See also: Solution

One calls homogeneous solution all Mélange of two or several substances, initially in a state (solid, Liquide, gas) identical or different.

The majority substance is called Solvant, the minority substances are the Soluté S.

Solution in a gas

See also: Gas, Perfect gas, homogeneous Mixture

One rather seldom speaks about “solution” for a gas. A mixture of gas is in general homogeneous after a short moment, because of thermal agitation (see the articles Brownian Movement and Diffusion ), but it can have there a stratification in the presence of a field of Gravité if the height of the container is important.

Solution in a liquid

The solution in a liquid is the most known example. A solution having water as solvent is called aqueous solution. It is possible to put in solution:

• a liquid in another: limited by the Miscibility of the two liquids.
• a solid in a liquid: limited by the Solubility of the solid in the solvent, beyond which the solid is not dissolved any more. One speaks then about saturated solution.
• a gas in a liquid.

Solid solution

See also:

• specific Defect
• Notation of Kröger and Vink

Coexistence of phases

A solution can be

• saturated: at a given temperature and a pressure, a saturated solution is a solution which cannot dissolve aqueous solution any more;
• unsaturated: an unsaturated solution is a solution which can dissolve more aqueous solution, in the conditions of the system;
• supersaturated: a supersaturated solution is a solution containing a greater quantity of dissolved aqueous solution than that which corresponds to the limit of saturation.

Proportion of phases and concentration

Are L component. The concentration of the component can be expressed several manners:

• the molar Fraction N_i (without unit or %mol), which is the relationship between the number n_i of moles of I on the number total N of moles
  $N\_i\; =\; \backslash \; frac\; \{n\_i\}\; \{N\}\; =\; \backslash \; frac\; \{n\_i\}\; \{\backslash \; sum\_\; \{j=1\}\; ^l\; n\_j\}$;
• the mass Percentage M_i (without unit or %m), which is the relationship between the mass m_i of I on the total mass m
  $M\_i\; =\; \backslash \; frac\; \{m\_i\}\; \{m\}\; =\; \backslash \; frac\; \{m\_i\}\; \{\backslash \; sum\_\; \{j=1\}\; ^l\; m\_j\}$.

In the case of a liquid solution, one is often brought back to a volume of a Liter of solution, and one defines:

• the molar Concentration C_i (mol·L^-1), relationship between the number of moles of I and the volume of liquid
  $C\_i\; =\; \backslash \; frac\; \{n\_i\}\; \{v\}$;
• the mass Concentration τ I , relationship between the mass of I and the volume of liquid
  $\backslash \; tau\_i\; =\; \backslash \; frac\; \{m\_i\}\; \{v\}$;
• the voluminal Percentage V_i (%vol): in the case of a mixture of liquids, it is volume v_i of I divided by total volume v
  $V\_i\; =\; \backslash \; frac\; \{v\_i\}\; \{v\}\; =\; \backslash \; frac\; \{v\_i\}\; \{\backslash \; sum\_\; \{j=1\}\; ^l\; v\_j\}$.

In the case of a gas, one uses

• the partial Pression p_i , which is the contribution of the phase I to the pressure;
• the voluminal Percentage (without unit or %vol), which is, under the conditions of Pression and fixed Température, the volume v_i which the phase I would all alone represent on total volume; in the case of Perfect gas S, one shows easily that the voluminal percentage is equal to the partial pressure divided by the total pressure p
  $V\_i\; =\; \backslash \; frac\; \{v\_i\}\; \{v\}\; =\; \backslash \; frac\; \{p\_i\}\; \{p\}$.

Diluted solution, activity

One calls a diluted solution the case of a solution for which the quantity of aqueous solutions is much lower than the total quantity of solution. If one indicates solvent by the index S , one can thus use the following approximations:

$n\; \backslash \; simeq\; n\_s$, $N\_i\; \backslash \; simeq\; \backslash \; frac\; \{n\_i\}\; \{n\_s\}$, $N\_s\; \backslash \; simeq\; 1$;

$m\; \backslash \; simeq\; m\_s$, $M\_i\; \backslash \; simeq\; \backslash \; frac\; \{m\_i\}\; \{m\_s\}$, $M\_s\; \backslash \; simeq\; 1$.

For the liquid solutions:

$C\_i\; \backslash \; simeq\; \backslash \; frac\; \{n\_i\}\; \{v\_s\}$, C_s is the reverse of the molar Volume of solvent;

$\backslash \; tau\_i\; \backslash \; simeq\; \backslash \; frac\; \{m\_i\}\; \{v\_s\}$, τ _s' is the Density solvent;

$v\; \backslash \; simeq\; v\_s$, $V\_i\; \backslash \; simeq\; \backslash \; frac\; \{v\_i\}\; \{v\_s\}$, $V\_s\; \backslash \; simeq\; 1$

In the case of a diluted solution, the chemical Potentiel is a function closely connected of the Logarithme of the concentration, for a fixed Température:

• in liquid solution, $\backslash \; mu\_i\; (T,\; P)\; =\; \backslash \; mu\_i^0\; (T)\; +\; R\; \backslash \; cdot\; T\; \backslash \; cdot\; \backslash \; ln\; (C\_i)$, C_i being expressed in mol·L^-1;
• in gas solution, $\backslash \; mu\_i\; (T,\; P)\; =\; \backslash \; mu\_i^0\; (T)\; +\; R\; \backslash \; cdot\; T\; \backslash \; cdot\; \backslash \; ln\; (p\_i)$, p_i being expressed in atmosphere.

When one is not any more in diluted solution (or in the case of gas, for high pressure, when one cannot make any more the approximation of the Perfect gas S), it is necessary to utilize the chemical Activité a_i:

$\backslash \; mu\_i\; (T,\; P)\; =\; \backslash \; mu\_i^0\; (T)\; +\; R\; \backslash \; cdot\; T\; \backslash \; cdot\; \backslash \; ln\; (a\_i)$

• in the case of a liquid solution, a_i = γ _I · C_i where γ _I is the coefficient of activity of I ;
• in the case of a gas solution, a_i = ƒ _I · p_i where ƒ _I is the Fugacité.

This is the approach from the “chemical” point of view: one starts from what one measures well (volume, mass…). From a thermodynamic point of view, one starts rather by defining the activity, then it is established that in the case of the diluted solutions,

• for a liquid, the activity of an aqueous solution is worth about its molar concentration (liquid) and the activity of solvent is worth 1;
• for a gas, the activity of the aqueous solution is partial pressure in atmosphere, a gas having a pressure partial of an atmosphere has an activity of 1;
• for a solid, the activity is worth 1.

See too

solution

• Dissolution
• Precipitated
• aqueous Solution
• Salting out

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