.58  0.728
## 10  1.60  0.928
## 11  1.61  1.128
## 12  1.63  1.328
## 13  1.66  1.528
## 14  1.67  1.728
## 15  1.69  1.928
## 16  1.71  2.128
## 17  1.73  2.328
## 18  1.74  2.528
## 19  1.75  2.728
## 20  1.77  2.928
## 21  1.78  3.129
## 22  1.79  3.329
## 23  1.81  3.529
## 24  1.82  3.729
## 25  1.83  3.929
## 26  1.88  4.129
## 27  1.90  4.329
## 28  1.91  4.529
## 29  1.93  4.729
## 30  1.97  4.929
## 31  1.98  5.129
## 32  2.00  5.329
## 33  2.04  5.529
## 34  2.09  5.729
## 35  2.10  5.929
## 36  2.13  6.129
## 37  2.15  6.329
## 38  2.18  6.529
## 39  2.22  6.729
## 40  2.27  6.929
## 41  2.32  7.129
## 42  2.36  7.329
## 43  2.42  7.529
## 44  2.46  7.729
## 45  2.53  7.929
## 46  2.58  8.129
## 47  2.71  8.329
## 48  2.81  8.529
## 49  2.88  8.729
## 50  2.97  8.929
## 51  2.99  9.129
## 52  3.06  9.329
## 53  3.12  9.529
## 54  3.17  9.730
## 55  3.24  9.930
## 56  3.29 10.130
## 57  3.33 10.330
## 58  3.43 10.530
## 59  3.46 10.730
## 60  3.51 10.930
## 61  3.56 11.130
## 62  3.62 11.330
## 63  3.64 11.530
## 64  3.70 11.730
## 65  3.75 11.930
## 66  3.81 12.130
## 67  3.82 12.330
## 68  3.88 12.530
## 69  3.91 12.730
## 70  3.96 12.930
## 71  4.00 13.130
## 72  4.07 13.330
## 73  4.13 13.530
## 74  4.17 13.730
## 75  4.21 13.930
## 76  4.24 14.130
## 77  4.31 14.330
## 78  4.37 14.530
## 79  4.38 14.730
## 80  4.41 14.930
## 81  4.49 15.130
## 82  4.55 15.330
## 83  4.64 15.530
## 84  4.72 15.730
## 85  4.79 15.930
## 86  4.86 16.130
## 87  4.96 16.330
## 88  5.07 16.531
## 89  5.16 16.731
## 90  5.31 16.931
## 91  5.42 17.131
## 92  5.53 17.331
## 93  5.59 17.531
## 94  5.75 17.731
## 95  5.86 17.931
## 96  5.95 18.131
## 97  6.24 18.331
## 98  6.34 18.413
## 99  6.42 18.575
## 100 6.73 18.775
## 101 6.89 18.845
## 102 7.14 18.895
## 103 7.36 18.912
## 104 7.57 18.918
## 105 7.63 18.923
## 106 7.66 18.936
## 107 7.72 18.967
## 108 7.97 19.045
## 109 8.03 19.082
## 110 8.28 19.173
## 111 8.45 19.208
## 112 8.47 19.230
## 113 8.75 19.285
## 114 8.93 19.293
## 115 8.95 19.298
## 116 8.98 19.310
## 117 9.00 19.342
## 118 9.03 19.421
## 119 9.08 19.618
## 120 9.14 19.818
## 121 9.59 20.018
volume <- Trial1$vol
pH <- Trial1$pH
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  7.329  7.529  7.729  7.929  8.129  8.329  8.529  8.729  8.929
##  [51]  9.129  9.329  9.529  9.730  9.930 10.130 10.330 10.530 10.730 10.930
##  [61] 11.130 11.330 11.530 11.730 11.930 12.130 12.330 12.530 12.730 12.930
##  [71] 13.130 13.330 13.530 13.730 13.930 14.130 14.330 14.530 14.730 14.930
##  [81] 15.130 15.330 15.530 15.730 15.930 16.130 16.330 16.531 16.731 16.931
##  [91] 17.131 17.331 17.531 17.731 17.931 18.131 18.331 18.413 18.575 18.775
## [101] 18.845 18.895 18.912 18.918 18.923 18.936 18.967 19.045 19.082 19.173
## [111] 19.208 19.230 19.285 19.293 19.298 19.310 19.342 19.421 19.618 19.818
## [121] 20.018
pH
##   [1] 1.51 1.51 1.51 1.51 1.51 1.51 1.52 1.55 1.58 1.60 1.61 1.63 1.66 1.67 1.69
##  [16] 1.71 1.73 1.74 1.75 1.77 1.78 1.79 1.81 1.82 1.83 1.88 1.90 1.91 1.93 1.97
##  [31] 1.98 2.00 2.04 2.09 2.10 2.13 2.15 2.18 2.22 2.27 2.32 2.36 2.42 2.46 2.53
##  [46] 2.58 2.71 2.81 2.88 2.97 2.99 3.06 3.12 3.17 3.24 3.29 3.33 3.43 3.46 3.51
##  [61] 3.56 3.62 3.64 3.70 3.75 3.81 3.82 3.88 3.91 3.96 4.00 4.07 4.13 4.17 4.21
##  [76] 4.24 4.31 4.37 4.38 4.41 4.49 4.55 4.64 4.72 4.79 4.86 4.96 5.07 5.16 5.31
##  [91] 5.42 5.53 5.59 5.75 5.86 5.95 6.24 6.34 6.42 6.73 6.89 7.14 7.36 7.57 7.63
## [106] 7.66 7.72 7.97 8.03 8.28 8.45 8.47 8.75 8.93 8.95 8.98 9.00 9.03 9.08 9.14
## [121] 9.59
plot (volume, pH, main = "Titration Curve T1", xlab = "Volume of NaOH Added (mL)", ylab = "pH")

