Summary of lab

In order to identify an unknown diprotic acid sample, an autotitrator was used to determine the equivalence points, molar mass, and acid dissociation constants of the acid. The unknown acid one was titrated with a 0.1000 M standard NaOH solution at 24 celsius. The pKa1 was determined by pH at the volume of the half equivalence point one and pka2 was determined by finding the pH at the volume at (VNaOH at 1st EQP + VNaOH at 2nd EQP)/2. The Ka1 and Ka2 was then determined by taking 10 to the negative pKa1 and 10 to the negative pKa2 respectively.

Titration graph

data <- read.csv("autotitration 2.csv")

VolVect <- data$mL
VolVect
##  [1]  0.000  0.005  0.010  0.023  0.054  0.132  0.328  0.528  0.728  0.928
## [11]  1.128  1.328  1.528  1.728  1.928  2.128  2.328  2.528  2.728  2.928
## [21]  3.129  3.329  3.529  3.729  3.929  4.129  4.329  4.529  4.729  4.929
## [31]  5.129  5.329  5.529  5.729  5.929  6.129  6.329  6.529  6.729  6.929
## [41]  7.129  7.329  7.529  7.729  7.929  8.129  8.329  8.529  8.729  8.929
## [51]  9.129  9.329  9.529  9.730  9.930 10.130 10.330 10.530 10.730 10.930
## [61] 11.130 11.276 11.476 11.676 11.876 12.076 12.276 12.309 12.314 12.327
## [71] 12.358 12.437 12.634 12.714 12.914 12.931 12.972 12.977 12.990 13.021
## [81] 13.026 13.039 13.044 13.056 13.088 13.093 13.100 13.119 13.124 13.137
## [91] 13.142 13.154 13.159 13.172 13.203
pHVect <- data$pH
pHVect
##  [1]  1.48  1.47  1.47  1.47  1.47  1.46  1.46  1.47  1.47  1.48  1.49  1.50
## [13]  1.51  1.52  1.54  1.55  1.56  1.58  1.60  1.62  1.65  1.67  1.73  1.76
## [25]  1.80  1.83  1.90  1.94  1.99  2.04  2.07  2.14  2.21  2.30  2.36  2.45
## [37]  2.60  2.66  2.73  2.86  2.97  3.02  3.14  3.23  3.28  3.35  3.40  3.48
## [49]  3.56  3.60  3.68  3.75  3.80  3.88  3.91  3.97  4.05  4.10  4.16  4.22
## [61]  4.44  4.34  4.42  4.52  4.61  4.72  5.18  4.87  4.86  4.86  4.87  4.89
## [73]  5.18  5.18  5.83  5.83  6.11  6.12  6.12  6.63  6.64  6.92  6.93  6.93
## [85]  8.77  8.96  8.97  9.56  9.57  9.78  9.80  9.96  9.97  9.98 10.36
plot(VolVect, pHVect, xlab= 'Volume (mL)', ylab= 'pH', main = "Titration curve" )

Hcon <- 10 ^(-pHVect)
Hcon
##  [1] 3.311311e-02 3.388442e-02 3.388442e-02 3.388442e-02 3.388442e-02
##  [6] 3.467369e-02 3.467369e-02 3.388442e-02 3.388442e-02 3.311311e-02
## [11] 3.235937e-02 3.162278e-02 3.090295e-02 3.019952e-02 2.884032e-02
## [16] 2.818383e-02 2.754229e-02 2.630268e-02 2.511886e-02 2.398833e-02
## [21] 2.238721e-02 2.137962e-02 1.862087e-02 1.737801e-02 1.584893e-02
## [26] 1.479108e-02 1.258925e-02 1.148154e-02 1.023293e-02 9.120108e-03
## [31] 8.511380e-03 7.244360e-03 6.165950e-03 5.011872e-03 4.365158e-03
## [36] 3.548134e-03 2.511886e-03 2.187762e-03 1.862087e-03 1.380384e-03
## [41] 1.071519e-03 9.549926e-04 7.244360e-04 5.888437e-04 5.248075e-04
## [46] 4.466836e-04 3.981072e-04 3.311311e-04 2.754229e-04 2.511886e-04
## [51] 2.089296e-04 1.778279e-04 1.584893e-04 1.318257e-04 1.230269e-04
## [56] 1.071519e-04 8.912509e-05 7.943282e-05 6.918310e-05 6.025596e-05
## [61] 3.630781e-05 4.570882e-05 3.801894e-05 3.019952e-05 2.454709e-05
## [66] 1.905461e-05 6.606934e-06 1.348963e-05 1.380384e-05 1.380384e-05
## [71] 1.348963e-05 1.288250e-05 6.606934e-06 6.606934e-06 1.479108e-06
## [76] 1.479108e-06 7.762471e-07 7.585776e-07 7.585776e-07 2.344229e-07
## [81] 2.290868e-07 1.202264e-07 1.174898e-07 1.174898e-07 1.698244e-09
## [86] 1.096478e-09 1.071519e-09 2.754229e-10 2.691535e-10 1.659587e-10
## [91] 1.584893e-10 1.096478e-10 1.071519e-10 1.047129e-10 4.365158e-11

