Mono-Diprotic Acid
Sammely Perez
2023-04-19
Monoprotic Acid
A monoprotic acid is an acid that will only donate a proton when it dissociates. In a monoprotic acid, there will only be one equivalent point visible on a titration curve. After titrating a monoprotic acid, data was recorded and used to determine the fractional bound. With the fractional bound of the solution calculated; using the data obtained a binding analysis will demonstrate the relationship between the fractional bound and pH of the solution.
Mydata<-read.csv("Fractional Bound.csv")
Mydata## Vol pH
## 1 0.00 3.17
## 2 1.00 3.47
## 3 3.00 3.90
## 4 4.00 4.06
## 5 5.00 4.18
## 6 6.00 4.27
## 7 7.00 4.37
## 8 8.00 4.47
## 9 8.45 4.49
## 10 9.00 4.54
## 11 9.60 4.61
## 12 10.00 4.64
## 13 11.00 4.71
## 14 12.00 4.80
## 15 13.00 4.88
## 16 14.00 4.97
## 17 14.50 5.03
## 18 14.90 5.06
## 19 15.10 5.08
## 20 15.20 5.08
## 21 15.60 5.12
## 22 16.10 5.19
## 23 16.60 5.25
## 24 17.00 5.32
## 25 17.50 5.40
## 26 18.10 5.50
## 27 18.50 5.59
## 28 19.10 5.74
## 29 19.50 5.86
## 30 20.00 6.39
## 31 21.10 9.55
## 32 21.50 10.51
## 33 22.00 10.89
## 34 25.00 11.50volume<- Mydata$Vol
pH<- Mydata$pH
volume## [1] 0.00 1.00 3.00 4.00 5.00 6.00 7.00 8.00 8.45 9.00 9.60 10.00
## [13] 11.00 12.00 13.00 14.00 14.50 14.90 15.10 15.20 15.60 16.10 16.60 17.00
## [25] 17.50 18.10 18.50 19.10 19.50 20.00 21.10 21.50 22.00 25.00plot(volume,pH,main="volume of NaOH vs. pH of solution",xlab="volume",ylab="pH",xlim=c(0,25),ylim=c(3,12))
H <- 10^(-pH)
tbase <- 0.10
Vini <- 25
Vend <- 21.5
fbound <- 1-(tbase*volume + H*(Vini+Vend))/(tbase*Vend)
fbound## [1] 9.853777e-01 9.461599e-01 8.577423e-01 8.120698e-01 7.660129e-01
## [6] 7.197687e-01 6.734960e-01 6.271741e-01 6.062769e-01 5.807716e-01
## [11] 5.529575e-01 5.343883e-01 4.879504e-01 4.415177e-01 3.950637e-01
## [16] 3.486055e-01 3.253796e-01 3.067884e-01 2.974945e-01 2.928434e-01
## [21] 2.742545e-01 2.510231e-01 2.277854e-01 2.091988e-01 1.859604e-01
## [26] 1.580711e-01 1.394793e-01 1.115886e-01 9.299340e-02 6.975863e-02
## [31] 1.860465e-02 -6.683663e-10 -2.325581e-02 -1.627907e-01plot(pH,fbound,xlim=c(3,11.59),ylim=c(0,1),main="Binding Analysis of Monoprotic Titration")
library(nls2)## Loading required package: protofit <- nls2(fbound ~ H/(KD+H), start=c(KD=0.0001))
summary(fit)##
## Formula: fbound ~ H/(KD + H)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## KD 1.981e-05 6.227e-07 31.82 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0321 on 33 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.253e-06lines(pH,predict(fit), col="green")
# use nls to do best fit and find Ka
Mydata <- read.csv("diprotic1.csv")
Mydata## pH Vol