H <- 10^-pH
#H+
CB <- 0.1
#Base concentration
IV <- 25 
#inital volume
VE <- 19.293
#volume of endpoint
VA <- volume
f = (2-(((VA*CB)+((H)*(IV+VA)))/(VE*CB)))
f
##   [1] 1.5995574 1.5992182 1.5988789 1.5979969 1.5958935 1.5906012 1.5865374
##   [8] 1.5997114 1.6115092 1.6143254 1.6090985 1.6112639 1.6199816 1.6142464
##  [15] 1.6150940 1.6155321 1.6155750 1.6093260 1.6030263 1.6024022 1.5958507
##  [22] 1.5893108 1.5880569 1.5813347 1.5745652 1.5869512 1.5842377 1.5769522
##  [29] 1.5738427 1.5782952 1.5706270 1.5665837 1.5691039 1.5735890 1.5653461
##  [36] 1.5627106 1.5569936 1.5536153 1.5521245 1.5519780 1.5507806 1.5469750
##  [43] 1.5456529 1.5405673 1.5386511 1.5334898 1.5346051 1.5310059 1.5245097
##  [50] 1.5183457 1.5087213 1.5009593 1.4925139 1.4835016 1.4748872 1.4656006
##  [57] 1.4560073 1.4473640 1.4374183 1.4277181 1.4179490 1.4082232 1.3980363
##  [64] 1.3882089 1.3782371 1.3682938 1.3579795 1.3479773 1.3377692 1.3276531
##  [71] 1.3174659 1.3073848 1.2972289 1.2869857 1.2767323 1.2664429 1.2562451
##  [78] 1.2460031 1.2356522 1.2253390 1.2151047 1.2048221 1.1945636 1.1842761
##  [85] 1.1739679 1.1636512 1.1533441 1.1429775 1.1326446 1.1223214 1.1119783
##  [92] 1.1016302 1.0912718 1.0809226 1.0705648 1.0602040 1.0498497 1.0456021
##  [99] 1.0372070 1.0268449 1.0232179 1.0206276 1.0197471 1.0194365 1.0191774
## [106] 1.0185036 1.0168969 1.0128542 1.0109364 1.0062198 1.0044057 1.0032654
## [113] 1.0004146 1.0000000 0.9997408 0.9991188 0.9974602 0.9933654 0.9831545
## [120] 0.9727880 0.9624216
plot (pH, f, main = "Binding Curve (T1)")

library(nls2)
## Loading required package: proto
tryfit <- nls2(f ~ (H/KD1 + 2*H^2/(KD1*KD2))/(1+H/KD1+H^2/(KD1*KD2)),
               start = c(KD1 = 0.0001,KD2 = 0.01))

tryfit
## Nonlinear regression model
##   model: f ~ (H/KD1 + 2 * H^2/(KD1 * KD2))/(1 + H/KD1 + H^2/(KD1 * KD2))
##    data: parent.frame()
##       KD1       KD2 
## 8.787e-12 5.769e-03 
##  residual sum-of-squares: 5.232
## 
## Number of iterations to convergence: 20 
## Achieved convergence tolerance: 8.611e-06
plot(pH,f)
lines(pH,f,col = "blue")

knitr::opts_chunk$set(echo = TRUE)