CHNOSZ (version 1.4.3)

NaCl: Simple NaCl-Water Solution

Description

Calculate speciation and ionic strength of aqueous solutions with a given molality of NaCl.

Usage

NaCl(T = seq(100, 500, 100), P = 1000, m_tot = 2, ...)

Value

A list with components IS (“true” ionic strength from concentrations of unpaired ions), m_Cl (molality of Cl^-), gam_Na, and gam_Cl (activity coefficients of Na⁺ and Cl^-).

Arguments

T

numeric, temperature in °C

P

numeric, pressure in bar (single value)

m_tot

numeric, total molality of NaCl (single value)

...

additional arguments for subcrt

Warning

This function provides only a first-order estimate of the solution composition, and is intended for solubility calculations of relatively insoluble metals in NaCl-dominated solutions. The formation of other species such as HCl or NaOH is not accounted for.

Details

This function calculates speciation (ion activities) and ionic strength in aqueous solutions given a total amount (m_tot, in mol/kg) of NaCl. The function is written for quick calculations along a temperature range (T) at constant pressure (P). The only reaction considered is Na⁺ + Cl^- = NaCl(aq). The algorithm starts by calculating the equilibrium constant (K) of the reaction and assuming complete dissociation of NaCl(aq). This also permits calculating the ionic strength from the molalities of Na⁺ and Cl^-. Then, uniroot is used to find the equilibrium molality of Cl^-; that is, where the affinity of the reaction (log(K/Q)) becomes zero. The activity quotient (Q) is evaluated taking account of activity coefficients of Na⁺, Cl^-, and NaCl(aq) calculated for the nominal ionic strength (see nonideal). The calculated molality of Cl^- yields a new estimate of the ionic strength of the system. The calculations are iterated until the deviation in ionic strength at all temperatures is less than 0.01.

References

Shvarov, Y. and Bastrakov, E. (1999) HCh: A software package for geochemical equilibrium modelling. User's Guide. Australian Geological Survey Organisation 1999/25. http://pid.geoscience.gov.au/dataset/ga/25473

See Also

demo("gold") for an application of this function.

Examples

reset()
# ionic strength of solution and activity coefficient of Cl-
# from HCh version 3.7 (Shvarov and Bastrakov, 1999) at 1000 bar,
# 100, 200, and 300 degress C, and 1 to 6 molal NaCl
m.HCh <- 1:6
IS.HCh <- list(`100`=c(0.992, 1.969, 2.926, 3.858, 4.758, 5.619),
               `300`=c(0.807, 1.499, 2.136, 2.739, 3.317, 3.875),
               `500`=c(0.311, 0.590, 0.861, 1.125, 1.385, 1.642))
gam_Cl.HCh <- list(`100`=c(0.565, 0.545, 0.551, 0.567, 0.589, 0.615),
                  `300`=c(0.366, 0.307, 0.275, 0.254, 0.238, 0.224),
                  `500`=c(0.19, 0.137, 0.111, 0.096, 0.085, 0.077))
# total molality in the calculation with NaCl()
m_tot <- seq(1, 6, 0.5)
N <- length(m_tot)
# where we'll put the calculated values
IS.calc <- data.frame(`100`=numeric(N), `300`=numeric(N), `500`=numeric(N))
gam_Cl.calc <- data.frame(`100`=numeric(N), `300`=numeric(N), `500`=numeric(N))
# NaCl() is *not* vectorized over m_tot, so we use a loop here
for(i in 1:length(m_tot)) {
  NaCl.out <- NaCl(c(100, 300, 500), P=1000, m_tot=m_tot[i])
  IS.calc[i, ] <- NaCl.out$IS
  gam_Cl.calc[i, ] <- NaCl.out$gam_Cl
}
# plot ionic strength from HCh and NaCl() as points and lines
opar <- par(mfrow=c(2, 1))
col <- c("black", "red", "orange")
plot(c(1,6), c(0,6), xlab="NaCl (mol/kg)", ylab=axis.label("IS"), type="n")
for(i in 1:3) {
  # NOTE: the differences are probably mostly due to different models
  # for the properties of NaCl(aq) (HCh: B.Ryhzenko model;
  # CHONSZ: revised HKF with parameters from Shock et al., 1997)
  points(m.HCh, IS.HCh[[i]], col=col[i])
  lines(m_tot, IS.calc[, i], col=col[i])
}
# add 1:1 line, legend, and title
abline(0, 1, lty=3)
dprop <- describe.property(rep("T", 3), c(100, 300, 500))
legend("topleft", dprop, lty=1, pch=1, col=col)
title(main="H2O + NaCl; HCh (points) and 'NaCl()' (lines)")
# plot activity coefficient (gamma)
plot(c(1,6), c(0,0.8), xlab="NaCl (mol/kg)", ylab=expression(gamma[Cl^"-"]), type="n")
for(i in 1:3) {
  points(m.HCh, gam_Cl.HCh[[i]], col=col[i])
  lines(m_tot, gam_Cl.calc[, i], col=col[i])
}
# we should be fairly close
maxdiff <- function(x, y) max(abs(y - x))
stopifnot(maxdiff(unlist(gam_Cl.calc[seq(1,11,2), ]), unlist(gam_Cl.HCh)) < 0.033)
par(opar)