User:Dbrogioli/Sodium chloride data

General values

Standard temperature: 20°C

Solubility at 20°C: 5.43 M

Molecular weight: 58.44

Conducibility of 10 mM salt solution: 0.1156 S/m

Definition of NaCl solutions

Solution	Concentration	Weight fraction (g/g)	Volume concentration (g/L)
Fresh water	20 mM	0.1167 %	1.169 g/L
Sea water	500 mM	2.868 %	29.22 g/L
Evaporation brine	5 M	24.60 %	292.2 g/L

The molarity is expressed as moles per L of solution; the weight fraction as g of salt per g of solution, and the volume concentration as g of salt per L of solution, not per L of solvent.

Definition of multi-ionic solutions

Table of concentration of ions in sea water

Density: 1.0255 kg/L.

Recipe for sea water:

Salt	concentration (mM)	Weight fraction (g/g)	Volume concentration (g/L)
[NaCl]	500	2.849 %	29.22 g/L
[MgCl2]	25	0.2321 %	2.380 g/L
[MgSO4]	30	0.3521 %	3.611 g/L
[KCl]	10	0.07269 %	0.7455 g/L
[CaCl2]	10	0.1082 %	1.110 g/L
[NaHCO3]	2.5	0.02047 %	0.2100 g/L

Comparison with typical concentrations of ions:

Ion	Obtained concentration (mM)	Typical concentration (mM)
Cl-	580	583
Na+	502.5	500
SO4--	30	30
Mg++	55	57
Ca++	10	11
HCO3-	2.5	2.5

Density

Density of NaCl solution in water (needed to prepare solutions at given molarity):

$\rho \left(c\right)=\rho _{0}+{\frac {c}{1000}}\left(M-\rho _{0}V_{part}\right)$

where:

Water density: $\rho _{0}$ = 1 g/cm^3

NaCl molar mass: M = 58.44 g/mole

Partial molar volume of NaCl in water $V_{part}$: 20.9 cm^3/mole

Note: c in M; other in cgs units.

The parameter $V_{part}$ has been obtained by fitting data provided in )

This formula has a precision of 0.2%. Since it is nearly linear, we assume that mixing respects volumes, that is, if we mix a volume Va at concentration ca and a volume Vb at a concentration cb, the resulting solution has volume Va+Vb (this is not always true for any solution).

Osmotic pressure

The van 't Hoff formula is an approximation giving an error of the order of 8% in this case. A better approximation is:

$\Pi \left(c\right)=2RT1000c(a+bc^{2})$

where:

$\Pi \left(c\right)$ is the osmotic pressure

R = 8.314472 J/mol/K

T is the temperature, 20°C

a = 0.93

b = 0.0113 /M^2

Note: c in M; b in 1/M^2; other in MKS units.

The parameters a and b are obtained by fitting data provided in

The formula has a precision of 1%.

Gibbs free energy

Using the parameters a and b given in the previous section, the Gibbs free energy density $g\left(c\right)$ (i.e. the free energy of a unity volume of solution at a given concentration c) can be expressed up to a constant and linear term:

$g\left(c\right)=-RT1000c\left[2a\log \left({\frac {c}{\tilde {c}}}\right)+bc^{2}\right]+\delta$

where ${\tilde {c}}$ and $\delta$ are irrelevant for calculations concerning mixing of solutions.

The Gibbs free energy density $g\left(c,c_{0}\right)$ relative to a concentration $c_{0}$ can be calculated:

$g\left(c,c_{0}\right)=-RT1000c\left[2a\log \left({\frac {c}{c_{0}}}\right)-2a+b\left(c^{2}-3c_{0}^{2}\right)\right]-RT1000c_{0}\left[2a+2bc_{0}^{2}\right]$

Note: c is in M; results in MKS.

See the page on thermodynamics for definitions.

There is an applet for the calculation of the free energy of mixing of two solutions of NaCl