Added two functions: O2 solubility in water

from empirical fits, and one function that returns water vapour pressure (simply interpolates based on the previously available dataset).

DESCRIPTION

@@ -1,7 +1,7 @@
 Package: common
 Type: Package
 Title: chepec common
-Version: 0.0.0.9007
+Version: 0.0.0.9008
 Description: Commonly used functions and scripts.
 Authors@R: person("Taha", "Ahmed", email = "taha@chepec.se", role = c("aut", "cre"))
 License: GPL-3

NAMESPACE

@@ -8,12 +8,14 @@ export(GenericXtableSetAttributes)
 export(Kelvin2Celsius)
 export(LoadRData2Variable)
 export(LongtableXtableHeader)
+export(OxygenSolubilityWater)
 export(ProvideSampleId)
 export(RefCanonicalName)
 export(SHE2AVS)
 export(SubfigureGenerator)
 export(SubstrateHistory)
 export(TabularXtableHeader)
+export(VapourPressureWater)
 export(as.SHE)
 export(as.degrees)
 export(as.radians)

R/chemistry-tools.R

@@ -16,3 +16,140 @@ molarity2mass <- function(formulamass, volume, molarity) {
    # [g * mol-1] * [liter] * [mole * liter-1] = [g]
    return(mass)
 }
+
+
+
+#' Vapour pressure of water
+#'
+#' Vapour pressure of water as a function of temperature
+#' This function returns the vapour pressure of water at the given
+#' temperature(s) from the common::vapourwater dataset.
+#'
+#' @param temperature numeric vector, in degrees Celsius
+#'
+#' @return vapour pressure of water, in kilopascal
+#' @export
+#'
+#' @examples
+#' \dontrun{
+#' VapourPressureWater(45)
+#' VapourPressureWater(c(20, 25, 45, 60))
+#' }
+VapourPressureWater <- function(temperature) {
+   data <- common::vapourwater
+   # if T outside range in data, warn the user
+   if (any(temperature < min(data$temperature)) | any(temperature > max(data$temperature))) {
+      warning("At least one supplied temperature is outside the data range (",
+           paste(range(data$temperature), collapse=" - "),
+           " Celsius). Returning NAs for those values.")
+   }
+   # The vapourwater dataset only contains data for every degree celsius (or less),
+   # so we use the interpolation function to fill in the rest.
+   # Note that approx(rule = 1) returns NAs for input outside the data range.
+   pressure <-
+      stats::approx(x = data$temperature, y = data$pressure,
+                    method = "linear", rule = 1,
+                    xout = temperature)$y
+   return(pressure)
+}
+
+
+
+#' Oxygen solubility in water
+#'
+#' Oxygen solubility in water  which is in contact with
+#' air saturated with water vapour, as a function of
+#' temperature and at a total pressure of 760 torr.
+#'
+#' Some background: as the temperature of a gasesous solution is raised the
+#' gas is driven off until complete degassing occurs at the boiling point
+#' of the solvent. This variation of solubility with temperature can be
+#' derived from thermodynamic first principles.
+#' But the variation of oxygen solubility in water cannot be represented by a
+#' simple relationship (derived from thermodynamic first principles), and so
+#' more complicated expressions which are fitted to empirical data have
+#' to be used.
+#'
+#' Hitchman, Measurement of Dissolved Oxygen, 1978 reproduce a table by
+#' Battino and Clever (1966) that presents experimental values of the
+#' so-called Bunsen absorption coefficient (this is the volume of gas, at 0 C
+#' and 760 torr, that, at the temperature of measurement, is dissolved in one
+#' volume of the solvent when the partial pressure of the gas is 760 torr)
+#' recorded by eleven research groups up until 1965. The standard error of the
+#'  mean value is never greater +-0.5%. The mean values from this table are
+#' probably accurate enough for most applications.
+#' Hitchman notes that the data in this table can be fitted by two forms of
+#' equations: one form obtained from Henry's law (under the restriction that
+#' the partial pressure of the gas remains constant), and another form by
+#' describing the variation with temperature by fitting a general power series.
+#' The latter approach is used in this function.
+#'
+#' Hitchman chooses to fit a fourth degree polynomial, and found that the
+#' square of the correlation coefficient was 0.999996.
+#'
+#' For more background and detailed derivation of the formula used here,
+#' see section 2.2 (pp. 11) in Hitchman.
+#'
+#' This formula is strictly speaking only valid for 0 < T < 50 celsius.
+#' The function will return values outside this range, but with a warning.
+#'
+#' @param temperature numeric, vector. In degrees Celsius.
+#'
+#' @return a dataframe with the following columns:
+#'     + "temperature" same as the supplied temperature
+#'     + "g/cm-3" oxygen solubility expressed as gram per cubic cm
+#'     + "mg/L" ditto expressed as milligram per litre
+#'     + "mol/L" ditto expressed as moles per litre (molarity)
+#'     + "permoleculewater" number of O2 molecules per molecule of water
+#'    Note: mg/L is equivalent to ppm by weight (since water has approx
+#'    unit density in the temperature range 0-50 Celsius).
+#' @export
+#' @examples
+#' \dontrun{
+#' OxygenSolubilityWater(22)
+#' OxygenSolubilityWater(c(2, 7, 12, 30))
+#' }
+OxygenSolubilityWater <- function(temperature) {
+   if (any(temperature < 0) | any(temperature > 50)) {
+      warning("This function is fitted to data within the range 0 - 50 Celsius. ",
+              "You are now extrapolating.")
+   }
+   # formula weight of oxygen
+   oxygen.fw <- 15.9994 # gram per mole
+   # formula weight of water
+   water.fw <- 18.02
+   # oxygen ratio in dry air (20.95%)
+   oxygen.dryair <- 20.95 / 100
+   # coefficients (from Hitchman)
+   A <-  4.9E1
+   B <- -1.335
+   C <-  2.759E-2
+   D <- -3.235E-4
+   E <-  1.614E-6
+   # conversion factor from Bunsen to g/cm-3
+   conv.factor <- (2 * oxygen.fw) / 22.414E3
+   # Bunsen absorption coefficient, commonly denoted as Greek alpha
+   alpha <-
+      1E-3 * (A + B * temperature + C * temperature^2 +
+                 D * temperature^3 + E * temperature^4)
+   # solubility of oxygen, in gram per cm-3
+   oxygen.solubility <-
+      data.frame(temperature = temperature,
+         grampercm3 =
+           (conv.factor * oxygen.dryair / 760) * alpha *
+           # keep in mind that VapourPressureWater() returns values in kilopascal
+           (760 - pascal2torr(1E3 * common::VapourPressureWater(temperature))),
+        mgperlitre =
+           1E6 * (conv.factor * oxygen.dryair / 760) * alpha *
+           (760 - pascal2torr(1E3 * common::VapourPressureWater(temperature))),
+        molperlitre =
+           1E3 * (conv.factor * oxygen.dryair / 760) * alpha *
+           (760 - pascal2torr(1E3 * common::VapourPressureWater(temperature))) /
+           (2 * oxygen.fw))
+   # Number of O2 molecules per water molecule
+   oxygen.solubility$permoleculewater <-
+      # note: using a water density value that's approx the average in the
+      # temperature range 0 - 50 Celsius
+      ((1E3 * oxygen.solubility$grampercm3) / oxygen.fw) / (995.00 / water.fw)
+   return(oxygen.solubility)
+}