Transforming diprotic data: Fraction bound curve formula

\(F=2- \frac {(volume \cdot Cbase) + (Hconc \cdot (Vi + Volume))} {Vend \cdot Cbase}\)

Where: F is the fraction bound

Cbase is the concentration of NaOH

Hconc is the concentration of H+ ions

Vi is the inital volume

Vend is the volume added to the first endpoint

Vend <- 6.729
  
Vi <- 0.00
Vi
## [1] 0
Cbase <- 0.1
Cbase
## [1] 0.1
Fbound <- 2 - (Cbase * VolVect + Hcon * (Vi + VolVect)) / (Cbase * Vend) 
Fbound 
##  [1] 2.00000000 1.99900517 1.99801034 1.99542378 1.98925582 1.97358162
##  [7] 1.93435433 1.89494580 1.85515254 1.81642299 1.77812251 1.74023622
## [13] 1.70274972 1.66564903 1.63084540 1.59462745 1.55874804 1.52549684
## [19] 1.49275634 1.46048770 1.43089674 1.39950549 1.37789708 1.34952802
## [25] 1.32356895 1.29562731 1.27567413 1.24966581 1.22530610 1.20069399
## [31] 1.17290107 1.15068332 1.12766899 1.10593994 1.08042648 1.05684870
## [37] 1.03581850 1.00849473 0.98137913 0.95606378 0.92920365 0.90043225
## [43] 0.87300598 0.84462599 0.81548343 0.78654913 0.75729553 0.72830403
## [49] 0.69920617 0.66972379 0.64050034 0.61114734 0.58164624 0.55211374
## [55] 0.52248231 0.49296263 0.46348542 0.43388850 0.40430623 0.37470858
## [61] 0.34536468 0.32350214 0.29389760 0.26429988 0.23466857 0.20503774
## [67] 0.17553707 0.17050670 0.16975779 0.16782559 0.16322380 0.15149321
## [73] 0.12233100 0.11044137 0.08081572 0.07828931 0.07220973 0.07146702
## [79] 0.06953507 0.06493825 0.06419530 0.06226547 0.06152247 0.05973914
## [85] 0.05498585 0.05424281 0.05320254 0.05037895 0.04963590 0.04770396
## [91] 0.04696091 0.04517759 0.04443453 0.04250260 0.03789567
tF <- Fbound

plot (pHVect, tF, xlab = 'pH', ylab= 'Fraction bound', main = "Binding curve")

Nls equation and fitline

\(F= \frac {(Hconc/KD1 +2 \cdot Hconc^2/ (KD1 \cdot KD2))} {(1+ Hconc/KD1 + Hconc^2/ (KD1 \cdot KD2))}\)

Where:

F is the fraction bound

Hconc is the concentration of H+ ions

KD1 is the binding dissociation constant of the first proton

KD2 is the binding dissociation constant for the second proton

plot (pHVect, tF, xlab = 'pH', ylab= 'Fraction bound', main = "Binding curve")

tryfit <- nls(tF ~ (Hcon/KD1+2*Hcon^2/(KD1*KD2))/(1+Hcon/KD1+Hcon^2/(KD1*KD2)), 
                start =c(KD1 = 0.0001, KD2 = 0.01))

summary(tryfit)
## 
## Formula: tF ~ (Hcon/KD1 + 2 * Hcon^2/(KD1 * KD2))/(1 + Hcon/KD1 + Hcon^2/(KD1 * 
##     KD2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## KD1 1.096e-04  1.268e-05   8.647 1.48e-13 ***
## KD2 1.639e-02  1.432e-03  11.445  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1202 on 93 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.49e-06
lines(pHVect, predict (tryfit))

Nls analysis

From the Ka1 and Ka2 found from nls was 1.096e-04 and 1.639e-02 respectively and the Ka1 and Ka2 determined experimentally was 1.905 * 10^-2 and 1.259 * 10^-4 respectively. The Ka1 and Ka2 determined experimentally seem to be flipped around with the nls and I wonder why especially since the value for Ka1 is usually larger than Ka2. The value determined experimentally for Ka1 is raised to the negative two power and Ka2 being raised to the negative four power verse the Ka1 from nls being to the negative four power and Ka2 value is raised to the negative second power.