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#' Titration Curve for Triprotic Weak Acid
#'
#' This function calculates and plots the titration curve for a
#' triprotic weak acid analyte using a monoprotic strong base as
#' the titrant. The calculation uses a single master equation
#' that finds the volume of titrant needed to achieve a fixed pH,
#' as outlined in R. de Levie's \emph{Principles of Quantitative
#' Chemical Analysis} (McGraw-Hill, 1997).
#'
#' @param conc.acid Molar concentration of the triprotic weak acid
#' analyte; defaults to 0.10 M.
#'
#' @param conc.base Molar concentration of the strong base titrant;
#' defaults to 0.10 M.
#'
#' @param pka1 The pKa1 value for the triprotic weak acid analyte;
#' defaults to a pKa1 of 4.
#'
#' @param pka2 The pKa2 value for the triprotic weak acid analyte;
#' defaults to a pKa2 of 7.
#'
#' @param pka3 The pKa3 value for the triprotic weak acid analyte;
#' defaults to a pKa3 of 10.
#'
#' @param pkw The pKw (or pKs) value for the solvent; defaults to water
#' as a solvent with a pKw of 14.
#'
#' @param vol.acid The initial volume, in mL, of the solution that
#' contains the weak acid analyte; defaults to 50.00 mL.
#'
#' @param plot Logical; if TRUE, plots the titration curve.
#'
#' @param eqpt Logical; if TRUE, draws a vertical line at the titration
#' curve's equivalence point.
#'
#' @param overlay Logical; if TRUE, adds the current titration curve
#' to the existing titration curve.
#'
#' @param \dots Additional arguments to pass to \code{plot()} function.
#'
#' @return A two-column data frame that contains the volume of titrant
#' in the first column and the solution's pH in the second column. Also
#' produces a plot of the titration curve with options to display the
#' equivalence point and to overlay titration curves.
#'
#' @author David T. Harvey, DePauw University. \email{harvey@@depauw.edu}
#'
#' @export
#'
#' @importFrom graphics plot lines
#'
#' @examples
#' ### Simple titration curve with equivalence points
#' ex7 = triwa_sb(eqpt = TRUE)
#' head(ex7)
#'
#' ### Overlay titration curves using different pKa1 and pKa2 values
#' triwa_sb(pka1 = 4, pka2 = 7, pka3 = 10, eqpt = TRUE)
#' triwa_sb(pka1 = 3, pka2 = 7, pka3 = 11, overlay = TRUE)
#' triwa_sb(pka1 = 5, pka2 = 7, pka3 = 9, overlay = TRUE)
triwa_sb = function(conc.acid = 0.1, conc.base = 0.1, pka1 = 4,
pka2 = 7, pka3 = 10, pkw = 14, vol.acid = 50,
plot = TRUE, eqpt = FALSE, overlay = FALSE, ...) {
veq1 = conc.acid * vol.acid/conc.base
ka1 = 10^-pka1
ka2 = 10^-pka2
ka3 = 10^-pka3
kw = 10^-pkw
ph = seq(1, pkw, 0.01)
h = 10^-ph
oh = kw/h
delta = h - oh
alpha1 = (ka1 * h^2)/
(ka1 * ka2 * ka3 + ka1 * ka2 * h + ka1 * h^2 + h^3)
alpha2 = (ka1 * ka2 * h)/
(ka1 * ka2 * ka3 + ka1 * ka2 * h + ka1 * h^2 + h^3)
alpha3 = (ka1 * ka2 * ka3)/
(ka1 * ka2 * ka3 + ka1 * ka2 * h + ka1 * h^2 + h^3)
volume = vol.acid *
(conc.acid * alpha1 + 2 * conc.acid * alpha2 + 3 *
conc.acid * alpha3 - delta)/(conc.base + delta)
df = data.frame(volume, ph)
df = df[df$volume > 0 & df$volume < 6 * veq1, ]
rownames(df) = 1:nrow(df)
if (plot == TRUE) {
if (overlay == FALSE) {
plot(df$volume, df$ph, type = "l", lwd = 2,
xlim = c(0, 1.5 * (3 * veq1)), ylim = c(0, pkw),
xlab = "volume of strong base (mL)", ylab = "pH",
xaxs = "i", yaxs = "i", ...)
} else {
lines(df$volume, df$ph, type = "l", lwd = 2, ...)
}
if (eqpt == TRUE) {
x1 = c(veq1, veq1)
x2 = c(2 * veq1, 2 * veq1)
x3 = c(3 * veq1, 3 * veq1)
y = c(0, pkw + 1)
lines(x1, y, type = "l", lty = 2, col = "red")
lines(x2, y, type = "l", lty = 2, col = "red")
lines(x3, y, type = "l", lty = 2, col = "red")
}
}
invisible(df)
}
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