man/OxygenSolubilityWater.Rd

@@ -0,0 +1,65 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/chemistry-tools.R
+\name{OxygenSolubilityWater}
+\alias{OxygenSolubilityWater}
+\title{Oxygen solubility in water}
+\usage{
+OxygenSolubilityWater(temperature)
+}
+\arguments{
+\item{temperature}{numeric, vector. In degrees Celsius.}
+}
+\value{
+a dataframe with the following columns:
+    + "temperature" same as the supplied temperature
+    + "g/cm-3" oxygen solubility expressed as gram per cubic cm
+    + "mg/L" ditto expressed as milligram per litre
+    + "mol/L" ditto expressed as moles per litre (molarity)
+    + "permoleculewater" number of O2 molecules per molecule of water
+   Note: mg/L is equivalent to ppm by weight (since water has approx
+   unit density in the temperature range 0-50 Celsius).
+}
+\description{
+Oxygen solubility in water  which is in contact with
+air saturated with water vapour, as a function of
+temperature and at a total pressure of 760 torr.
+}
+\details{
+Some background: as the temperature of a gasesous solution is raised the
+gas is driven off until complete degassing occurs at the boiling point
+of the solvent. This variation of solubility with temperature can be
+derived from thermodynamic first principles.
+But the variation of oxygen solubility in water cannot be represented by a
+simple relationship (derived from thermodynamic first principles), and so
+more complicated expressions which are fitted to empirical data have
+to be used.
+
+Hitchman, Measurement of Dissolved Oxygen, 1978 reproduce a table by
+Battino and Clever (1966) that presents experimental values of the
+so-called Bunsen absorption coefficient (this is the volume of gas, at 0 C
+and 760 torr, that, at the temperature of measurement, is dissolved in one
+volume of the solvent when the partial pressure of the gas is 760 torr)
+recorded by eleven research groups up until 1965. The standard error of the
+ mean value is never greater +-0.5%. The mean values from this table are
+probably accurate enough for most applications.
+Hitchman notes that the data in this table can be fitted by two forms of
+equations: one form obtained from Henry's law (under the restriction that
+the partial pressure of the gas remains constant), and another form by
+describing the variation with temperature by fitting a general power series.
+The latter approach is used in this function.
+
+Hitchman chooses to fit a fourth degree polynomial, and found that the
+square of the correlation coefficient was 0.999996.
+
+For more background and detailed derivation of the formula used here,
+see section 2.2 (pp. 11) in Hitchman.
+
+This formula is strictly speaking only valid for 0 < T < 50 celsius.
+The function will return values outside this range, but with a warning.
+}
+\examples{
+\dontrun{
+OxygenSolubilityWater(22)
+OxygenSolubilityWater(c(2, 7, 12, 30))
+}
+}

man/VapourPressureWater.Rd

@@ -0,0 +1,25 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/chemistry-tools.R
+\name{VapourPressureWater}
+\alias{VapourPressureWater}
+\title{Vapour pressure of water}
+\usage{
+VapourPressureWater(temperature)
+}
+\arguments{
+\item{temperature}{numeric vector, in degrees Celsius}
+}
+\value{
+vapour pressure of water, in kilopascal
+}
+\description{
+Vapour pressure of water as a function of temperature
+This function returns the vapour pressure of water at the given
+temperature(s) from the common::vapourwater dataset.
+}
+\examples{
+\dontrun{
+VapourPressureWater(45)
+VapourPressureWater(c(20, 25, 45, 60))
+}
+}