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
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:

Comparison with typical concentrations of ions:

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:

$$ \Pi\left(c\right)=2 R T 1000 c (a + b c^2 ) $$

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:

$$ g\left(c\right) = -RT 1000c \left[ 2a \log\left(\frac{c}{\tilde{c}}\right) + bc^2 \right] + \delta $$

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:

$$ g\left(c, c_0\right) = -RT 1000c \left[ 2a \log\left(\frac{c}{c_0}\right) -2a + b\left(c^2-3c_0^2\right) \right] - RT 1000c_0\left[ 2a + 2bc_0^2 \right] $$

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