Abstract

Monoprotic Acid

\(F = \frac {H}{H+KD}\)

Mydata <- read.csv("Titration.csv")
Mydata
##    Volume..ml...measured. pH..measured.
## 1                     0.0         3.130
## 2                     1.0         3.579
## 3                     2.0         3.757
## 4                     3.0         3.909
## 5                     4.0         4.032
## 6                     5.0         4.032
## 7                     6.0         4.150
## 8                     7.0         4.257
## 9                     8.0         4.355
## 10                    9.0         4.445
## 11                   10.0         4.505
## 12                   11.0         4.628
## 13                   12.0         4.710
## 14                   13.0         4.813
## 15                   14.0         4.914
## 16                   15.0         5.033
## 17                   16.0         5.165
## 18                   16.5         5.293
## 19                   17.0         5.354
## 20                   17.5         5.436
## 21                   18.0         5.556
## 22                   18.5         5.715
## 23                   19.0         5.928
## 24                   19.5         6.255
## 25                   20.0         7.019
## 26                   20.5         9.452
Volume <- Mydata$Vol   #volume Vector
Volume
##  [1]  0.0  1.0  2.0  3.0  4.0  5.0  6.0  7.0  8.0  9.0 10.0 11.0 12.0 13.0 14.0
## [16] 15.0 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5
pH <- Mydata$pH     #pH Vector  
pH
##  [1] 3.130 3.579 3.757 3.909 4.032 4.032 4.150 4.257 4.355 4.445 4.505 4.628
## [13] 4.710 4.813 4.914 5.033 5.165 5.293 5.354 5.436 5.556 5.715 5.928 6.255
## [25] 7.019 9.452
plot(Volume,pH,main = "Volume of NaoH vs. pH of Solution",xlab = "volume (mL)", ylab = "pH")

H <- 10^-(pH)  # H+ from pH
H
##  [1] 7.413102e-04 2.636331e-04 1.749847e-04 1.233105e-04 9.289664e-05
##  [6] 9.289664e-05 7.079458e-05 5.533501e-05 4.415704e-05 3.589219e-05
## [11] 3.126079e-05 2.355049e-05 1.949845e-05 1.538155e-05 1.218990e-05
## [16] 9.268298e-06 6.839116e-06 5.093309e-06 4.425884e-06 3.664376e-06
## [21] 2.779713e-06 1.927525e-06 1.180321e-06 5.559043e-07 9.571941e-08
## [26] 3.531832e-10
#volume added at the endpoint:
VE <- 20.5

#initial volume of unknown acid:
VI <- 20

#concentration of base NaOH:
CB <- 0.0954

# fraction bound for each data point
F <- (1-(((Volume*CB)+ ((H)*(VI+Volume)))/(VE*CB)))
F
##  [1]  9.924190e-01  9.483887e-01  9.004706e-01  8.522083e-01  8.037380e-01
##  [6]  7.549100e-01  7.063759e-01  6.577726e-01  6.091239e-01  5.604434e-01
## [11]  5.117156e-01  4.630413e-01  4.143151e-01  3.655941e-01  3.168612e-01
## [16]  2.681268e-01  2.193863e-01  1.950269e-01  1.706480e-01  1.462712e-01
## [21]  1.218972e-01  9.752303e-02  7.314719e-02  4.876926e-02  2.438829e-02
## [26] -7.313963e-09
library(nls2)
## Loading required package: proto
fit <- nls(F ~ H/(KD+H), start=c(KD=0.0001))
fit
## Nonlinear regression model
##   model: F ~ H/(KD + H)
##    data: parent.frame()
##        KD 
## 2.627e-05 
##  residual sum-of-squares: 0.01417
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.467e-07
plot(pH,F)

lines(pH,F,col="blue")

length(pH)
## [1] 26
length(F)
## [1] 26
length(H)
## [1] 26