## 1 2.10 0.000
## 2 2.10 0.005
## 3 2.10 0.010
## 4 2.10 0.023
## 5 2.10 0.054
## 6 2.11 0.132
## 7 2.11 0.328
## 8 2.12 0.528
## 9 2.20 0.728
## 10 2.20 0.928
## 11 2.26 1.128
## 12 2.26 1.328
## 13 2.32 1.528
## 14 2.32 1.728
## 15 2.34 1.928
## 16 2.41 2.128
## 17 2.42 2.328
## 18 2.48 2.528
## 19 2.49 2.728
## 20 2.55 2.928
## 21 2.56 3.129
## 22 2.61 3.329
## 23 2.62 3.529
## 24 2.68 3.729
## 25 2.69 3.929
## 26 2.76 4.129
## 27 2.76 4.329
## 28 2.83 4.529
## 29 2.84 4.729
## 30 2.91 4.929
## 31 2.91 5.129
## 32 2.99 5.329
## 33 3.00 5.529
## 34 3.08 5.729
## 35 3.09 5.929
## 36 3.19 6.129
## 37 3.20 6.329
## 38 3.31 6.529
## 39 3.31 6.729
## 40 3.44 6.929
## 41 3.45 7.129
## 42 3.62 7.329
## 43 3.62 7.529
## 44 3.82 7.729
## 45 3.83 7.877
## 46 4.04 8.078
## 47 4.04 8.222
## 48 4.25 8.422
## 49 4.25 8.568
## 50 4.43 8.768
## 51 4.52 8.968
## 52 4.53 9.168
## 53 4.68 9.368
## 54 4.70 9.568
## 55 4.81 9.768
## 56 4.83 9.968
## 57 4.92 10.168
## 58 4.98 10.369
## 59 4.98 10.569
## 60 5.07 10.769
## 61 5.08 10.969
## 62 5.16 11.169
## 63 5.17 11.369
## 64 5.25 11.569
## 65 5.26 11.769
## 66 5.27 11.969
## 67 5.37 12.169
## 68 5.38 12.369
## 69 5.46 12.569
## 70 5.47 12.769
## 71 5.53 12.969
## 72 5.55 13.169
## 73 5.63 13.369
## 74 5.64 13.569
## 75 5.71 13.769
## 76 5.72 13.969
## 77 5.74 14.169
## 78 5.87 14.369
## 79 5.87 14.569
## 80 5.97 14.769
## 81 5.99 14.969
## 82 6.09 15.169
## 83 6.10 15.369
## 84 6.23 15.569
## 85 6.31 15.769
## 86 6.32 15.969
## 87 6.51 16.169
## 88 6.52 16.346
## 89 6.76 16.546
## 90 6.77 16.656
## 91 7.07 16.856
## 92 7.08 16.928
## 93 7.39 17.110
## 94 7.42 17.164
## 95 7.60 17.300
## 96 7.61 17.390
## 97 8.30 17.590volume <- Mydata$Vol ## Volume vector
pH <- Mydata$pH ## pH vector
plot(volume,pH,main="Volume of NaOH vs. pH of Solution",xlab="Volume (mL)",
ylab="pH")
H <- 10^-(pH) ## H+ from pH
Vini <- 25 ## Initial Volume
Vend <- 9.3025 ## Volume added in endpoint
tbase <- 0.10 ## [Base]
Fb <-(2-(((volume*tbase)+((H)*(Vini+volume)))/(Vend*tbase)))
library(nls2)
fit <- nls2(Fb~(H/KD1+2*H^2/(KD1*KD2))/(1+H/KD1+H^2/(KD1*KD2))
,start = c(KD1=0.001,KD2=0.000001))
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 1.608e-06 8.373e-08 19.21 <2e-16 ***
## KD2 1.809e-03 8.166e-05 22.16 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.05993 on 95 degrees of freedom
##
## Number of iterations to convergence: 16
## Achieved convergence tolerance: 2.495e-06plot(pH,Fb)
Diprotic Acid Titration
In a diprotic acid, there will be two protons that will be dissociate and when titrated there will be two equivalent points as a result of being titrated with a strong base; sodium hydroxide. The unknown acid undergoes deprotonation twice and demonstrates two stages of dissociation.
