The eutectic composition of sodium chloride in water is around 24 wt percentage and eutectic temperature of sodium chloride brine is around -21 Celsius. Considering this concentration of 24 wt. percentage to be 24 grams in 100 grams of brine, we get a mole fraction of sodium chloride to be 0.0885 where as we get a freezing point of sodium chloride brine to be -21 Celsius using popular equations given in literature for a mole fraction of sodium chloride of 0.15 which correspond to a wt percentage of around 36 % of sodium chloride in brine. Is the percentage of sodium chloride in brine at -21 Celsius, 24 wt percentage or 36 wt percentage?
The eutectic point is not the maximum solubility. If it is the solubility at the eutectic point that you want I suggest you go with the quoted measured value, rather than inferring a concentration from a correlation on freezing point depressions.
According to Merck - A 23% aqueous solution of sodium chloride freezes at -20.5 C , so given the 2 choices I would guess 24%
we use saturated solution of sodium chloride in chlor alkali industry for production of NaOH by electrolysis. This brine consists 28% - 30 % NaCl.
I have a large amount of saturated brine to dispose of - would that be interesting for the chlor-alkali industry?
I have (quadratically) correlated some saturated concentrations for NaCl aqueous solutions, available for the temperature interval 0―100 ºC from signalled reference (*), defined as csat = (msalt/msol)•100%, for its dependency on the absolute temperature, as:
csat = c1•T2 + c2•T + c3
with: c1 = 1.360000E-04, c2 = - 6.449680E-02, c3 = 3.338622E+01
Extrapolation to 252 K (-21ºC) would then yield a saturation concentration of 25.8 wt% (anhydrous salt).
Such a wide extrapolation may possibly be affected by a somewhat significant error.
(*) A. N. Campbell, N. O. Smith, Alexander Findlay (original author), "The Phase Rule and its Applications", 9th ed., Dover Publications Inc. (USA), 1951, p. 391.
Tabulated values for the density (ρ) of NaCl aq. solutions can be retrieved from the indicated reference (*). I have correlated this data, with concentration range 1―26 wt% (**) and temperature range 0―100 ºC, for both concentration and temperature dependency, by the exponential correlation:
ρ = A·exp(B·c), with ρ in g/cm3 and c in wt%, defined as (msalt/msol.)·100%.
where, alternatively, the density of pure water (ρw) could substitute for A.
A and B were quadratically correlated with the reciprocal of the absolute temperature, T (K):
A = a1·(1/T)2 + a2·(1/T) + a3 and B = b1·(1/T)2 + b2·(1/T) + b3
The temperature dependency parameters ― given without dimensions for simplicity ― were least-squares fitted as:
a1 = -4.805250E+04, a2 = 3.475451E+02, a3 = 3.724003E-01;
b1 = 1.034301E+03, b2 = - 6.302323, b3 = 1.643704E-02.
The maximum correlation (relative) error did not exceeded ±0.1%.
Substitution on this correlation of the saturation concentration (csat = 25.8 wt%) estimated (cf. previous post) for a solution of NaCl at 252 K (-21ºC), yields, for the corresponding (extrapolated) density:
ρsat = 0.994863·exp(7.71500E-03·csat) = 1.2140 g/cm3
Which, owing to the somewhat wide extrapolation, may also be affected by considerable error.
(*) R.H. Perry, D.W. Green, J.O. Maloney (Eds.), "Perry's Chemical Engineers’ Handbook", 7th ed., McGraw-Hill, 1997, Table 2-88.
(**) Obviously, the concentration range could be extended to 0 wt%, by considering also pure water data.
Based on the (extrapolated) saturation concentration of a NaCl aq. sol. at -21ºC (25.8 wt%) and the corresponding (extrapolated) density (1.2140 g/cm3), obtained as shown at both previous posts, its molar concentration (Csat; M or mol/dm3) ― or solubility* ― can now be obtained:
Csat = 1000(cm3/dm3)•[(csat/100%) / Mw)]•ρsat = 5.36 M
where Mw denotes the molar mass of the (anhydrous) salt, 58.44 g•mol-1.
* also called molar solubility
As seen in the H2O-NaCl phase diagram
http://www.phasediagram.dk/binary/sodium_chloride.htm
extrapolation of the saturation curve down to the eutectic using NaCl doesn't work because below some 0.1 deg C the stable phase in equilibrium with concentrated brine is NaCl.2H2O. Regarding the maximum possible concentration of NaCl in (saturated) brine, it is achieved at high temperatures in the range mentioned above (Sajjad Rafique).
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