Mydata <- read.csv("diprotic1.csv")
Mydata## pH Vol
## 1 2.10 0.000
## 2 2.10 0.005
## 3 2.10 0.010
## 4 2.10 0.023
## 5 2.10 0.054
## 6 2.11 0.132
## 7 2.11 0.328
## 8 2.12 0.528
## 9 2.20 0.728
## 10 2.20 0.928
## 11 2.26 1.128
## 12 2.26 1.328
## 13 2.32 1.528
## 14 2.32 1.728
## 15 2.34 1.928
## 16 2.41 2.128
## 17 2.42 2.328
## 18 2.48 2.528
## 19 2.49 2.728
## 20 2.55 2.928
## 21 2.56 3.129
## 22 2.61 3.329
## 23 2.62 3.529
## 24 2.68 3.729
## 25 2.69 3.929
## 26 2.76 4.129
## 27 2.76 4.329
## 28 2.83 4.529
## 29 2.84 4.729
## 30 2.91 4.929
## 31 2.91 5.129
## 32 2.99 5.329
## 33 3.00 5.529
## 34 3.08 5.729
## 35 3.09 5.929
## 36 3.19 6.129
## 37 3.20 6.329
## 38 3.31 6.529
## 39 3.31 6.729
## 40 3.44 6.929
## 41 3.45 7.129
## 42 3.62 7.329
## 43 3.62 7.529
## 44 3.82 7.729
## 45 3.83 7.877
## 46 4.04 8.078
## 47 4.04 8.222
## 48 4.25 8.422
## 49 4.25 8.568
## 50 4.43 8.768
## 51 4.52 8.968
## 52 4.53 9.168
## 53 4.68 9.368
## 54 4.70 9.568
## 55 4.81 9.768
## 56 4.83 9.968
## 57 4.92 10.168
## 58 4.98 10.369
## 59 4.98 10.569
## 60 5.07 10.769
## 61 5.08 10.969
## 62 5.16 11.169
## 63 5.17 11.369
## 64 5.25 11.569
## 65 5.26 11.769
## 66 5.27 11.969
## 67 5.37 12.169
## 68 5.38 12.369
## 69 5.46 12.569
## 70 5.47 12.769
## 71 5.53 12.969
## 72 5.55 13.169
## 73 5.63 13.369
## 74 5.64 13.569
## 75 5.71 13.769
## 76 5.72 13.969
## 77 5.74 14.169
## 78 5.87 14.369
## 79 5.87 14.569
## 80 5.97 14.769
## 81 5.99 14.969
## 82 6.09 15.169
## 83 6.10 15.369
## 84 6.23 15.569
## 85 6.31 15.769
## 86 6.32 15.969
## 87 6.51 16.169
## 88 6.52 16.346
## 89 6.76 16.546
## 90 6.77 16.656
## 91 7.07 16.856
## 92 7.08 16.928
## 93 7.39 17.110
## 94 7.42 17.164
## 95 7.60 17.300
## 96 7.61 17.390
## 97 8.30 17.590volume <- Mydata$Vol ## Volume vector
pH <- Mydata$pH ## pH vector
plot(volume,pH,main="Volume of NaOH vs. pH of Solution",xlab="Volume (mL)",
ylab="pH")
H <- 10^-(pH) ## H+ from pH
Vini <- 25 ## Initial Volume
Vend <- 9.3025 ## Volume added in endpoint
tbase <- 0.10 ## [Base]
Fb <- (2-(((volume*tbase)+((H)*(Vini+volume)))/(Vend*tbase)))
library(nls2)
fit <- nls2(Fb~(H/KD1+2*H^2/(KD1*KD2))/(1+H/KD1+H^2/(KD1*KD2))
,start = c(KD1=0.001,KD2=0.000001))
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 1.608e-06 8.373e-08 19.21 <2e-16 ***
## KD2 1.809e-03 8.166e-05 22.16 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.05993 on 95 degrees of freedom
##
## Number of iterations to convergence: 16
## Achieved convergence tolerance: 2.495e-06plot(pH,Fb)
lines(pH,Fb,col="maroon")
Using the data, to graph the relationship between the increasing volume of NaOH and the pH of the solution. Calculating the fractional bound to make a graph that demonstrates the relationship between the fractional bound and pH of the solution. The graph displays a very good fit. Viewing this graph, the two equivalence points present are a great indicator that the acid used is a diprotic acid. When the solution has a pH of 4, one of the protons from the diprotic acid has dissociated and at pH 8, the second proton has dissociated. With the use of R, the KD values were concluded to be 0.001 and 0.000001. From the values it can be inferred that the acid has successfully dissociated.